TSTP Solution File: NUM378+1.010.010 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM378+1.010.010 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Sun Sep 18 13:04:09 EDT 2022
% Result : Unsatisfiable 1.13s 1.07s
% Output : Proof 10.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM378+1.010.010 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 09:48:33 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.13/1.07 % SZS status Unsatisfiable
% 1.13/1.07 % SZS output start Proof
% 1.13/1.07 tff(tptp_fun_Y10_40_type, type, (
% 1.13/1.07 tptp_fun_Y10_40: $i)).
% 1.13/1.07 tff(tptp_fun_X10_41_type, type, (
% 1.13/1.07 tptp_fun_X10_41: $i)).
% 1.13/1.07 tff(sum_type, type, (
% 1.13/1.07 sum: ( $i * $i ) > $i)).
% 1.13/1.07 tff(succ_type, type, (
% 1.13/1.07 succ: $i > $i)).
% 1.13/1.07 tff(tptp_fun_NPY9_2_type, type, (
% 1.13/1.07 tptp_fun_NPY9_2: $i)).
% 1.13/1.07 tff(pred_type, type, (
% 1.13/1.07 pred: $i > $i)).
% 1.13/1.07 tff(tptp_fun_NSY9_0_type, type, (
% 1.13/1.07 tptp_fun_NSY9_0: $i)).
% 1.13/1.07 tff(tptp_fun_NPX9_3_type, type, (
% 1.13/1.07 tptp_fun_NPX9_3: $i)).
% 1.13/1.07 tff(tptp_fun_NSX9_1_type, type, (
% 1.13/1.07 tptp_fun_NSX9_1: $i)).
% 1.13/1.07 tff(n10_type, type, (
% 1.13/1.07 n10: $i)).
% 1.13/1.07 tff(n9_type, type, (
% 1.13/1.07 n9: $i)).
% 1.13/1.07 tff(n8_type, type, (
% 1.13/1.07 n8: $i)).
% 1.13/1.07 tff(n7_type, type, (
% 1.13/1.07 n7: $i)).
% 1.13/1.07 tff(n6_type, type, (
% 1.13/1.07 n6: $i)).
% 1.13/1.07 tff(n5_type, type, (
% 1.13/1.07 n5: $i)).
% 1.13/1.07 tff(n4_type, type, (
% 1.13/1.07 n4: $i)).
% 1.13/1.07 tff(n3_type, type, (
% 1.13/1.07 n3: $i)).
% 1.13/1.07 tff(n2_type, type, (
% 1.13/1.07 n2: $i)).
% 1.13/1.07 tff(n1_type, type, (
% 1.13/1.07 n1: $i)).
% 1.13/1.07 tff(n0_type, type, (
% 1.13/1.07 n0: $i)).
% 1.13/1.07 tff(tptp_fun_Y7_46_type, type, (
% 1.13/1.07 tptp_fun_Y7_46: $i)).
% 1.13/1.07 tff(tptp_fun_X7_47_type, type, (
% 1.13/1.07 tptp_fun_X7_47: $i)).
% 1.13/1.07 tff(tptp_fun_Y8_44_type, type, (
% 1.13/1.07 tptp_fun_Y8_44: $i)).
% 1.13/1.07 tff(tptp_fun_X8_45_type, type, (
% 1.13/1.07 tptp_fun_X8_45: $i)).
% 1.13/1.07 tff(tptp_fun_Y9_42_type, type, (
% 1.13/1.07 tptp_fun_Y9_42: $i)).
% 1.13/1.07 tff(tptp_fun_X9_43_type, type, (
% 1.13/1.07 tptp_fun_X9_43: $i)).
% 1.13/1.07 tff(tptp_fun_NPY8_6_type, type, (
% 1.13/1.07 tptp_fun_NPY8_6: $i)).
% 1.13/1.07 tff(tptp_fun_NSY8_4_type, type, (
% 1.13/1.07 tptp_fun_NSY8_4: $i)).
% 1.13/1.07 tff(tptp_fun_NPX8_7_type, type, (
% 1.13/1.07 tptp_fun_NPX8_7: $i)).
% 1.13/1.07 tff(tptp_fun_NSX8_5_type, type, (
% 1.13/1.07 tptp_fun_NSX8_5: $i)).
% 1.13/1.07 tff(tptp_fun_NPY7_10_type, type, (
% 1.13/1.07 tptp_fun_NPY7_10: $i)).
% 1.13/1.07 tff(tptp_fun_NSY7_8_type, type, (
% 1.13/1.07 tptp_fun_NSY7_8: $i)).
% 1.13/1.07 tff(tptp_fun_NPX7_11_type, type, (
% 1.13/1.07 tptp_fun_NPX7_11: $i)).
% 1.13/1.07 tff(tptp_fun_NSX7_9_type, type, (
% 1.13/1.07 tptp_fun_NSX7_9: $i)).
% 1.13/1.07 tff(tptp_fun_NPY6_14_type, type, (
% 1.13/1.07 tptp_fun_NPY6_14: $i)).
% 1.13/1.07 tff(tptp_fun_NSY6_12_type, type, (
% 1.13/1.07 tptp_fun_NSY6_12: $i)).
% 1.13/1.07 tff(tptp_fun_NPX6_15_type, type, (
% 1.13/1.07 tptp_fun_NPX6_15: $i)).
% 1.13/1.07 tff(tptp_fun_NSX6_13_type, type, (
% 1.13/1.07 tptp_fun_NSX6_13: $i)).
% 1.13/1.07 tff(tptp_fun_X6_49_type, type, (
% 1.13/1.07 tptp_fun_X6_49: $i)).
% 1.13/1.07 tff(tptp_fun_Y6_48_type, type, (
% 1.13/1.07 tptp_fun_Y6_48: $i)).
% 1.13/1.07 tff(tptp_fun_NPY5_18_type, type, (
% 1.13/1.07 tptp_fun_NPY5_18: $i)).
% 1.13/1.07 tff(tptp_fun_NSY5_16_type, type, (
% 1.13/1.07 tptp_fun_NSY5_16: $i)).
% 1.13/1.07 tff(tptp_fun_NPX5_19_type, type, (
% 1.13/1.07 tptp_fun_NPX5_19: $i)).
% 1.13/1.07 tff(tptp_fun_NSX5_17_type, type, (
% 1.13/1.07 tptp_fun_NSX5_17: $i)).
% 1.13/1.07 tff(tptp_fun_X5_51_type, type, (
% 1.13/1.07 tptp_fun_X5_51: $i)).
% 1.13/1.07 tff(tptp_fun_Y5_50_type, type, (
% 1.13/1.07 tptp_fun_Y5_50: $i)).
% 1.13/1.07 tff(tptp_fun_NPY4_22_type, type, (
% 1.13/1.07 tptp_fun_NPY4_22: $i)).
% 1.13/1.07 tff(tptp_fun_NSY4_20_type, type, (
% 1.13/1.07 tptp_fun_NSY4_20: $i)).
% 1.13/1.07 tff(tptp_fun_NPX4_23_type, type, (
% 1.13/1.07 tptp_fun_NPX4_23: $i)).
% 1.13/1.07 tff(tptp_fun_NSX4_21_type, type, (
% 1.13/1.07 tptp_fun_NSX4_21: $i)).
% 1.13/1.07 tff(tptp_fun_X4_53_type, type, (
% 1.13/1.07 tptp_fun_X4_53: $i)).
% 1.13/1.07 tff(tptp_fun_Y4_52_type, type, (
% 1.13/1.07 tptp_fun_Y4_52: $i)).
% 1.13/1.07 tff(tptp_fun_NPY3_26_type, type, (
% 1.13/1.07 tptp_fun_NPY3_26: $i)).
% 1.13/1.07 tff(tptp_fun_NSY3_24_type, type, (
% 1.13/1.07 tptp_fun_NSY3_24: $i)).
% 1.13/1.07 tff(tptp_fun_NPX3_27_type, type, (
% 1.13/1.07 tptp_fun_NPX3_27: $i)).
% 1.13/1.07 tff(tptp_fun_NSX3_25_type, type, (
% 1.13/1.07 tptp_fun_NSX3_25: $i)).
% 1.13/1.07 tff(tptp_fun_X3_55_type, type, (
% 1.13/1.07 tptp_fun_X3_55: $i)).
% 1.13/1.07 tff(tptp_fun_Y3_54_type, type, (
% 1.13/1.07 tptp_fun_Y3_54: $i)).
% 1.13/1.07 tff(tptp_fun_NPY2_30_type, type, (
% 1.13/1.07 tptp_fun_NPY2_30: $i)).
% 1.13/1.07 tff(tptp_fun_NSY2_28_type, type, (
% 1.13/1.07 tptp_fun_NSY2_28: $i)).
% 1.13/1.07 tff(tptp_fun_NPX2_31_type, type, (
% 1.13/1.07 tptp_fun_NPX2_31: $i)).
% 1.13/1.07 tff(tptp_fun_NSX2_29_type, type, (
% 1.13/1.07 tptp_fun_NSX2_29: $i)).
% 1.13/1.07 tff(tptp_fun_X2_57_type, type, (
% 1.13/1.07 tptp_fun_X2_57: $i)).
% 1.13/1.07 tff(tptp_fun_Y2_56_type, type, (
% 1.13/1.07 tptp_fun_Y2_56: $i)).
% 1.13/1.07 tff(tptp_fun_NPY1_34_type, type, (
% 1.13/1.07 tptp_fun_NPY1_34: $i)).
% 1.13/1.07 tff(tptp_fun_NSY1_32_type, type, (
% 1.13/1.07 tptp_fun_NSY1_32: $i)).
% 1.13/1.07 tff(tptp_fun_NPX1_35_type, type, (
% 1.13/1.07 tptp_fun_NPX1_35: $i)).
% 1.13/1.07 tff(tptp_fun_NSX1_33_type, type, (
% 1.13/1.07 tptp_fun_NSX1_33: $i)).
% 1.13/1.07 tff(tptp_fun_X1_59_type, type, (
% 1.13/1.07 tptp_fun_X1_59: $i)).
% 1.13/1.07 tff(tptp_fun_Y1_58_type, type, (
% 1.13/1.07 tptp_fun_Y1_58: $i)).
% 1.13/1.07 tff(tptp_fun_NPY0_38_type, type, (
% 1.13/1.07 tptp_fun_NPY0_38: $i)).
% 1.13/1.07 tff(tptp_fun_NSY0_36_type, type, (
% 1.13/1.07 tptp_fun_NSY0_36: $i)).
% 1.13/1.07 tff(tptp_fun_NPX0_39_type, type, (
% 1.13/1.08 tptp_fun_NPX0_39: $i)).
% 1.13/1.08 tff(tptp_fun_NSX0_37_type, type, (
% 1.13/1.08 tptp_fun_NSX0_37: $i)).
% 1.13/1.08 tff(tptp_fun_X0_61_type, type, (
% 1.13/1.08 tptp_fun_X0_61: $i)).
% 1.13/1.08 tff(tptp_fun_Y0_60_type, type, (
% 1.13/1.08 tptp_fun_Y0_60: $i)).
% 1.13/1.08 tff(1,plain,
% 1.13/1.08 (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0!61 = n10) | (X0!61 = n9) | (X0!61 = n8) | (X0!61 = n7) | (X0!61 = n6) | (X0!61 = n5) | (X0!61 = n4) | (X0!61 = n3) | (X0!61 = n2) | (X0!61 = n1) | (X0!61 = n0)) & ((Y0!60 = n10) | (Y0!60 = n9) | (Y0!60 = n8) | (Y0!60 = n7) | (Y0!60 = n6) | (Y0!60 = n5) | (Y0!60 = n4) | (Y0!60 = n3) | (Y0!60 = n2) | (Y0!60 = n1) | (Y0!60 = n0)) & (NPX0!39 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))))) & (NSX0!37 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))))) & (NPY0!38 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))))) & (NSY0!36 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))))) & (NPX1!35 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))))) & (NSX1!33 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))))) & (NPY1!34 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))))) & (NSY1!32 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))))) & (NPX2!31 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))))) & (NSX2!29 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))))) & (NPY2!30 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))))) & (NSY2!28 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))))) & (NPX3!27 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))))) & (NSX3!25 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))))) & (NPY3!26 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))))) & (NSY3!24 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))))) & (NPX4!23 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))))) & (NSX4!21 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))))) & (NPY4!22 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))))) & (NSY4!20 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))))) & (NPX5!19 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))))) & (NSX5!17 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))))) & (NPY5!18 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))))) & (NSY5!16 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))))) & (NPX6!15 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))))) & (NSX6!13 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))))) & (NPY6!14 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))))) & (NSY6!12 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))))) & (NPX7!11 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7!47)))))))))))) & (NSX7!9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7!47)))))))))))) & (NPY7!10 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7!46)))))))))))) & (NSY7!8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7!46)))))))))))) & (NPX8!7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8!45)))))))))))) & (NSX8!5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8!45)))))))))))) & (NPY8!6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8!44)))))))))))) & (NSY8!4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8!44)))))))))))) & (NPX9!3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9!43)))))))))))) & (NSX9!1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9!43)))))))))))) & (NPY9!2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9!42)))))))))))) & (NSY9!0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9!42)))))))))))) & (X1!59 = sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61)))) & (Y1!58 = sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))))) & (X2!57 = sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59)))) & (Y2!56 = sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))))) & (X3!55 = sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57)))) & (Y3!54 = sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))))) & (X4!53 = sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55)))) & (Y4!52 = sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))))) & (X5!51 = sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53)))) & (Y5!50 = sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))))) & (X6!49 = sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51)))) & (Y6!48 = sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))))) & (X7!47 = sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49)))) & (Y7!46 = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))) & (X8!45 = sum(sum(pred(X7!47), succ(Y7!46)), sum(pred(Y7!46), succ(X7!47)))) & (Y8!44 = sum(pred(NSX7!9), sum(succ(NPX7!11), sum(pred(NSY7!8), succ(NPY7!10))))) & (X9!43 = sum(sum(pred(X8!45), succ(Y8!44)), sum(pred(Y8!44), succ(X8!45)))) & (Y9!42 = sum(pred(NSX8!5), sum(succ(NPX8!7), sum(pred(NSY8!4), succ(NPY8!6))))) & (X10!41 = sum(sum(pred(X9!43), succ(Y9!42)), sum(pred(Y9!42), succ(X9!43)))) & (Y10!40 = sum(pred(NSX9!1), sum(succ(NPX9!3), sum(pred(NSY9!0), succ(NPY9!2))))) & ((~(X10!41 = Y10!40)) | (~(X9!43 = Y9!42)) | (~(X8!45 = Y8!44)) | (~(X7!47 = Y7!46))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0!61 = n10) | (X0!61 = n9) | (X0!61 = n8) | (X0!61 = n7) | (X0!61 = n6) | (X0!61 = n5) | (X0!61 = n4) | (X0!61 = n3) | (X0!61 = n2) | (X0!61 = n1) | (X0!61 = n0)) & ((Y0!60 = n10) | (Y0!60 = n9) | (Y0!60 = n8) | (Y0!60 = n7) | (Y0!60 = n6) | (Y0!60 = n5) | (Y0!60 = n4) | (Y0!60 = n3) | (Y0!60 = n2) | (Y0!60 = n1) | (Y0!60 = n0)) & (NPX0!39 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))))) & (NSX0!37 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))))) & (NPY0!38 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))))) & (NSY0!36 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))))) & (NPX1!35 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))))) & (NSX1!33 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))))) & (NPY1!34 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))))) & (NSY1!32 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))))) & (NPX2!31 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))))) & (NSX2!29 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))))) & (NPY2!30 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))))) & (NSY2!28 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))))) & (NPX3!27 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))))) & (NSX3!25 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))))) & (NPY3!26 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))))) & (NSY3!24 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))))) & (NPX4!23 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))))) & (NSX4!21 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))))) & (NPY4!22 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))))) & (NSY4!20 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))))) & (NPX5!19 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))))) & (NSX5!17 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))))) & (NPY5!18 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))))) & (NSY5!16 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))))) & (NPX6!15 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))))) & (NSX6!13 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))))) & (NPY6!14 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))))) & (NSY6!12 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))))) & (NPX7!11 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7!47)))))))))))) & (NSX7!9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7!47)))))))))))) & (NPY7!10 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7!46)))))))))))) & (NSY7!8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7!46)))))))))))) & (NPX8!7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8!45)))))))))))) & (NSX8!5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8!45)))))))))))) & (NPY8!6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8!44)))))))))))) & (NSY8!4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8!44)))))))))))) & (NPX9!3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9!43)))))))))))) & (NSX9!1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9!43)))))))))))) & (NPY9!2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9!42)))))))))))) & (NSY9!0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9!42)))))))))))) & (X1!59 = sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61)))) & (Y1!58 = sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))))) & (X2!57 = sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59)))) & (Y2!56 = sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))))) & (X3!55 = sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57)))) & (Y3!54 = sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))))) & (X4!53 = sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55)))) & (Y4!52 = sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))))) & (X5!51 = sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53)))) & (Y5!50 = sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))))) & (X6!49 = sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51)))) & (Y6!48 = sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))))) & (X7!47 = sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49)))) & (Y7!46 = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))) & (X8!45 = sum(sum(pred(X7!47), succ(Y7!46)), sum(pred(Y7!46), succ(X7!47)))) & (Y8!44 = sum(pred(NSX7!9), sum(succ(NPX7!11), sum(pred(NSY7!8), succ(NPY7!10))))) & (X9!43 = sum(sum(pred(X8!45), succ(Y8!44)), sum(pred(Y8!44), succ(X8!45)))) & (Y9!42 = sum(pred(NSX8!5), sum(succ(NPX8!7), sum(pred(NSY8!4), succ(NPY8!6))))) & (X10!41 = sum(sum(pred(X9!43), succ(Y9!42)), sum(pred(Y9!42), succ(X9!43)))) & (Y10!40 = sum(pred(NSX9!1), sum(succ(NPX9!3), sum(pred(NSY9!0), succ(NPY9!2))))) & ((~(X10!41 = Y10!40)) | (~(X9!43 = Y9!42)) | (~(X8!45 = Y8!44)) | (~(X7!47 = Y7!46))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10)))),
% 1.13/1.09 inference(rewrite,[status(thm)],[])).
% 1.13/1.09 tff(2,plain,
% 1.13/1.09 (?[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10))) <=> ?[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10)))),
% 1.13/1.10 inference(rewrite,[status(thm)],[])).
% 1.13/1.10 tff(3,plain,
% 1.13/1.10 (^[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3))), (((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3)) & (succ(n3) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3)) & (succ(n3) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4))), (((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4)))), ((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4)) & (succ(n4) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4)) & (succ(n4) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5))), ((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5)))), (((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5)) & (succ(n5) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5)) & (succ(n5) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6))), (((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6)))), ((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6)) & (succ(n6) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6)) & (succ(n6) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7))), ((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7)))), (((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7)) & (succ(n7) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7)) & (succ(n7) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8))), (((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8)))), ((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8)) & (succ(n8) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8)) & (succ(n8) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9))), ((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9)))), (((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9)) & (succ(n9) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9)) & (succ(n9) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10))), (((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10)))), ((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10)) & (succ(n10) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10)) & (succ(n10) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0))), ((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0)))), (((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0)) & (pred(n0) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0)) & (pred(n0) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10))), (((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10)))), ((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10)) & (pred(n1) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10)) & (pred(n1) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0))), ((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0)))), (((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0)) & (pred(n2) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0)) & (pred(n2) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1))), (((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1)))), ((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1)) & (pred(n3) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1)) & (pred(n3) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2))), ((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2)))), (((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2)) & (pred(n4) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2)) & (pred(n4) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3))), (((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3)))), ((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3)) & (pred(n5) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3)) & (pred(n5) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4))), ((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4)))), (((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4)) & (pred(n6) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4)) & (pred(n6) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5))), (((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5)))), ((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5)) & (pred(n7) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5)) & (pred(n7) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6))), ((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6)))), (((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6)) & (pred(n8) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6)) & (pred(n8) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7))), (((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7)))), ((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7)) & (pred(n9) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7)) & (pred(n9) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8))), ((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8)))), (((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8)) & (pred(n10) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8)) & (pred(n10) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9))), (((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9)))), ((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9)) & (sum(n0, n0) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0))), ((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0)))), (((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1))), (((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1)))), ((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2))), ((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2)))), (((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3))), (((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3)))), ((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4))), ((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4)))), (((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5))), (((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5)))), ((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6))), ((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6)))), (((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7))), (((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7)))), ((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8))), ((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8)))), (((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9))), (((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9)))), ((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10))), ((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10)))), (((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1))), (((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1)))), ((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2))), ((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2)))), (((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3))), (((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3)))), ((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4))), ((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4)))), (((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5))), (((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5)))), ((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6))), ((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6)))), (((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7))), (((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7)))), ((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8))), ((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8)))), (((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9))), (((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10))), ((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0))), (((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2))), ((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2)))), (((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3))), (((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3)))), ((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4))), ((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4)))), (((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5))), (((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5)))), ((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6))), ((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7))), (((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8))), ((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9)))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((X0 = n0) | (X0 = n1)) | (X0 = n2)) <=> ((X0 = n2) | (X0 = n1) | (X0 = n0))), (((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) <=> (((X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n3)))), rewrite((((X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n3)) <=> ((X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), (((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) <=> ((X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), ((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) <=> (((X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n4)))), rewrite((((X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n4)) <=> ((X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), ((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) <=> ((X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), (((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) <=> (((X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n5)))), rewrite((((X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n5)) <=> ((X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), (((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) <=> ((X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), ((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) <=> (((X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n6)))), rewrite((((X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n6)) <=> ((X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), ((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) <=> ((X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), (((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) <=> (((X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n7)))), rewrite((((X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n7)) <=> ((X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), (((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) <=> ((X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), ((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) <=> (((X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n8)))), rewrite((((X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n8)) <=> ((X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), ((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) <=> ((X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) <=> (((X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n9)))), rewrite((((X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n9)) <=> ((X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) <=> ((X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), ((((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10)) <=> (((X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n10)))), rewrite((((X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) | (X0 = n10)) <=> ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))), ((((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10)) <=> ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9)) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9)) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) <=> ((Y0 = n2) | (Y0 = n1) | (Y0 = n0))), (((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) <=> (((Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n3)))), rewrite((((Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n3)) <=> ((Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), (((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) <=> ((Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), ((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) <=> (((Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n4)))), rewrite((((Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n4)) <=> ((Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), ((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) <=> ((Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), (((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) <=> (((Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n5)))), rewrite((((Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n5)) <=> ((Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), (((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) <=> ((Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), ((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) <=> (((Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n6)))), rewrite((((Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n6)) <=> ((Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), ((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) <=> ((Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), (((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) <=> (((Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n7)))), rewrite((((Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n7)) <=> ((Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), (((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) <=> ((Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), ((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) <=> (((Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n8)))), rewrite((((Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n8)) <=> ((Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), ((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) <=> ((Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) <=> (((Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n9)))), rewrite((((Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n9)) <=> ((Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) <=> ((Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), ((((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10)) <=> (((Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n10)))), rewrite((((Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) | (Y0 = n10)) <=> ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))), ((((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10)) <=> ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0))) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))))), trans(monotonicity(trans(monotonicity(rewrite(((~(X7 = Y7)) | (~(X8 = Y8))) <=> ((~(X8 = Y8)) | (~(X7 = Y7)))), ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) <=> (((~(X8 = Y8)) | (~(X7 = Y7))) | (~(X9 = Y9))))), rewrite((((~(X8 = Y8)) | (~(X7 = Y7))) | (~(X9 = Y9))) <=> ((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)))), ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) <=> ((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))))), (((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10))) <=> (((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) | (~(X10 = Y10))))), rewrite((((~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) | (~(X10 = Y10))) <=> ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)))), (((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10))) <=> ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)))) & (~(n0 = n1))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7)))) & (~(n0 = n1))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1))) & (~(n0 = n2))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1))) & (~(n0 = n2))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2))) & (~(n0 = n3))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2))) & (~(n0 = n3))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3))) & (~(n0 = n4))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3))) & (~(n0 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4))) & (~(n0 = n5))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4))) & (~(n0 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5))) & (~(n0 = n6))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5))) & (~(n0 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6))) & (~(n0 = n7))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6))) & (~(n0 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7))) & (~(n0 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7))) & (~(n0 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8))) & (~(n0 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8))) & (~(n0 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9))) & (~(n0 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9))) & (~(n0 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10))) & (~(n1 = n2))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10))) & (~(n1 = n2))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2))) & (~(n1 = n3))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2))) & (~(n1 = n3))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3))) & (~(n1 = n4))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3))) & (~(n1 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4))) & (~(n1 = n5))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4))) & (~(n1 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5))) & (~(n1 = n6))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5))) & (~(n1 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6))) & (~(n1 = n7))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6))) & (~(n1 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7))) & (~(n1 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7))) & (~(n1 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8))) & (~(n1 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8))) & (~(n1 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9))) & (~(n1 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9))) & (~(n1 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10))) & (~(n2 = n3))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10))) & (~(n2 = n3))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3))) & (~(n2 = n4))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3))) & (~(n2 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4))) & (~(n2 = n5))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4))) & (~(n2 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5))) & (~(n2 = n6))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5))) & (~(n2 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6))) & (~(n2 = n7))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6))) & (~(n2 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7))) & (~(n2 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7))) & (~(n2 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8))) & (~(n2 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8))) & (~(n2 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9))) & (~(n2 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9))) & (~(n2 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10))) & (~(n3 = n4))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10))) & (~(n3 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4))) & (~(n3 = n5))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4))) & (~(n3 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5))) & (~(n3 = n6))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5))) & (~(n3 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6))) & (~(n3 = n7))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6))) & (~(n3 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7))) & (~(n3 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7))) & (~(n3 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8))) & (~(n3 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8))) & (~(n3 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9))) & (~(n3 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9))) & (~(n3 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10))) & (~(n4 = n5))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10))) & (~(n4 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5))) & (~(n4 = n6))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5))) & (~(n4 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6))) & (~(n4 = n7))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6))) & (~(n4 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7))) & (~(n4 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7))) & (~(n4 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8))) & (~(n4 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8))) & (~(n4 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9))) & (~(n4 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9))) & (~(n4 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10))) & (~(n5 = n6))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10))) & (~(n5 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6))) & (~(n5 = n7))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6))) & (~(n5 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7))) & (~(n5 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7))) & (~(n5 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8))) & (~(n5 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8))) & (~(n5 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9))) & (~(n5 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9))) & (~(n5 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10))) & (~(n6 = n7))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10))) & (~(n6 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7))) & (~(n6 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7))) & (~(n6 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8))) & (~(n6 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8))) & (~(n6 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9))) & (~(n6 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9))) & (~(n6 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10))) & (~(n7 = n8))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10))) & (~(n7 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8))) & (~(n7 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8))) & (~(n7 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9))) & (~(n7 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9))) & (~(n7 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10))) & (~(n8 = n9))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10))) & (~(n8 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9))))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) & (~(n8 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9))) & (~(n8 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9))) & (~(n8 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)))), (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) & (~(n8 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10))))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) & (~(n8 = n10))) & (~(n9 = n10))) <=> (((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10))) & (~(n9 = n10))))), rewrite((((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10))) & (~(n9 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10)))), ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) & (~(n8 = n10))) & (~(n9 = n10))) <=> ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10)))))),
% 5.44/5.39 inference(bind,[status(th)],[])).
% 5.44/5.39 tff(4,plain,
% 5.44/5.39 (?[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) & (~(n8 = n10))) & (~(n9 = n10))) <=> ?[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10)))),
% 5.44/5.40 inference(quant_intro,[status(thm)],[3])).
% 5.44/5.40 tff(5,axiom,(?[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((succ(n0) = n1) & (succ(n1) = n2)) & (succ(n2) = n3)) & (succ(n3) = n4)) & (succ(n4) = n5)) & (succ(n5) = n6)) & (succ(n6) = n7)) & (succ(n7) = n8)) & (succ(n8) = n9)) & (succ(n9) = n10)) & (succ(n10) = n0)) & (pred(n0) = n10)) & (pred(n1) = n0)) & (pred(n2) = n1)) & (pred(n3) = n2)) & (pred(n4) = n3)) & (pred(n5) = n4)) & (pred(n6) = n5)) & (pred(n7) = n6)) & (pred(n8) = n7)) & (pred(n9) = n8)) & (pred(n10) = n9)) & (sum(n0, n0) = n0)) & (sum(n0, n1) = n1)) & (sum(n0, n2) = n2)) & (sum(n0, n3) = n3)) & (sum(n0, n4) = n4)) & (sum(n0, n5) = n5)) & (sum(n0, n6) = n6)) & (sum(n0, n7) = n7)) & (sum(n0, n8) = n8)) & (sum(n0, n9) = n9)) & (sum(n0, n10) = n10)) & (sum(n1, n0) = n1)) & (sum(n1, n1) = n2)) & (sum(n1, n2) = n3)) & (sum(n1, n3) = n4)) & (sum(n1, n4) = n5)) & (sum(n1, n5) = n6)) & (sum(n1, n6) = n7)) & (sum(n1, n7) = n8)) & (sum(n1, n8) = n9)) & (sum(n1, n9) = n10)) & (sum(n1, n10) = n0)) & (sum(n2, n0) = n2)) & (sum(n2, n1) = n3)) & (sum(n2, n2) = n4)) & (sum(n2, n3) = n5)) & (sum(n2, n4) = n6)) & (sum(n2, n5) = n7)) & (sum(n2, n6) = n8)) & (sum(n2, n7) = n9)) & (sum(n2, n8) = n10)) & (sum(n2, n9) = n0)) & (sum(n2, n10) = n1)) & (sum(n3, n0) = n3)) & (sum(n3, n1) = n4)) & (sum(n3, n2) = n5)) & (sum(n3, n3) = n6)) & (sum(n3, n4) = n7)) & (sum(n3, n5) = n8)) & (sum(n3, n6) = n9)) & (sum(n3, n7) = n10)) & (sum(n3, n8) = n0)) & (sum(n3, n9) = n1)) & (sum(n3, n10) = n2)) & (sum(n4, n0) = n4)) & (sum(n4, n1) = n5)) & (sum(n4, n2) = n6)) & (sum(n4, n3) = n7)) & (sum(n4, n4) = n8)) & (sum(n4, n5) = n9)) & (sum(n4, n6) = n10)) & (sum(n4, n7) = n0)) & (sum(n4, n8) = n1)) & (sum(n4, n9) = n2)) & (sum(n4, n10) = n3)) & (sum(n5, n0) = n5)) & (sum(n5, n1) = n6)) & (sum(n5, n2) = n7)) & (sum(n5, n3) = n8)) & (sum(n5, n4) = n9)) & (sum(n5, n5) = n10)) & (sum(n5, n6) = n0)) & (sum(n5, n7) = n1)) & (sum(n5, n8) = n2)) & (sum(n5, n9) = n3)) & (sum(n5, n10) = n4)) & (sum(n6, n0) = n6)) & (sum(n6, n1) = n7)) & (sum(n6, n2) = n8)) & (sum(n6, n3) = n9)) & (sum(n6, n4) = n10)) & (sum(n6, n5) = n0)) & (sum(n6, n6) = n1)) & (sum(n6, n7) = n2)) & (sum(n6, n8) = n3)) & (sum(n6, n9) = n4)) & (sum(n6, n10) = n5)) & (sum(n7, n0) = n7)) & (sum(n7, n1) = n8)) & (sum(n7, n2) = n9)) & (sum(n7, n3) = n10)) & (sum(n7, n4) = n0)) & (sum(n7, n5) = n1)) & (sum(n7, n6) = n2)) & (sum(n7, n7) = n3)) & (sum(n7, n8) = n4)) & (sum(n7, n9) = n5)) & (sum(n7, n10) = n6)) & (sum(n8, n0) = n8)) & (sum(n8, n1) = n9)) & (sum(n8, n2) = n10)) & (sum(n8, n3) = n0)) & (sum(n8, n4) = n1)) & (sum(n8, n5) = n2)) & (sum(n8, n6) = n3)) & (sum(n8, n7) = n4)) & (sum(n8, n8) = n5)) & (sum(n8, n9) = n6)) & (sum(n8, n10) = n7)) & (sum(n9, n0) = n9)) & (sum(n9, n1) = n10)) & (sum(n9, n2) = n0)) & (sum(n9, n3) = n1)) & (sum(n9, n4) = n2)) & (sum(n9, n5) = n3)) & (sum(n9, n6) = n4)) & (sum(n9, n7) = n5)) & (sum(n9, n8) = n6)) & (sum(n9, n9) = n7)) & (sum(n9, n10) = n8)) & (sum(n10, n0) = n10)) & (sum(n10, n1) = n0)) & (sum(n10, n2) = n1)) & (sum(n10, n3) = n2)) & (sum(n10, n4) = n3)) & (sum(n10, n5) = n4)) & (sum(n10, n6) = n5)) & (sum(n10, n7) = n6)) & (sum(n10, n8) = n7)) & (sum(n10, n9) = n8)) & (sum(n10, n10) = n9)) & (((((((((((X0 = n0) | (X0 = n1)) | (X0 = n2)) | (X0 = n3)) | (X0 = n4)) | (X0 = n5)) | (X0 = n6)) | (X0 = n7)) | (X0 = n8)) | (X0 = n9)) | (X0 = n10))) & (((((((((((Y0 = n0) | (Y0 = n1)) | (Y0 = n2)) | (Y0 = n3)) | (Y0 = n4)) | (Y0 = n5)) | (Y0 = n6)) | (Y0 = n7)) | (Y0 = n8)) | (Y0 = n9)) | (Y0 = n10))) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0))))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0))))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0))))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0))))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1))))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1))))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1))))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1))))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2))))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2))))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2))))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3))))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3))))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3))))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3))))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4))))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4))))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4))))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4))))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5))))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5))))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5))))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5))))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6))))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6))))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6))))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6))))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7))))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7))))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7))))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7))))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8))))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8))))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8))))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8))))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9))))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9))))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9))))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9))))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0))))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0)))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1))))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1)))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2))))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2)))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3))))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3)))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4))))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4)))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5))))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5)))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6))))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6)))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7))))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7)))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8))))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8)))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9))))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9)))))) & ((((~(X7 = Y7)) | (~(X8 = Y8))) | (~(X9 = Y9))) | (~(X10 = Y10)))) & (~(n0 = n1))) & (~(n0 = n2))) & (~(n0 = n3))) & (~(n0 = n4))) & (~(n0 = n5))) & (~(n0 = n6))) & (~(n0 = n7))) & (~(n0 = n8))) & (~(n0 = n9))) & (~(n0 = n10))) & (~(n1 = n2))) & (~(n1 = n3))) & (~(n1 = n4))) & (~(n1 = n5))) & (~(n1 = n6))) & (~(n1 = n7))) & (~(n1 = n8))) & (~(n1 = n9))) & (~(n1 = n10))) & (~(n2 = n3))) & (~(n2 = n4))) & (~(n2 = n5))) & (~(n2 = n6))) & (~(n2 = n7))) & (~(n2 = n8))) & (~(n2 = n9))) & (~(n2 = n10))) & (~(n3 = n4))) & (~(n3 = n5))) & (~(n3 = n6))) & (~(n3 = n7))) & (~(n3 = n8))) & (~(n3 = n9))) & (~(n3 = n10))) & (~(n4 = n5))) & (~(n4 = n6))) & (~(n4 = n7))) & (~(n4 = n8))) & (~(n4 = n9))) & (~(n4 = n10))) & (~(n5 = n6))) & (~(n5 = n7))) & (~(n5 = n8))) & (~(n5 = n9))) & (~(n5 = n10))) & (~(n6 = n7))) & (~(n6 = n8))) & (~(n6 = n9))) & (~(n6 = n10))) & (~(n7 = n8))) & (~(n7 = n9))) & (~(n7 = n10))) & (~(n8 = n9))) & (~(n8 = n10))) & (~(n9 = n10)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','try_satisfy_this')).
% 5.44/5.40 tff(6,plain,
% 5.44/5.40 (?[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10)))),
% 5.44/5.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 5.44/5.41 tff(7,plain,
% 5.44/5.41 (?[X0: $i, Y0: $i, X1: $i, Y1: $i, X2: $i, Y2: $i, X3: $i, Y3: $i, X4: $i, Y4: $i, X5: $i, Y5: $i, X6: $i, Y6: $i, X7: $i, Y7: $i, X8: $i, Y8: $i, X9: $i, Y9: $i, X10: $i, Y10: $i, NPX0: $i, NPY0: $i, NSX0: $i, NSY0: $i, NPX1: $i, NPY1: $i, NSX1: $i, NSY1: $i, NPX2: $i, NPY2: $i, NSX2: $i, NSY2: $i, NPX3: $i, NPY3: $i, NSX3: $i, NSY3: $i, NPX4: $i, NPY4: $i, NSX4: $i, NSY4: $i, NPX5: $i, NPY5: $i, NSX5: $i, NSY5: $i, NPX6: $i, NPY6: $i, NSX6: $i, NSY6: $i, NPX7: $i, NPY7: $i, NSX7: $i, NSY7: $i, NPX8: $i, NPY8: $i, NSX8: $i, NSY8: $i, NPX9: $i, NPY9: $i, NSX9: $i, NSY9: $i] : ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0 = n10) | (X0 = n9) | (X0 = n8) | (X0 = n7) | (X0 = n6) | (X0 = n5) | (X0 = n4) | (X0 = n3) | (X0 = n2) | (X0 = n1) | (X0 = n0)) & ((Y0 = n10) | (Y0 = n9) | (Y0 = n8) | (Y0 = n7) | (Y0 = n6) | (Y0 = n5) | (Y0 = n4) | (Y0 = n3) | (Y0 = n2) | (Y0 = n1) | (Y0 = n0)) & (NPX0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0)))))))))))) & (NSX0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0)))))))))))) & (NPY0 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0)))))))))))) & (NSY0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0)))))))))))) & (NPX1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1)))))))))))) & (NSX1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1)))))))))))) & (NPY1 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1)))))))))))) & (NSY1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1)))))))))))) & (NPX2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2)))))))))))) & (NSX2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2)))))))))))) & (NPY2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2)))))))))))) & (NSY2 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2)))))))))))) & (NPX3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3)))))))))))) & (NSX3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3)))))))))))) & (NPY3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3)))))))))))) & (NSY3 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3)))))))))))) & (NPX4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4)))))))))))) & (NSX4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4)))))))))))) & (NPY4 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4)))))))))))) & (NSY4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4)))))))))))) & (NPX5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5)))))))))))) & (NSX5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5)))))))))))) & (NPY5 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5)))))))))))) & (NSY5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5)))))))))))) & (NPX6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6)))))))))))) & (NSX6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6)))))))))))) & (NPY6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6)))))))))))) & (NSY6 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6)))))))))))) & (NPX7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7)))))))))))) & (NSX7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7)))))))))))) & (NPY7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7)))))))))))) & (NSY7 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7)))))))))))) & (NPX8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8)))))))))))) & (NSX8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8)))))))))))) & (NPY8 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8)))))))))))) & (NSY8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8)))))))))))) & (NPX9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9)))))))))))) & (NSX9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9)))))))))))) & (NPY9 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9)))))))))))) & (NSY9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9)))))))))))) & (X1 = sum(sum(pred(X0), succ(Y0)), sum(pred(Y0), succ(X0)))) & (Y1 = sum(pred(NSX0), sum(succ(NPX0), sum(pred(NSY0), succ(NPY0))))) & (X2 = sum(sum(pred(X1), succ(Y1)), sum(pred(Y1), succ(X1)))) & (Y2 = sum(pred(NSX1), sum(succ(NPX1), sum(pred(NSY1), succ(NPY1))))) & (X3 = sum(sum(pred(X2), succ(Y2)), sum(pred(Y2), succ(X2)))) & (Y3 = sum(pred(NSX2), sum(succ(NPX2), sum(pred(NSY2), succ(NPY2))))) & (X4 = sum(sum(pred(X3), succ(Y3)), sum(pred(Y3), succ(X3)))) & (Y4 = sum(pred(NSX3), sum(succ(NPX3), sum(pred(NSY3), succ(NPY3))))) & (X5 = sum(sum(pred(X4), succ(Y4)), sum(pred(Y4), succ(X4)))) & (Y5 = sum(pred(NSX4), sum(succ(NPX4), sum(pred(NSY4), succ(NPY4))))) & (X6 = sum(sum(pred(X5), succ(Y5)), sum(pred(Y5), succ(X5)))) & (Y6 = sum(pred(NSX5), sum(succ(NPX5), sum(pred(NSY5), succ(NPY5))))) & (X7 = sum(sum(pred(X6), succ(Y6)), sum(pred(Y6), succ(X6)))) & (Y7 = sum(pred(NSX6), sum(succ(NPX6), sum(pred(NSY6), succ(NPY6))))) & (X8 = sum(sum(pred(X7), succ(Y7)), sum(pred(Y7), succ(X7)))) & (Y8 = sum(pred(NSX7), sum(succ(NPX7), sum(pred(NSY7), succ(NPY7))))) & (X9 = sum(sum(pred(X8), succ(Y8)), sum(pred(Y8), succ(X8)))) & (Y9 = sum(pred(NSX8), sum(succ(NPX8), sum(pred(NSY8), succ(NPY8))))) & (X10 = sum(sum(pred(X9), succ(Y9)), sum(pred(Y9), succ(X9)))) & (Y10 = sum(pred(NSX9), sum(succ(NPX9), sum(pred(NSY9), succ(NPY9))))) & ((~(X10 = Y10)) | (~(X9 = Y9)) | (~(X8 = Y8)) | (~(X7 = Y7))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10)))),
% 5.44/5.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 5.44/5.42 tff(8,plain,(
% 5.44/5.42 (succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0!61 = n10) | (X0!61 = n9) | (X0!61 = n8) | (X0!61 = n7) | (X0!61 = n6) | (X0!61 = n5) | (X0!61 = n4) | (X0!61 = n3) | (X0!61 = n2) | (X0!61 = n1) | (X0!61 = n0)) & ((Y0!60 = n10) | (Y0!60 = n9) | (Y0!60 = n8) | (Y0!60 = n7) | (Y0!60 = n6) | (Y0!60 = n5) | (Y0!60 = n4) | (Y0!60 = n3) | (Y0!60 = n2) | (Y0!60 = n1) | (Y0!60 = n0)) & (NPX0!39 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))))) & (NSX0!37 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))))) & (NPY0!38 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))))) & (NSY0!36 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))))) & (NPX1!35 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))))) & (NSX1!33 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))))) & (NPY1!34 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))))) & (NSY1!32 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))))) & (NPX2!31 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))))) & (NSX2!29 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))))) & (NPY2!30 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))))) & (NSY2!28 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))))) & (NPX3!27 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))))) & (NSX3!25 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))))) & (NPY3!26 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))))) & (NSY3!24 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))))) & (NPX4!23 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))))) & (NSX4!21 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))))) & (NPY4!22 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))))) & (NSY4!20 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))))) & (NPX5!19 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))))) & (NSX5!17 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))))) & (NPY5!18 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))))) & (NSY5!16 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))))) & (NPX6!15 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))))) & (NSX6!13 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))))) & (NPY6!14 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))))) & (NSY6!12 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))))) & (NPX7!11 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7!47)))))))))))) & (NSX7!9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7!47)))))))))))) & (NPY7!10 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7!46)))))))))))) & (NSY7!8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7!46)))))))))))) & (NPX8!7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8!45)))))))))))) & (NSX8!5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8!45)))))))))))) & (NPY8!6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8!44)))))))))))) & (NSY8!4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8!44)))))))))))) & (NPX9!3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9!43)))))))))))) & (NSX9!1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9!43)))))))))))) & (NPY9!2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9!42)))))))))))) & (NSY9!0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9!42)))))))))))) & (X1!59 = sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61)))) & (Y1!58 = sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))))) & (X2!57 = sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59)))) & (Y2!56 = sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))))) & (X3!55 = sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57)))) & (Y3!54 = sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))))) & (X4!53 = sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55)))) & (Y4!52 = sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))))) & (X5!51 = sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53)))) & (Y5!50 = sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))))) & (X6!49 = sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51)))) & (Y6!48 = sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))))) & (X7!47 = sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49)))) & (Y7!46 = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))) & (X8!45 = sum(sum(pred(X7!47), succ(Y7!46)), sum(pred(Y7!46), succ(X7!47)))) & (Y8!44 = sum(pred(NSX7!9), sum(succ(NPX7!11), sum(pred(NSY7!8), succ(NPY7!10))))) & (X9!43 = sum(sum(pred(X8!45), succ(Y8!44)), sum(pred(Y8!44), succ(X8!45)))) & (Y9!42 = sum(pred(NSX8!5), sum(succ(NPX8!7), sum(pred(NSY8!4), succ(NPY8!6))))) & (X10!41 = sum(sum(pred(X9!43), succ(Y9!42)), sum(pred(Y9!42), succ(X9!43)))) & (Y10!40 = sum(pred(NSX9!1), sum(succ(NPX9!3), sum(pred(NSY9!0), succ(NPY9!2))))) & ((~(X10!41 = Y10!40)) | (~(X9!43 = Y9!42)) | (~(X8!45 = Y8!44)) | (~(X7!47 = Y7!46))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10))),
% 5.44/5.42 inference(skolemize,[status(sab)],[7])).
% 5.44/5.42 tff(9,plain,
% 5.44/5.42 ((succ(n0) = n1) & (succ(n1) = n2) & (succ(n2) = n3) & (succ(n3) = n4) & (succ(n4) = n5) & (succ(n5) = n6) & (succ(n6) = n7) & (succ(n7) = n8) & (succ(n8) = n9) & (succ(n9) = n10) & (succ(n10) = n0) & (pred(n0) = n10) & (pred(n1) = n0) & (pred(n2) = n1) & (pred(n3) = n2) & (pred(n4) = n3) & (pred(n5) = n4) & (pred(n6) = n5) & (pred(n7) = n6) & (pred(n8) = n7) & (pred(n9) = n8) & (pred(n10) = n9) & (sum(n0, n0) = n0) & (sum(n0, n1) = n1) & (sum(n0, n2) = n2) & (sum(n0, n3) = n3) & (sum(n0, n4) = n4) & (sum(n0, n5) = n5) & (sum(n0, n6) = n6) & (sum(n0, n7) = n7) & (sum(n0, n8) = n8) & (sum(n0, n9) = n9) & (sum(n0, n10) = n10) & (sum(n1, n0) = n1) & (sum(n1, n1) = n2) & (sum(n1, n2) = n3) & (sum(n1, n3) = n4) & (sum(n1, n4) = n5) & (sum(n1, n5) = n6) & (sum(n1, n6) = n7) & (sum(n1, n7) = n8) & (sum(n1, n8) = n9) & (sum(n1, n9) = n10) & (sum(n1, n10) = n0) & (sum(n2, n0) = n2) & (sum(n2, n1) = n3) & (sum(n2, n2) = n4) & (sum(n2, n3) = n5) & (sum(n2, n4) = n6) & (sum(n2, n5) = n7) & (sum(n2, n6) = n8) & (sum(n2, n7) = n9) & (sum(n2, n8) = n10) & (sum(n2, n9) = n0) & (sum(n2, n10) = n1) & (sum(n3, n0) = n3) & (sum(n3, n1) = n4) & (sum(n3, n2) = n5) & (sum(n3, n3) = n6) & (sum(n3, n4) = n7) & (sum(n3, n5) = n8) & (sum(n3, n6) = n9) & (sum(n3, n7) = n10) & (sum(n3, n8) = n0) & (sum(n3, n9) = n1) & (sum(n3, n10) = n2) & (sum(n4, n0) = n4) & (sum(n4, n1) = n5) & (sum(n4, n2) = n6) & (sum(n4, n3) = n7) & (sum(n4, n4) = n8) & (sum(n4, n5) = n9) & (sum(n4, n6) = n10) & (sum(n4, n7) = n0) & (sum(n4, n8) = n1) & (sum(n4, n9) = n2) & (sum(n4, n10) = n3) & (sum(n5, n0) = n5) & (sum(n5, n1) = n6) & (sum(n5, n2) = n7) & (sum(n5, n3) = n8) & (sum(n5, n4) = n9) & (sum(n5, n5) = n10) & (sum(n5, n6) = n0) & (sum(n5, n7) = n1) & (sum(n5, n8) = n2) & (sum(n5, n9) = n3) & (sum(n5, n10) = n4) & (sum(n6, n0) = n6) & (sum(n6, n1) = n7) & (sum(n6, n2) = n8) & (sum(n6, n3) = n9) & (sum(n6, n4) = n10) & (sum(n6, n5) = n0) & (sum(n6, n6) = n1) & (sum(n6, n7) = n2) & (sum(n6, n8) = n3) & (sum(n6, n9) = n4) & (sum(n6, n10) = n5) & (sum(n7, n0) = n7) & (sum(n7, n1) = n8) & (sum(n7, n2) = n9) & (sum(n7, n3) = n10) & (sum(n7, n4) = n0) & (sum(n7, n5) = n1) & (sum(n7, n6) = n2) & (sum(n7, n7) = n3) & (sum(n7, n8) = n4) & (sum(n7, n9) = n5) & (sum(n7, n10) = n6) & (sum(n8, n0) = n8) & (sum(n8, n1) = n9) & (sum(n8, n2) = n10) & (sum(n8, n3) = n0) & (sum(n8, n4) = n1) & (sum(n8, n5) = n2) & (sum(n8, n6) = n3) & (sum(n8, n7) = n4) & (sum(n8, n8) = n5) & (sum(n8, n9) = n6) & (sum(n8, n10) = n7) & (sum(n9, n0) = n9) & (sum(n9, n1) = n10) & (sum(n9, n2) = n0) & (sum(n9, n3) = n1) & (sum(n9, n4) = n2) & (sum(n9, n5) = n3) & (sum(n9, n6) = n4) & (sum(n9, n7) = n5) & (sum(n9, n8) = n6) & (sum(n9, n9) = n7) & (sum(n9, n10) = n8) & (sum(n10, n0) = n10) & (sum(n10, n1) = n0) & (sum(n10, n2) = n1) & (sum(n10, n3) = n2) & (sum(n10, n4) = n3) & (sum(n10, n5) = n4) & (sum(n10, n6) = n5) & (sum(n10, n7) = n6) & (sum(n10, n8) = n7) & (sum(n10, n9) = n8) & (sum(n10, n10) = n9) & ((X0!61 = n10) | (X0!61 = n9) | (X0!61 = n8) | (X0!61 = n7) | (X0!61 = n6) | (X0!61 = n5) | (X0!61 = n4) | (X0!61 = n3) | (X0!61 = n2) | (X0!61 = n1) | (X0!61 = n0)) & ((Y0!60 = n10) | (Y0!60 = n9) | (Y0!60 = n8) | (Y0!60 = n7) | (Y0!60 = n6) | (Y0!60 = n5) | (Y0!60 = n4) | (Y0!60 = n3) | (Y0!60 = n2) | (Y0!60 = n1) | (Y0!60 = n0)) & (NPX0!39 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))))) & (NSX0!37 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))))) & (NPY0!38 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))))) & (NSY0!36 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))))) & (NPX1!35 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))))) & (NSX1!33 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))))) & (NPY1!34 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))))) & (NSY1!32 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))))) & (NPX2!31 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))))) & (NSX2!29 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))))) & (NPY2!30 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))))) & (NSY2!28 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))))) & (NPX3!27 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))))) & (NSX3!25 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))))) & (NPY3!26 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))))) & (NSY3!24 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))))) & (NPX4!23 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))))) & (NSX4!21 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))))) & (NPY4!22 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))))) & (NSY4!20 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))))) & (NPX5!19 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))))) & (NSX5!17 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))))) & (NPY5!18 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))))) & (NSY5!16 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))))) & (NPX6!15 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))))) & (NSX6!13 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))))) & (NPY6!14 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))))) & (NSY6!12 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))))) & (NPX7!11 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X7!47)))))))))))) & (NSX7!9 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X7!47)))))))))))) & (NPY7!10 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y7!46)))))))))))) & (NSY7!8 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y7!46)))))))))))) & (NPX8!7 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X8!45)))))))))))) & (NSX8!5 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X8!45)))))))))))) & (NPY8!6 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y8!44)))))))))))) & (NSY8!4 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y8!44)))))))))))) & (NPX9!3 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X9!43)))))))))))) & (NSX9!1 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X9!43)))))))))))) & (NPY9!2 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y9!42)))))))))))) & (NSY9!0 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y9!42)))))))))))) & (X1!59 = sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61)))) & (Y1!58 = sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))))) & (X2!57 = sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59)))) & (Y2!56 = sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))))) & (X3!55 = sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57)))) & (Y3!54 = sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))))) & (X4!53 = sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55)))) & (Y4!52 = sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))))) & (X5!51 = sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53)))) & (Y5!50 = sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))))) & (X6!49 = sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51)))) & (Y6!48 = sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))))) & (X7!47 = sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49)))) & (Y7!46 = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))) & (X8!45 = sum(sum(pred(X7!47), succ(Y7!46)), sum(pred(Y7!46), succ(X7!47)))) & (Y8!44 = sum(pred(NSX7!9), sum(succ(NPX7!11), sum(pred(NSY7!8), succ(NPY7!10))))) & (X9!43 = sum(sum(pred(X8!45), succ(Y8!44)), sum(pred(Y8!44), succ(X8!45)))) & (Y9!42 = sum(pred(NSX8!5), sum(succ(NPX8!7), sum(pred(NSY8!4), succ(NPY8!6))))) & (X10!41 = sum(sum(pred(X9!43), succ(Y9!42)), sum(pred(Y9!42), succ(X9!43)))) & (Y10!40 = sum(pred(NSX9!1), sum(succ(NPX9!3), sum(pred(NSY9!0), succ(NPY9!2))))) & ((~(X10!41 = Y10!40)) | (~(X9!43 = Y9!42)) | (~(X8!45 = Y8!44)) | (~(X7!47 = Y7!46))) & (~(n0 = n1)) & (~(n0 = n2)) & (~(n0 = n3)) & (~(n0 = n4)) & (~(n0 = n5)) & (~(n0 = n6)) & (~(n0 = n7)) & (~(n0 = n8)) & (~(n0 = n9)) & (~(n0 = n10)) & (~(n1 = n2)) & (~(n1 = n3)) & (~(n1 = n4)) & (~(n1 = n5)) & (~(n1 = n6)) & (~(n1 = n7)) & (~(n1 = n8)) & (~(n1 = n9)) & (~(n1 = n10)) & (~(n2 = n3)) & (~(n2 = n4)) & (~(n2 = n5)) & (~(n2 = n6)) & (~(n2 = n7)) & (~(n2 = n8)) & (~(n2 = n9)) & (~(n2 = n10)) & (~(n3 = n4)) & (~(n3 = n5)) & (~(n3 = n6)) & (~(n3 = n7)) & (~(n3 = n8)) & (~(n3 = n9)) & (~(n3 = n10)) & (~(n4 = n5)) & (~(n4 = n6)) & (~(n4 = n7)) & (~(n4 = n8)) & (~(n4 = n9)) & (~(n4 = n10)) & (~(n5 = n6)) & (~(n5 = n7)) & (~(n5 = n8)) & (~(n5 = n9)) & (~(n5 = n10)) & (~(n6 = n7)) & (~(n6 = n8)) & (~(n6 = n9)) & (~(n6 = n10)) & (~(n7 = n8)) & (~(n7 = n9)) & (~(n7 = n10)) & (~(n8 = n9)) & (~(n8 = n10)) & (~(n9 = n10))),
% 5.44/5.43 inference(modus_ponens,[status(thm)],[8, 1])).
% 5.44/5.43 tff(10,plain,
% 5.44/5.43 (Y10!40 = sum(pred(NSX9!1), sum(succ(NPX9!3), sum(pred(NSY9!0), succ(NPY9!2))))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(11,plain,
% 5.44/5.43 (sum(pred(NSX9!1), sum(succ(NPX9!3), sum(pred(NSY9!0), succ(NPY9!2)))) = Y10!40),
% 5.44/5.43 inference(symmetry,[status(thm)],[10])).
% 5.44/5.43 tff(12,plain,
% 5.44/5.43 (sum(n4, n6) = n10),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(13,plain,
% 5.44/5.43 (sum(n2, n4) = n6),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(14,plain,
% 5.44/5.43 (succ(n3) = n4),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(15,plain,
% 5.44/5.43 (pred(n4) = n3),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(16,plain,
% 5.44/5.43 (pred(n5) = n4),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(17,plain,
% 5.44/5.43 (pred(n6) = n5),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(18,plain,
% 5.44/5.43 (pred(n7) = n6),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(19,plain,
% 5.44/5.43 (pred(n8) = n7),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(20,plain,
% 5.44/5.43 (pred(n9) = n8),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(21,plain,
% 5.44/5.43 (pred(n10) = n9),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(22,plain,
% 5.44/5.43 (pred(n0) = n10),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(23,plain,
% 5.44/5.43 (pred(n1) = n0),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(24,plain,
% 5.44/5.43 (pred(n2) = n1),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(25,plain,
% 5.44/5.43 (pred(n3) = n2),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(26,plain,
% 5.44/5.43 (sum(n7, n7) = n3),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(27,plain,
% 5.44/5.43 (sum(n8, n10) = n7),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(28,plain,
% 5.44/5.43 (succ(n9) = n10),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(29,plain,
% 5.44/5.43 (sum(n10, n10) = n9),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(30,plain,
% 5.44/5.43 (succ(n5) = n6),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(31,plain,
% 5.44/5.43 (sum(n8, n8) = n5),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(32,plain,
% 5.44/5.43 (sum(n3, n5) = n8),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(33,plain,
% 5.44/5.43 (succ(n4) = n5),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(34,plain,
% 5.44/5.43 (sum(n2, n2) = n4),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(35,plain,
% 5.44/5.43 (sum(n0, n2) = n2),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(36,plain,
% 5.44/5.43 (succ(n1) = n2),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(37,plain,
% 5.44/5.43 (sum(n6, n6) = n1),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(38,plain,
% 5.44/5.43 (sum(n6, n7) = n2),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(39,plain,
% 5.44/5.43 (succ(n6) = n7),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(40,plain,
% 5.44/5.43 (sum(n0, n9) = n9),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(41,plain,
% 5.44/5.43 (sum(n9, n0) = n9),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(42,plain,
% 5.44/5.43 (succ(n10) = n0),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(43,plain,
% 5.44/5.43 (sum(n5, n5) = n10),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(44,plain,
% 5.44/5.43 (sum(n7, n9) = n5),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(45,plain,
% 5.44/5.43 (succ(n8) = n9),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(46,plain,
% 5.44/5.43 (sum(n4, n4) = n8),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(47,plain,
% 5.44/5.43 (sum(n1, n3) = n4),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(48,plain,
% 5.44/5.43 (succ(n2) = n3),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(49,plain,
% 5.44/5.43 (sum(n1, n1) = n2),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(50,plain,
% 5.44/5.43 (sum(n5, n7) = n1),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(51,plain,
% 5.44/5.43 (sum(n3, n3) = n6),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(52,plain,
% 5.44/5.43 (sum(n6, n8) = n3),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(53,plain,
% 5.44/5.43 (succ(n7) = n8),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(54,plain,
% 5.44/5.43 (sum(n9, n9) = n7),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(55,assumption,(~(X0!61 = n6)), introduced(assumption)).
% 5.44/5.43 tff(56,plain,
% 5.44/5.43 (sum(n1, n0) = n1),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(57,plain,
% 5.44/5.43 (sum(n10, n1) = n0),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(58,plain,
% 5.44/5.43 (succ(n0) = n1),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(59,plain,
% 5.44/5.43 (sum(n0, n0) = n0),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(60,plain,
% 5.44/5.43 (sum(n5, n6) = n0),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(61,assumption,(~(Y0!60 = n7)), introduced(assumption)).
% 5.44/5.43 tff(62,plain,
% 5.44/5.43 (sum(n5, n9) = n3),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(63,assumption,(~(X0!61 = n5)), introduced(assumption)).
% 5.44/5.43 tff(64,plain,
% 5.44/5.43 (sum(n8, n3) = n0),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(65,plain,
% 5.44/5.43 (sum(n3, n9) = n1),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(66,assumption,(~(Y0!60 = n6)), introduced(assumption)).
% 5.44/5.43 tff(67,plain,
% 5.44/5.43 (sum(n4, n9) = n2),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(68,assumption,(~(Y0!60 = n4)), introduced(assumption)).
% 5.44/5.43 tff(69,plain,
% 5.44/5.43 (sum(n10, n7) = n6),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(70,plain,
% 5.44/5.43 (sum(n4, n2) = n6),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(71,assumption,(~(X0!61 = n8)), introduced(assumption)).
% 5.44/5.43 tff(72,plain,
% 5.44/5.43 (sum(n3, n8) = n0),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(73,assumption,(X0!61 = n7), introduced(assumption)).
% 5.44/5.43 tff(74,plain,
% 5.44/5.43 (succ(X0!61) = succ(n7)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[73])).
% 5.44/5.43 tff(75,plain,
% 5.44/5.43 (succ(X0!61) = n8),
% 5.44/5.43 inference(transitivity,[status(thm)],[74, 53])).
% 5.44/5.43 tff(76,plain,
% 5.44/5.43 (Y9!42 = sum(pred(NSX8!5), sum(succ(NPX8!7), sum(pred(NSY8!4), succ(NPY8!6))))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(77,plain,
% 5.44/5.43 (sum(pred(NSX8!5), sum(succ(NPX8!7), sum(pred(NSY8!4), succ(NPY8!6)))) = Y9!42),
% 5.44/5.43 inference(symmetry,[status(thm)],[76])).
% 5.44/5.43 tff(78,assumption,(~(X9!43 = Y9!42)), introduced(assumption)).
% 5.44/5.43 tff(79,plain,
% 5.44/5.43 (sum(n2, n8) = n10),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(80,assumption,(Y0!60 = n3), introduced(assumption)).
% 5.44/5.43 tff(81,plain,
% 5.44/5.43 (pred(Y0!60) = pred(n3)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[80])).
% 5.44/5.43 tff(82,plain,
% 5.44/5.43 (pred(Y0!60) = n2),
% 5.44/5.43 inference(transitivity,[status(thm)],[81, 25])).
% 5.44/5.43 tff(83,plain,
% 5.44/5.43 (sum(pred(Y0!60), succ(X0!61)) = sum(n2, n8)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[82, 75])).
% 5.44/5.43 tff(84,plain,
% 5.44/5.43 (sum(pred(Y0!60), succ(X0!61)) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[83, 79])).
% 5.44/5.43 tff(85,plain,
% 5.44/5.43 (sum(n6, n4) = n10),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(86,plain,
% 5.44/5.43 (succ(Y0!60) = succ(n3)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[80])).
% 5.44/5.43 tff(87,plain,
% 5.44/5.43 (succ(Y0!60) = n4),
% 5.44/5.43 inference(transitivity,[status(thm)],[86, 14])).
% 5.44/5.43 tff(88,plain,
% 5.44/5.43 (pred(X0!61) = pred(n7)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[73])).
% 5.44/5.43 tff(89,plain,
% 5.44/5.43 (pred(X0!61) = n6),
% 5.44/5.43 inference(transitivity,[status(thm)],[88, 18])).
% 5.44/5.43 tff(90,plain,
% 5.44/5.43 (sum(pred(X0!61), succ(Y0!60)) = sum(n6, n4)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[89, 87])).
% 5.44/5.43 tff(91,plain,
% 5.44/5.43 (sum(pred(X0!61), succ(Y0!60)) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[90, 85])).
% 5.44/5.43 tff(92,plain,
% 5.44/5.43 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n10, n10)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[91, 84])).
% 5.44/5.43 tff(93,plain,
% 5.44/5.43 (X1!59 = sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61)))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(94,plain,
% 5.44/5.43 (X1!59 = n9),
% 5.44/5.43 inference(transitivity,[status(thm)],[93, 92, 29])).
% 5.44/5.43 tff(95,plain,
% 5.44/5.43 (succ(X1!59) = succ(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[94])).
% 5.44/5.43 tff(96,plain,
% 5.44/5.43 (succ(X1!59) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[95, 28])).
% 5.44/5.43 tff(97,plain,
% 5.44/5.43 (sum(n6, n3) = n9),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(98,plain,
% 5.44/5.43 (sum(n8, n6) = n3),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(99,plain,
% 5.44/5.43 (pred(pred(Y0!60)) = pred(n2)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[82])).
% 5.44/5.43 tff(100,plain,
% 5.44/5.43 (pred(pred(Y0!60)) = n1),
% 5.44/5.43 inference(transitivity,[status(thm)],[99, 24])).
% 5.44/5.43 tff(101,plain,
% 5.44/5.43 (pred(pred(pred(Y0!60))) = pred(n1)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[100])).
% 5.44/5.43 tff(102,plain,
% 5.44/5.43 (pred(pred(pred(Y0!60))) = n0),
% 5.44/5.43 inference(transitivity,[status(thm)],[101, 23])).
% 5.44/5.43 tff(103,plain,
% 5.44/5.43 (pred(pred(pred(pred(Y0!60)))) = pred(n0)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[102])).
% 5.44/5.43 tff(104,plain,
% 5.44/5.43 (pred(pred(pred(pred(Y0!60)))) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[103, 22])).
% 5.44/5.43 tff(105,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n10)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[104])).
% 5.44/5.43 tff(106,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(Y0!60))))) = n9),
% 5.44/5.43 inference(transitivity,[status(thm)],[105, 21])).
% 5.44/5.43 tff(107,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[106])).
% 5.44/5.43 tff(108,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n8),
% 5.44/5.43 inference(transitivity,[status(thm)],[107, 20])).
% 5.44/5.43 tff(109,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n8)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[108])).
% 5.44/5.43 tff(110,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n7),
% 5.44/5.43 inference(transitivity,[status(thm)],[109, 19])).
% 5.44/5.43 tff(111,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n7)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[110])).
% 5.44/5.43 tff(112,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n6),
% 5.44/5.43 inference(transitivity,[status(thm)],[111, 18])).
% 5.44/5.43 tff(113,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n6)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[112])).
% 5.44/5.43 tff(114,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n5),
% 5.44/5.43 inference(transitivity,[status(thm)],[113, 17])).
% 5.44/5.43 tff(115,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n5)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[114])).
% 5.44/5.43 tff(116,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n4),
% 5.44/5.43 inference(transitivity,[status(thm)],[115, 16])).
% 5.44/5.43 tff(117,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n4)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[116])).
% 5.44/5.43 tff(118,plain,
% 5.44/5.43 (NPY0!38 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(119,plain,
% 5.44/5.43 (NPY0!38 = n3),
% 5.44/5.43 inference(transitivity,[status(thm)],[118, 117, 15])).
% 5.44/5.43 tff(120,plain,
% 5.44/5.43 (succ(NPY0!38) = succ(n3)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[119])).
% 5.44/5.43 tff(121,plain,
% 5.44/5.43 (succ(NPY0!38) = n4),
% 5.44/5.43 inference(transitivity,[status(thm)],[120, 14])).
% 5.44/5.43 tff(122,plain,
% 5.44/5.43 (succ(succ(Y0!60)) = succ(n4)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[87])).
% 5.44/5.43 tff(123,plain,
% 5.44/5.43 (succ(succ(Y0!60)) = n5),
% 5.44/5.43 inference(transitivity,[status(thm)],[122, 33])).
% 5.44/5.43 tff(124,plain,
% 5.44/5.43 (succ(succ(succ(Y0!60))) = succ(n5)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[123])).
% 5.44/5.43 tff(125,plain,
% 5.44/5.43 (succ(succ(succ(Y0!60))) = n6),
% 5.44/5.43 inference(transitivity,[status(thm)],[124, 30])).
% 5.44/5.43 tff(126,plain,
% 5.44/5.43 (succ(succ(succ(succ(Y0!60)))) = succ(n6)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[125])).
% 5.44/5.43 tff(127,plain,
% 5.44/5.43 (succ(succ(succ(succ(Y0!60)))) = n7),
% 5.44/5.43 inference(transitivity,[status(thm)],[126, 39])).
% 5.44/5.43 tff(128,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n7)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[127])).
% 5.44/5.43 tff(129,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(Y0!60))))) = n8),
% 5.44/5.43 inference(transitivity,[status(thm)],[128, 53])).
% 5.44/5.43 tff(130,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n8)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[129])).
% 5.44/5.43 tff(131,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n9),
% 5.44/5.43 inference(transitivity,[status(thm)],[130, 45])).
% 5.44/5.43 tff(132,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[131])).
% 5.44/5.43 tff(133,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[132, 28])).
% 5.44/5.43 tff(134,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n10)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[133])).
% 5.44/5.43 tff(135,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n0),
% 5.44/5.43 inference(transitivity,[status(thm)],[134, 42])).
% 5.44/5.43 tff(136,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n0)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[135])).
% 5.44/5.43 tff(137,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n1),
% 5.44/5.43 inference(transitivity,[status(thm)],[136, 58])).
% 5.44/5.43 tff(138,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n1)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[137])).
% 5.44/5.43 tff(139,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n2),
% 5.44/5.43 inference(transitivity,[status(thm)],[138, 36])).
% 5.44/5.43 tff(140,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n2)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[139])).
% 5.44/5.43 tff(141,plain,
% 5.44/5.43 (NSY0!36 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(142,plain,
% 5.44/5.43 (NSY0!36 = n3),
% 5.44/5.43 inference(transitivity,[status(thm)],[141, 140, 48])).
% 5.44/5.43 tff(143,plain,
% 5.44/5.43 (pred(NSY0!36) = pred(n3)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[142])).
% 5.44/5.43 tff(144,plain,
% 5.44/5.43 (pred(NSY0!36) = n2),
% 5.44/5.43 inference(transitivity,[status(thm)],[143, 25])).
% 5.44/5.43 tff(145,plain,
% 5.44/5.43 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n2, n4)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[144, 121])).
% 5.44/5.43 tff(146,plain,
% 5.44/5.43 (sum(pred(NSY0!36), succ(NPY0!38)) = n6),
% 5.44/5.43 inference(transitivity,[status(thm)],[145, 13])).
% 5.44/5.43 tff(147,plain,
% 5.44/5.43 (pred(pred(X0!61)) = pred(n6)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[89])).
% 5.44/5.43 tff(148,plain,
% 5.44/5.43 (pred(pred(X0!61)) = n5),
% 5.44/5.43 inference(transitivity,[status(thm)],[147, 17])).
% 5.44/5.43 tff(149,plain,
% 5.44/5.43 (pred(pred(pred(X0!61))) = pred(n5)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[148])).
% 5.44/5.43 tff(150,plain,
% 5.44/5.43 (pred(pred(pred(X0!61))) = n4),
% 5.44/5.43 inference(transitivity,[status(thm)],[149, 16])).
% 5.44/5.43 tff(151,plain,
% 5.44/5.43 (pred(pred(pred(pred(X0!61)))) = pred(n4)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[150])).
% 5.44/5.43 tff(152,plain,
% 5.44/5.43 (pred(pred(pred(pred(X0!61)))) = n3),
% 5.44/5.43 inference(transitivity,[status(thm)],[151, 15])).
% 5.44/5.43 tff(153,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(X0!61))))) = pred(n3)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[152])).
% 5.44/5.43 tff(154,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(X0!61))))) = n2),
% 5.44/5.43 inference(transitivity,[status(thm)],[153, 25])).
% 5.44/5.43 tff(155,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n2)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[154])).
% 5.44/5.43 tff(156,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n1),
% 5.44/5.43 inference(transitivity,[status(thm)],[155, 24])).
% 5.44/5.43 tff(157,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n1)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[156])).
% 5.44/5.43 tff(158,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n0),
% 5.44/5.43 inference(transitivity,[status(thm)],[157, 23])).
% 5.44/5.43 tff(159,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n0)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[158])).
% 5.44/5.43 tff(160,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[159, 22])).
% 5.44/5.43 tff(161,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n10)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[160])).
% 5.44/5.43 tff(162,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n9),
% 5.44/5.43 inference(transitivity,[status(thm)],[161, 21])).
% 5.44/5.43 tff(163,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[162])).
% 5.44/5.43 tff(164,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n8),
% 5.44/5.43 inference(transitivity,[status(thm)],[163, 20])).
% 5.44/5.43 tff(165,plain,
% 5.44/5.43 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n8)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[164])).
% 5.44/5.43 tff(166,plain,
% 5.44/5.43 (NPX0!39 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(167,plain,
% 5.44/5.43 (NPX0!39 = n7),
% 5.44/5.43 inference(transitivity,[status(thm)],[166, 165, 19])).
% 5.44/5.43 tff(168,plain,
% 5.44/5.43 (succ(NPX0!39) = succ(n7)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[167])).
% 5.44/5.43 tff(169,plain,
% 5.44/5.43 (succ(NPX0!39) = n8),
% 5.44/5.43 inference(transitivity,[status(thm)],[168, 53])).
% 5.44/5.43 tff(170,plain,
% 5.44/5.43 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n8, n6)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[169, 146])).
% 5.44/5.43 tff(171,plain,
% 5.44/5.43 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n3),
% 5.44/5.43 inference(transitivity,[status(thm)],[170, 98])).
% 5.44/5.43 tff(172,plain,
% 5.44/5.43 (succ(succ(X0!61)) = succ(n8)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[75])).
% 5.44/5.43 tff(173,plain,
% 5.44/5.43 (succ(succ(X0!61)) = n9),
% 5.44/5.43 inference(transitivity,[status(thm)],[172, 45])).
% 5.44/5.43 tff(174,plain,
% 5.44/5.43 (succ(succ(succ(X0!61))) = succ(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[173])).
% 5.44/5.43 tff(175,plain,
% 5.44/5.43 (succ(succ(succ(X0!61))) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[174, 28])).
% 5.44/5.43 tff(176,plain,
% 5.44/5.43 (succ(succ(succ(succ(X0!61)))) = succ(n10)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[175])).
% 5.44/5.43 tff(177,plain,
% 5.44/5.43 (succ(succ(succ(succ(X0!61)))) = n0),
% 5.44/5.43 inference(transitivity,[status(thm)],[176, 42])).
% 5.44/5.43 tff(178,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(X0!61))))) = succ(n0)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[177])).
% 5.44/5.43 tff(179,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(X0!61))))) = n1),
% 5.44/5.43 inference(transitivity,[status(thm)],[178, 58])).
% 5.44/5.43 tff(180,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n1)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[179])).
% 5.44/5.43 tff(181,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n2),
% 5.44/5.43 inference(transitivity,[status(thm)],[180, 36])).
% 5.44/5.43 tff(182,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n2)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[181])).
% 5.44/5.43 tff(183,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n3),
% 5.44/5.43 inference(transitivity,[status(thm)],[182, 48])).
% 5.44/5.43 tff(184,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n3)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[183])).
% 5.44/5.43 tff(185,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n4),
% 5.44/5.43 inference(transitivity,[status(thm)],[184, 14])).
% 5.44/5.43 tff(186,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n4)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[185])).
% 5.44/5.43 tff(187,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n5),
% 5.44/5.43 inference(transitivity,[status(thm)],[186, 33])).
% 5.44/5.43 tff(188,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n5)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[187])).
% 5.44/5.43 tff(189,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n6),
% 5.44/5.43 inference(transitivity,[status(thm)],[188, 30])).
% 5.44/5.43 tff(190,plain,
% 5.44/5.43 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n6)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[189])).
% 5.44/5.43 tff(191,plain,
% 5.44/5.43 (NSX0!37 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(192,plain,
% 5.44/5.43 (NSX0!37 = n7),
% 5.44/5.43 inference(transitivity,[status(thm)],[191, 190, 39])).
% 5.44/5.43 tff(193,plain,
% 5.44/5.43 (pred(NSX0!37) = pred(n7)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[192])).
% 5.44/5.43 tff(194,plain,
% 5.44/5.43 (pred(NSX0!37) = n6),
% 5.44/5.43 inference(transitivity,[status(thm)],[193, 18])).
% 5.44/5.43 tff(195,plain,
% 5.44/5.43 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n6, n3)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[194, 171])).
% 5.44/5.43 tff(196,plain,
% 5.44/5.43 (Y1!58 = sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))))),
% 5.44/5.43 inference(and_elim,[status(thm)],[9])).
% 5.44/5.43 tff(197,plain,
% 5.44/5.43 (Y1!58 = n9),
% 5.44/5.43 inference(transitivity,[status(thm)],[196, 195, 97])).
% 5.44/5.43 tff(198,plain,
% 5.44/5.43 (pred(Y1!58) = pred(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[197])).
% 5.44/5.43 tff(199,plain,
% 5.44/5.43 (pred(Y1!58) = n8),
% 5.44/5.43 inference(transitivity,[status(thm)],[198, 20])).
% 5.44/5.43 tff(200,plain,
% 5.44/5.43 (sum(pred(Y1!58), succ(X1!59)) = sum(n8, n10)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[199, 96])).
% 5.44/5.43 tff(201,plain,
% 5.44/5.43 (sum(pred(Y1!58), succ(X1!59)) = n7),
% 5.44/5.43 inference(transitivity,[status(thm)],[200, 27])).
% 5.44/5.43 tff(202,plain,
% 5.44/5.43 (succ(Y1!58) = succ(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[197])).
% 5.44/5.43 tff(203,plain,
% 5.44/5.43 (succ(Y1!58) = n10),
% 5.44/5.43 inference(transitivity,[status(thm)],[202, 28])).
% 5.44/5.43 tff(204,plain,
% 5.44/5.43 (pred(X1!59) = pred(n9)),
% 5.44/5.43 inference(monotonicity,[status(thm)],[94])).
% 5.44/5.43 tff(205,plain,
% 5.44/5.43 (pred(X1!59) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[204, 20])).
% 5.44/5.44 tff(206,plain,
% 5.44/5.44 (sum(pred(X1!59), succ(Y1!58)) = sum(n8, n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[205, 203])).
% 5.44/5.44 tff(207,plain,
% 5.44/5.44 (sum(pred(X1!59), succ(Y1!58)) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[206, 27])).
% 5.44/5.44 tff(208,plain,
% 5.44/5.44 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n7, n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[207, 201])).
% 5.44/5.44 tff(209,plain,
% 5.44/5.44 (X2!57 = sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59)))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(210,plain,
% 5.44/5.44 (X2!57 = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[209, 208, 26])).
% 5.44/5.44 tff(211,plain,
% 5.44/5.44 (succ(X2!57) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[210])).
% 5.44/5.44 tff(212,plain,
% 5.44/5.44 (succ(X2!57) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[211, 14])).
% 5.44/5.44 tff(213,plain,
% 5.44/5.44 (pred(pred(Y1!58)) = pred(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[199])).
% 5.44/5.44 tff(214,plain,
% 5.44/5.44 (pred(pred(Y1!58)) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[213, 19])).
% 5.44/5.44 tff(215,plain,
% 5.44/5.44 (pred(pred(pred(Y1!58))) = pred(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[214])).
% 5.44/5.44 tff(216,plain,
% 5.44/5.44 (pred(pred(pred(Y1!58))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[215, 18])).
% 5.44/5.44 tff(217,plain,
% 5.44/5.44 (pred(pred(pred(pred(Y1!58)))) = pred(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[216])).
% 5.44/5.44 tff(218,plain,
% 5.44/5.44 (pred(pred(pred(pred(Y1!58)))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[217, 17])).
% 5.44/5.44 tff(219,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[218])).
% 5.44/5.44 tff(220,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(Y1!58))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[219, 16])).
% 5.44/5.44 tff(221,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[220])).
% 5.44/5.44 tff(222,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[221, 15])).
% 5.44/5.44 tff(223,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[222])).
% 5.44/5.44 tff(224,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[223, 25])).
% 5.44/5.44 tff(225,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[224])).
% 5.44/5.44 tff(226,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[225, 24])).
% 5.44/5.44 tff(227,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[226])).
% 5.44/5.44 tff(228,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[227, 23])).
% 5.44/5.44 tff(229,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[228])).
% 5.44/5.44 tff(230,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[229, 22])).
% 5.44/5.44 tff(231,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[230])).
% 5.44/5.44 tff(232,plain,
% 5.44/5.44 (NPY1!34 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(233,plain,
% 5.44/5.44 (NPY1!34 = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[232, 231, 21])).
% 5.44/5.44 tff(234,plain,
% 5.44/5.44 (succ(NPY1!34) = succ(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[233])).
% 5.44/5.44 tff(235,plain,
% 5.44/5.44 (succ(NPY1!34) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[234, 28])).
% 5.44/5.44 tff(236,plain,
% 5.44/5.44 (succ(succ(Y1!58)) = succ(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[203])).
% 5.44/5.44 tff(237,plain,
% 5.44/5.44 (succ(succ(Y1!58)) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[236, 42])).
% 5.44/5.44 tff(238,plain,
% 5.44/5.44 (succ(succ(succ(Y1!58))) = succ(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[237])).
% 5.44/5.44 tff(239,plain,
% 5.44/5.44 (succ(succ(succ(Y1!58))) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[238, 58])).
% 5.44/5.44 tff(240,plain,
% 5.44/5.44 (succ(succ(succ(succ(Y1!58)))) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[239])).
% 5.44/5.44 tff(241,plain,
% 5.44/5.44 (succ(succ(succ(succ(Y1!58)))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[240, 36])).
% 5.44/5.44 tff(242,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[241])).
% 5.44/5.44 tff(243,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(Y1!58))))) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[242, 48])).
% 5.44/5.44 tff(244,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[243])).
% 5.44/5.44 tff(245,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[244, 14])).
% 5.44/5.44 tff(246,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[245])).
% 5.44/5.44 tff(247,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[246, 33])).
% 5.44/5.44 tff(248,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[247])).
% 5.44/5.44 tff(249,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[248, 30])).
% 5.44/5.44 tff(250,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[249])).
% 5.44/5.44 tff(251,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[250, 39])).
% 5.44/5.44 tff(252,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[251])).
% 5.44/5.44 tff(253,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[252, 53])).
% 5.44/5.44 tff(254,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[253])).
% 5.44/5.44 tff(255,plain,
% 5.44/5.44 (NSY1!32 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(256,plain,
% 5.44/5.44 (NSY1!32 = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[255, 254, 45])).
% 5.44/5.44 tff(257,plain,
% 5.44/5.44 (pred(NSY1!32) = pred(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[256])).
% 5.44/5.44 tff(258,plain,
% 5.44/5.44 (pred(NSY1!32) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[257, 20])).
% 5.44/5.44 tff(259,plain,
% 5.44/5.44 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n8, n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[258, 235])).
% 5.44/5.44 tff(260,plain,
% 5.44/5.44 (sum(pred(NSY1!32), succ(NPY1!34)) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[259, 27])).
% 5.44/5.44 tff(261,plain,
% 5.44/5.44 (pred(pred(X1!59)) = pred(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[205])).
% 5.44/5.44 tff(262,plain,
% 5.44/5.44 (pred(pred(X1!59)) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[261, 19])).
% 5.44/5.44 tff(263,plain,
% 5.44/5.44 (pred(pred(pred(X1!59))) = pred(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[262])).
% 5.44/5.44 tff(264,plain,
% 5.44/5.44 (pred(pred(pred(X1!59))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[263, 18])).
% 5.44/5.44 tff(265,plain,
% 5.44/5.44 (pred(pred(pred(pred(X1!59)))) = pred(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[264])).
% 5.44/5.44 tff(266,plain,
% 5.44/5.44 (pred(pred(pred(pred(X1!59)))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[265, 17])).
% 5.44/5.44 tff(267,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(X1!59))))) = pred(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[266])).
% 5.44/5.44 tff(268,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(X1!59))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[267, 16])).
% 5.44/5.44 tff(269,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[268])).
% 5.44/5.44 tff(270,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[269, 15])).
% 5.44/5.44 tff(271,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[270])).
% 5.44/5.44 tff(272,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[271, 25])).
% 5.44/5.44 tff(273,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[272])).
% 5.44/5.44 tff(274,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[273, 24])).
% 5.44/5.44 tff(275,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[274])).
% 5.44/5.44 tff(276,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[275, 23])).
% 5.44/5.44 tff(277,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[276])).
% 5.44/5.44 tff(278,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[277, 22])).
% 5.44/5.44 tff(279,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[278])).
% 5.44/5.44 tff(280,plain,
% 5.44/5.44 (NPX1!35 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(281,plain,
% 5.44/5.44 (NPX1!35 = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[280, 279, 21])).
% 5.44/5.44 tff(282,plain,
% 5.44/5.44 (succ(NPX1!35) = succ(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[281])).
% 5.44/5.44 tff(283,plain,
% 5.44/5.44 (succ(NPX1!35) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[282, 28])).
% 5.44/5.44 tff(284,plain,
% 5.44/5.44 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n10, n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[283, 260])).
% 5.44/5.44 tff(285,plain,
% 5.44/5.44 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[284, 69])).
% 5.44/5.44 tff(286,plain,
% 5.44/5.44 (succ(succ(X1!59)) = succ(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[96])).
% 5.44/5.44 tff(287,plain,
% 5.44/5.44 (succ(succ(X1!59)) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[286, 42])).
% 5.44/5.44 tff(288,plain,
% 5.44/5.44 (succ(succ(succ(X1!59))) = succ(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[287])).
% 5.44/5.44 tff(289,plain,
% 5.44/5.44 (succ(succ(succ(X1!59))) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[288, 58])).
% 5.44/5.44 tff(290,plain,
% 5.44/5.44 (succ(succ(succ(succ(X1!59)))) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[289])).
% 5.44/5.44 tff(291,plain,
% 5.44/5.44 (succ(succ(succ(succ(X1!59)))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[290, 36])).
% 5.44/5.44 tff(292,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(X1!59))))) = succ(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[291])).
% 5.44/5.44 tff(293,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(X1!59))))) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[292, 48])).
% 5.44/5.44 tff(294,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[293])).
% 5.44/5.44 tff(295,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[294, 14])).
% 5.44/5.44 tff(296,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[295])).
% 5.44/5.44 tff(297,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[296, 33])).
% 5.44/5.44 tff(298,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[297])).
% 5.44/5.44 tff(299,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[298, 30])).
% 5.44/5.44 tff(300,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[299])).
% 5.44/5.44 tff(301,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[300, 39])).
% 5.44/5.44 tff(302,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[301])).
% 5.44/5.44 tff(303,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[302, 53])).
% 5.44/5.44 tff(304,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[303])).
% 5.44/5.44 tff(305,plain,
% 5.44/5.44 (NSX1!33 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(306,plain,
% 5.44/5.44 (NSX1!33 = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[305, 304, 45])).
% 5.44/5.44 tff(307,plain,
% 5.44/5.44 (pred(NSX1!33) = pred(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[306])).
% 5.44/5.44 tff(308,plain,
% 5.44/5.44 (pred(NSX1!33) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[307, 20])).
% 5.44/5.44 tff(309,plain,
% 5.44/5.44 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n8, n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[308, 285])).
% 5.44/5.44 tff(310,plain,
% 5.44/5.44 (Y2!56 = sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(311,plain,
% 5.44/5.44 (Y2!56 = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[310, 309, 98])).
% 5.44/5.44 tff(312,plain,
% 5.44/5.44 (pred(Y2!56) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[311])).
% 5.44/5.44 tff(313,plain,
% 5.44/5.44 (pred(Y2!56) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[312, 25])).
% 5.44/5.44 tff(314,plain,
% 5.44/5.44 (sum(pred(Y2!56), succ(X2!57)) = sum(n2, n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[313, 212])).
% 5.44/5.44 tff(315,plain,
% 5.44/5.44 (sum(pred(Y2!56), succ(X2!57)) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[314, 13])).
% 5.44/5.44 tff(316,plain,
% 5.44/5.44 (succ(Y2!56) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[311])).
% 5.44/5.44 tff(317,plain,
% 5.44/5.44 (succ(Y2!56) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[316, 14])).
% 5.44/5.44 tff(318,plain,
% 5.44/5.44 (pred(X2!57) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[210])).
% 5.44/5.44 tff(319,plain,
% 5.44/5.44 (pred(X2!57) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[318, 25])).
% 5.44/5.44 tff(320,plain,
% 5.44/5.44 (sum(pred(X2!57), succ(Y2!56)) = sum(n2, n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[319, 317])).
% 5.44/5.44 tff(321,plain,
% 5.44/5.44 (sum(pred(X2!57), succ(Y2!56)) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[320, 13])).
% 5.44/5.44 tff(322,plain,
% 5.44/5.44 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n6, n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[321, 315])).
% 5.44/5.44 tff(323,plain,
% 5.44/5.44 (X3!55 = sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57)))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(324,plain,
% 5.44/5.44 (X3!55 = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[323, 322, 37])).
% 5.44/5.44 tff(325,plain,
% 5.44/5.44 (succ(X3!55) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[324])).
% 5.44/5.44 tff(326,plain,
% 5.44/5.44 (succ(X3!55) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[325, 36])).
% 5.44/5.44 tff(327,plain,
% 5.44/5.44 (sum(n2, n10) = n1),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(328,plain,
% 5.44/5.44 (pred(pred(Y2!56)) = pred(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[313])).
% 5.44/5.44 tff(329,plain,
% 5.44/5.44 (pred(pred(Y2!56)) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[328, 24])).
% 5.44/5.44 tff(330,plain,
% 5.44/5.44 (pred(pred(pred(Y2!56))) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[329])).
% 5.44/5.44 tff(331,plain,
% 5.44/5.44 (pred(pred(pred(Y2!56))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[330, 23])).
% 5.44/5.44 tff(332,plain,
% 5.44/5.44 (pred(pred(pred(pred(Y2!56)))) = pred(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[331])).
% 5.44/5.44 tff(333,plain,
% 5.44/5.44 (pred(pred(pred(pred(Y2!56)))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[332, 22])).
% 5.44/5.44 tff(334,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[333])).
% 5.44/5.44 tff(335,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(Y2!56))))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[334, 21])).
% 5.44/5.44 tff(336,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[335])).
% 5.44/5.44 tff(337,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[336, 20])).
% 5.44/5.44 tff(338,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[337])).
% 5.44/5.44 tff(339,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[338, 19])).
% 5.44/5.44 tff(340,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[339])).
% 5.44/5.44 tff(341,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[340, 18])).
% 5.44/5.44 tff(342,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[341])).
% 5.44/5.44 tff(343,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[342, 17])).
% 5.44/5.44 tff(344,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[343])).
% 5.44/5.44 tff(345,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[344, 16])).
% 5.44/5.44 tff(346,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[345])).
% 5.44/5.44 tff(347,plain,
% 5.44/5.44 (NPY2!30 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(348,plain,
% 5.44/5.44 (NPY2!30 = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[347, 346, 15])).
% 5.44/5.44 tff(349,plain,
% 5.44/5.44 (succ(NPY2!30) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[348])).
% 5.44/5.44 tff(350,plain,
% 5.44/5.44 (succ(NPY2!30) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[349, 14])).
% 5.44/5.44 tff(351,plain,
% 5.44/5.44 (succ(succ(Y2!56)) = succ(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[317])).
% 5.44/5.44 tff(352,plain,
% 5.44/5.44 (succ(succ(Y2!56)) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[351, 33])).
% 5.44/5.44 tff(353,plain,
% 5.44/5.44 (succ(succ(succ(Y2!56))) = succ(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[352])).
% 5.44/5.44 tff(354,plain,
% 5.44/5.44 (succ(succ(succ(Y2!56))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[353, 30])).
% 5.44/5.44 tff(355,plain,
% 5.44/5.44 (succ(succ(succ(succ(Y2!56)))) = succ(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[354])).
% 5.44/5.44 tff(356,plain,
% 5.44/5.44 (succ(succ(succ(succ(Y2!56)))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[355, 39])).
% 5.44/5.44 tff(357,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[356])).
% 5.44/5.44 tff(358,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(Y2!56))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[357, 53])).
% 5.44/5.44 tff(359,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[358])).
% 5.44/5.44 tff(360,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[359, 45])).
% 5.44/5.44 tff(361,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[360])).
% 5.44/5.44 tff(362,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[361, 28])).
% 5.44/5.44 tff(363,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[362])).
% 5.44/5.44 tff(364,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[363, 42])).
% 5.44/5.44 tff(365,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[364])).
% 5.44/5.44 tff(366,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[365, 58])).
% 5.44/5.44 tff(367,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[366])).
% 5.44/5.44 tff(368,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[367, 36])).
% 5.44/5.44 tff(369,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[368])).
% 5.44/5.44 tff(370,plain,
% 5.44/5.44 (NSY2!28 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(371,plain,
% 5.44/5.44 (NSY2!28 = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[370, 369, 48])).
% 5.44/5.44 tff(372,plain,
% 5.44/5.44 (pred(NSY2!28) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[371])).
% 5.44/5.44 tff(373,plain,
% 5.44/5.44 (pred(NSY2!28) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[372, 25])).
% 5.44/5.44 tff(374,plain,
% 5.44/5.44 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n2, n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[373, 350])).
% 5.44/5.44 tff(375,plain,
% 5.44/5.44 (sum(pred(NSY2!28), succ(NPY2!30)) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[374, 13])).
% 5.44/5.44 tff(376,plain,
% 5.44/5.44 (pred(pred(X2!57)) = pred(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[319])).
% 5.44/5.44 tff(377,plain,
% 5.44/5.44 (pred(pred(X2!57)) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[376, 24])).
% 5.44/5.44 tff(378,plain,
% 5.44/5.44 (pred(pred(pred(X2!57))) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[377])).
% 5.44/5.44 tff(379,plain,
% 5.44/5.44 (pred(pred(pred(X2!57))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[378, 23])).
% 5.44/5.44 tff(380,plain,
% 5.44/5.44 (pred(pred(pred(pred(X2!57)))) = pred(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[379])).
% 5.44/5.44 tff(381,plain,
% 5.44/5.44 (pred(pred(pred(pred(X2!57)))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[380, 22])).
% 5.44/5.44 tff(382,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(X2!57))))) = pred(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[381])).
% 5.44/5.44 tff(383,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(X2!57))))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[382, 21])).
% 5.44/5.44 tff(384,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[383])).
% 5.44/5.44 tff(385,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[384, 20])).
% 5.44/5.44 tff(386,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[385])).
% 5.44/5.44 tff(387,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[386, 19])).
% 5.44/5.44 tff(388,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[387])).
% 5.44/5.44 tff(389,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[388, 18])).
% 5.44/5.44 tff(390,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[389])).
% 5.44/5.44 tff(391,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[390, 17])).
% 5.44/5.44 tff(392,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[391])).
% 5.44/5.44 tff(393,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[392, 16])).
% 5.44/5.44 tff(394,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[393])).
% 5.44/5.44 tff(395,plain,
% 5.44/5.44 (NPX2!31 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(396,plain,
% 5.44/5.44 (NPX2!31 = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[395, 394, 15])).
% 5.44/5.44 tff(397,plain,
% 5.44/5.44 (succ(NPX2!31) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[396])).
% 5.44/5.44 tff(398,plain,
% 5.44/5.44 (succ(NPX2!31) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[397, 14])).
% 5.44/5.44 tff(399,plain,
% 5.44/5.44 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n4, n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[398, 375])).
% 5.44/5.44 tff(400,plain,
% 5.44/5.44 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[399, 12])).
% 5.44/5.44 tff(401,plain,
% 5.44/5.44 (succ(succ(X2!57)) = succ(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[212])).
% 5.44/5.44 tff(402,plain,
% 5.44/5.44 (succ(succ(X2!57)) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[401, 33])).
% 5.44/5.44 tff(403,plain,
% 5.44/5.44 (succ(succ(succ(X2!57))) = succ(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[402])).
% 5.44/5.44 tff(404,plain,
% 5.44/5.44 (succ(succ(succ(X2!57))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[403, 30])).
% 5.44/5.44 tff(405,plain,
% 5.44/5.44 (succ(succ(succ(succ(X2!57)))) = succ(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[404])).
% 5.44/5.44 tff(406,plain,
% 5.44/5.44 (succ(succ(succ(succ(X2!57)))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[405, 39])).
% 5.44/5.44 tff(407,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(X2!57))))) = succ(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[406])).
% 5.44/5.44 tff(408,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(X2!57))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[407, 53])).
% 5.44/5.44 tff(409,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[408])).
% 5.44/5.44 tff(410,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[409, 45])).
% 5.44/5.44 tff(411,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[410])).
% 5.44/5.44 tff(412,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[411, 28])).
% 5.44/5.44 tff(413,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[412])).
% 5.44/5.44 tff(414,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[413, 42])).
% 5.44/5.44 tff(415,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[414])).
% 5.44/5.44 tff(416,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[415, 58])).
% 5.44/5.44 tff(417,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[416])).
% 5.44/5.44 tff(418,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[417, 36])).
% 5.44/5.44 tff(419,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[418])).
% 5.44/5.44 tff(420,plain,
% 5.44/5.44 (NSX2!29 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(421,plain,
% 5.44/5.44 (NSX2!29 = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[420, 419, 48])).
% 5.44/5.44 tff(422,plain,
% 5.44/5.44 (pred(NSX2!29) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[421])).
% 5.44/5.44 tff(423,plain,
% 5.44/5.44 (pred(NSX2!29) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[422, 25])).
% 5.44/5.44 tff(424,plain,
% 5.44/5.44 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n2, n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[423, 400])).
% 5.44/5.44 tff(425,plain,
% 5.44/5.44 (Y3!54 = sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(426,plain,
% 5.44/5.44 (Y3!54 = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[425, 424, 327])).
% 5.44/5.44 tff(427,plain,
% 5.44/5.44 (pred(Y3!54) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[426])).
% 5.44/5.44 tff(428,plain,
% 5.44/5.44 (pred(Y3!54) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[427, 23])).
% 5.44/5.44 tff(429,plain,
% 5.44/5.44 (sum(pred(Y3!54), succ(X3!55)) = sum(n0, n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[428, 326])).
% 5.44/5.44 tff(430,plain,
% 5.44/5.44 (sum(pred(Y3!54), succ(X3!55)) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[429, 35])).
% 5.44/5.44 tff(431,plain,
% 5.44/5.44 (succ(Y3!54) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[426])).
% 5.44/5.44 tff(432,plain,
% 5.44/5.44 (succ(Y3!54) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[431, 36])).
% 5.44/5.44 tff(433,plain,
% 5.44/5.44 (pred(X3!55) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[324])).
% 5.44/5.44 tff(434,plain,
% 5.44/5.44 (pred(X3!55) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[433, 23])).
% 5.44/5.44 tff(435,plain,
% 5.44/5.44 (sum(pred(X3!55), succ(Y3!54)) = sum(n0, n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[434, 432])).
% 5.44/5.44 tff(436,plain,
% 5.44/5.44 (sum(pred(X3!55), succ(Y3!54)) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[435, 35])).
% 5.44/5.44 tff(437,plain,
% 5.44/5.44 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n2, n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[436, 430])).
% 5.44/5.44 tff(438,plain,
% 5.44/5.44 (X4!53 = sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55)))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(439,plain,
% 5.44/5.44 (X4!53 = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[438, 437, 34])).
% 5.44/5.44 tff(440,plain,
% 5.44/5.44 (succ(X4!53) = succ(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[439])).
% 5.44/5.44 tff(441,plain,
% 5.44/5.44 (succ(X4!53) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[440, 33])).
% 5.44/5.44 tff(442,plain,
% 5.44/5.44 (sum(n0, n4) = n4),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(443,plain,
% 5.44/5.44 (pred(pred(Y3!54)) = pred(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[428])).
% 5.44/5.44 tff(444,plain,
% 5.44/5.44 (pred(pred(Y3!54)) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[443, 22])).
% 5.44/5.44 tff(445,plain,
% 5.44/5.44 (pred(pred(pred(Y3!54))) = pred(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[444])).
% 5.44/5.44 tff(446,plain,
% 5.44/5.44 (pred(pred(pred(Y3!54))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[445, 21])).
% 5.44/5.44 tff(447,plain,
% 5.44/5.44 (pred(pred(pred(pred(Y3!54)))) = pred(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[446])).
% 5.44/5.44 tff(448,plain,
% 5.44/5.44 (pred(pred(pred(pred(Y3!54)))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[447, 20])).
% 5.44/5.44 tff(449,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[448])).
% 5.44/5.44 tff(450,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(Y3!54))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[449, 19])).
% 5.44/5.44 tff(451,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[450])).
% 5.44/5.44 tff(452,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[451, 18])).
% 5.44/5.44 tff(453,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[452])).
% 5.44/5.44 tff(454,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[453, 17])).
% 5.44/5.44 tff(455,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[454])).
% 5.44/5.44 tff(456,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[455, 16])).
% 5.44/5.44 tff(457,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[456])).
% 5.44/5.44 tff(458,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[457, 15])).
% 5.44/5.44 tff(459,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[458])).
% 5.44/5.44 tff(460,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[459, 25])).
% 5.44/5.44 tff(461,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[460])).
% 5.44/5.44 tff(462,plain,
% 5.44/5.44 (NPY3!26 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(463,plain,
% 5.44/5.44 (NPY3!26 = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[462, 461, 24])).
% 5.44/5.44 tff(464,plain,
% 5.44/5.44 (succ(NPY3!26) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[463])).
% 5.44/5.44 tff(465,plain,
% 5.44/5.44 (succ(NPY3!26) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[464, 36])).
% 5.44/5.44 tff(466,plain,
% 5.44/5.44 (succ(succ(Y3!54)) = succ(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[432])).
% 5.44/5.44 tff(467,plain,
% 5.44/5.44 (succ(succ(Y3!54)) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[466, 48])).
% 5.44/5.44 tff(468,plain,
% 5.44/5.44 (succ(succ(succ(Y3!54))) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[467])).
% 5.44/5.44 tff(469,plain,
% 5.44/5.44 (succ(succ(succ(Y3!54))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[468, 14])).
% 5.44/5.44 tff(470,plain,
% 5.44/5.44 (succ(succ(succ(succ(Y3!54)))) = succ(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[469])).
% 5.44/5.44 tff(471,plain,
% 5.44/5.44 (succ(succ(succ(succ(Y3!54)))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[470, 33])).
% 5.44/5.44 tff(472,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[471])).
% 5.44/5.44 tff(473,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(Y3!54))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[472, 30])).
% 5.44/5.44 tff(474,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[473])).
% 5.44/5.44 tff(475,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[474, 39])).
% 5.44/5.44 tff(476,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[475])).
% 5.44/5.44 tff(477,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[476, 53])).
% 5.44/5.44 tff(478,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[477])).
% 5.44/5.44 tff(479,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[478, 45])).
% 5.44/5.44 tff(480,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[479])).
% 5.44/5.44 tff(481,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[480, 28])).
% 5.44/5.44 tff(482,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[481])).
% 5.44/5.44 tff(483,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[482, 42])).
% 5.44/5.44 tff(484,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[483])).
% 5.44/5.44 tff(485,plain,
% 5.44/5.44 (NSY3!24 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(486,plain,
% 5.44/5.44 (NSY3!24 = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[485, 484, 58])).
% 5.44/5.44 tff(487,plain,
% 5.44/5.44 (pred(NSY3!24) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[486])).
% 5.44/5.44 tff(488,plain,
% 5.44/5.44 (pred(NSY3!24) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[487, 23])).
% 5.44/5.44 tff(489,plain,
% 5.44/5.44 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n0, n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[488, 465])).
% 5.44/5.44 tff(490,plain,
% 5.44/5.44 (sum(pred(NSY3!24), succ(NPY3!26)) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[489, 35])).
% 5.44/5.44 tff(491,plain,
% 5.44/5.44 (pred(pred(X3!55)) = pred(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[434])).
% 5.44/5.44 tff(492,plain,
% 5.44/5.44 (pred(pred(X3!55)) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[491, 22])).
% 5.44/5.44 tff(493,plain,
% 5.44/5.44 (pred(pred(pred(X3!55))) = pred(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[492])).
% 5.44/5.44 tff(494,plain,
% 5.44/5.44 (pred(pred(pred(X3!55))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[493, 21])).
% 5.44/5.44 tff(495,plain,
% 5.44/5.44 (pred(pred(pred(pred(X3!55)))) = pred(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[494])).
% 5.44/5.44 tff(496,plain,
% 5.44/5.44 (pred(pred(pred(pred(X3!55)))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[495, 20])).
% 5.44/5.44 tff(497,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(X3!55))))) = pred(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[496])).
% 5.44/5.44 tff(498,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(X3!55))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[497, 19])).
% 5.44/5.44 tff(499,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[498])).
% 5.44/5.44 tff(500,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[499, 18])).
% 5.44/5.44 tff(501,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[500])).
% 5.44/5.44 tff(502,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[501, 17])).
% 5.44/5.44 tff(503,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[502])).
% 5.44/5.44 tff(504,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[503, 16])).
% 5.44/5.44 tff(505,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[504])).
% 5.44/5.44 tff(506,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[505, 15])).
% 5.44/5.44 tff(507,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[506])).
% 5.44/5.44 tff(508,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[507, 25])).
% 5.44/5.44 tff(509,plain,
% 5.44/5.44 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[508])).
% 5.44/5.44 tff(510,plain,
% 5.44/5.44 (NPX3!27 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(511,plain,
% 5.44/5.44 (NPX3!27 = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[510, 509, 24])).
% 5.44/5.44 tff(512,plain,
% 5.44/5.44 (succ(NPX3!27) = succ(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[511])).
% 5.44/5.44 tff(513,plain,
% 5.44/5.44 (succ(NPX3!27) = n2),
% 5.44/5.44 inference(transitivity,[status(thm)],[512, 36])).
% 5.44/5.44 tff(514,plain,
% 5.44/5.44 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n2, n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[513, 490])).
% 5.44/5.44 tff(515,plain,
% 5.44/5.44 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[514, 34])).
% 5.44/5.44 tff(516,plain,
% 5.44/5.44 (succ(succ(X3!55)) = succ(n2)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[326])).
% 5.44/5.44 tff(517,plain,
% 5.44/5.44 (succ(succ(X3!55)) = n3),
% 5.44/5.44 inference(transitivity,[status(thm)],[516, 48])).
% 5.44/5.44 tff(518,plain,
% 5.44/5.44 (succ(succ(succ(X3!55))) = succ(n3)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[517])).
% 5.44/5.44 tff(519,plain,
% 5.44/5.44 (succ(succ(succ(X3!55))) = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[518, 14])).
% 5.44/5.44 tff(520,plain,
% 5.44/5.44 (succ(succ(succ(succ(X3!55)))) = succ(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[519])).
% 5.44/5.44 tff(521,plain,
% 5.44/5.44 (succ(succ(succ(succ(X3!55)))) = n5),
% 5.44/5.44 inference(transitivity,[status(thm)],[520, 33])).
% 5.44/5.44 tff(522,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(X3!55))))) = succ(n5)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[521])).
% 5.44/5.44 tff(523,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(X3!55))))) = n6),
% 5.44/5.44 inference(transitivity,[status(thm)],[522, 30])).
% 5.44/5.44 tff(524,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n6)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[523])).
% 5.44/5.44 tff(525,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n7),
% 5.44/5.44 inference(transitivity,[status(thm)],[524, 39])).
% 5.44/5.44 tff(526,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n7)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[525])).
% 5.44/5.44 tff(527,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n8),
% 5.44/5.44 inference(transitivity,[status(thm)],[526, 53])).
% 5.44/5.44 tff(528,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n8)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[527])).
% 5.44/5.44 tff(529,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n9),
% 5.44/5.44 inference(transitivity,[status(thm)],[528, 45])).
% 5.44/5.44 tff(530,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n9)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[529])).
% 5.44/5.44 tff(531,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n10),
% 5.44/5.44 inference(transitivity,[status(thm)],[530, 28])).
% 5.44/5.44 tff(532,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n10)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[531])).
% 5.44/5.44 tff(533,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[532, 42])).
% 5.44/5.44 tff(534,plain,
% 5.44/5.44 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n0)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[533])).
% 5.44/5.44 tff(535,plain,
% 5.44/5.44 (NSX3!25 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(536,plain,
% 5.44/5.44 (NSX3!25 = n1),
% 5.44/5.44 inference(transitivity,[status(thm)],[535, 534, 58])).
% 5.44/5.44 tff(537,plain,
% 5.44/5.44 (pred(NSX3!25) = pred(n1)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[536])).
% 5.44/5.44 tff(538,plain,
% 5.44/5.44 (pred(NSX3!25) = n0),
% 5.44/5.44 inference(transitivity,[status(thm)],[537, 23])).
% 5.44/5.44 tff(539,plain,
% 5.44/5.44 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n0, n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[538, 515])).
% 5.44/5.44 tff(540,plain,
% 5.44/5.44 (Y4!52 = sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))))),
% 5.44/5.44 inference(and_elim,[status(thm)],[9])).
% 5.44/5.44 tff(541,plain,
% 5.44/5.44 (Y4!52 = n4),
% 5.44/5.44 inference(transitivity,[status(thm)],[540, 539, 442])).
% 5.44/5.44 tff(542,plain,
% 5.44/5.44 (pred(Y4!52) = pred(n4)),
% 5.44/5.44 inference(monotonicity,[status(thm)],[541])).
% 5.44/5.45 tff(543,plain,
% 5.44/5.45 (pred(Y4!52) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[542, 15])).
% 5.44/5.45 tff(544,plain,
% 5.44/5.45 (sum(pred(Y4!52), succ(X4!53)) = sum(n3, n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[543, 441])).
% 5.44/5.45 tff(545,plain,
% 5.44/5.45 (sum(pred(Y4!52), succ(X4!53)) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[544, 32])).
% 5.44/5.45 tff(546,plain,
% 5.44/5.45 (succ(Y4!52) = succ(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[541])).
% 5.44/5.45 tff(547,plain,
% 5.44/5.45 (succ(Y4!52) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[546, 33])).
% 5.44/5.45 tff(548,plain,
% 5.44/5.45 (pred(X4!53) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[439])).
% 5.44/5.45 tff(549,plain,
% 5.44/5.45 (pred(X4!53) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[548, 15])).
% 5.44/5.45 tff(550,plain,
% 5.44/5.45 (sum(pred(X4!53), succ(Y4!52)) = sum(n3, n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[549, 547])).
% 5.44/5.45 tff(551,plain,
% 5.44/5.45 (sum(pred(X4!53), succ(Y4!52)) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[550, 32])).
% 5.44/5.45 tff(552,plain,
% 5.44/5.45 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n8, n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[551, 545])).
% 5.44/5.45 tff(553,plain,
% 5.44/5.45 (X5!51 = sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53)))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(554,plain,
% 5.44/5.45 (X5!51 = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[553, 552, 31])).
% 5.44/5.45 tff(555,plain,
% 5.44/5.45 (succ(X5!51) = succ(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[554])).
% 5.44/5.45 tff(556,plain,
% 5.44/5.45 (succ(X5!51) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[555, 30])).
% 5.44/5.45 tff(557,plain,
% 5.44/5.45 (sum(n3, n2) = n5),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(558,plain,
% 5.44/5.45 (sum(n5, n8) = n2),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(559,plain,
% 5.44/5.45 (pred(pred(Y4!52)) = pred(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[543])).
% 5.44/5.45 tff(560,plain,
% 5.44/5.45 (pred(pred(Y4!52)) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[559, 25])).
% 5.44/5.45 tff(561,plain,
% 5.44/5.45 (pred(pred(pred(Y4!52))) = pred(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[560])).
% 5.44/5.45 tff(562,plain,
% 5.44/5.45 (pred(pred(pred(Y4!52))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[561, 24])).
% 5.44/5.45 tff(563,plain,
% 5.44/5.45 (pred(pred(pred(pred(Y4!52)))) = pred(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[562])).
% 5.44/5.45 tff(564,plain,
% 5.44/5.45 (pred(pred(pred(pred(Y4!52)))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[563, 23])).
% 5.44/5.45 tff(565,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[564])).
% 5.44/5.45 tff(566,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(Y4!52))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[565, 22])).
% 5.44/5.45 tff(567,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[566])).
% 5.44/5.45 tff(568,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[567, 21])).
% 5.44/5.45 tff(569,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[568])).
% 5.44/5.45 tff(570,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[569, 20])).
% 5.44/5.45 tff(571,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[570])).
% 5.44/5.45 tff(572,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[571, 19])).
% 5.44/5.45 tff(573,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[572])).
% 5.44/5.45 tff(574,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[573, 18])).
% 5.44/5.45 tff(575,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[574])).
% 5.44/5.45 tff(576,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[575, 17])).
% 5.44/5.45 tff(577,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[576])).
% 5.44/5.45 tff(578,plain,
% 5.44/5.45 (NPY4!22 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(579,plain,
% 5.44/5.45 (NPY4!22 = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[578, 577, 16])).
% 5.44/5.45 tff(580,plain,
% 5.44/5.45 (succ(NPY4!22) = succ(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[579])).
% 5.44/5.45 tff(581,plain,
% 5.44/5.45 (succ(NPY4!22) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[580, 33])).
% 5.44/5.45 tff(582,plain,
% 5.44/5.45 (succ(succ(Y4!52)) = succ(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[547])).
% 5.44/5.45 tff(583,plain,
% 5.44/5.45 (succ(succ(Y4!52)) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[582, 30])).
% 5.44/5.45 tff(584,plain,
% 5.44/5.45 (succ(succ(succ(Y4!52))) = succ(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[583])).
% 5.44/5.45 tff(585,plain,
% 5.44/5.45 (succ(succ(succ(Y4!52))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[584, 39])).
% 5.44/5.45 tff(586,plain,
% 5.44/5.45 (succ(succ(succ(succ(Y4!52)))) = succ(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[585])).
% 5.44/5.45 tff(587,plain,
% 5.44/5.45 (succ(succ(succ(succ(Y4!52)))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[586, 53])).
% 5.44/5.45 tff(588,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[587])).
% 5.44/5.45 tff(589,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(Y4!52))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[588, 45])).
% 5.44/5.45 tff(590,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[589])).
% 5.44/5.45 tff(591,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[590, 28])).
% 5.44/5.45 tff(592,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[591])).
% 5.44/5.45 tff(593,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[592, 42])).
% 5.44/5.45 tff(594,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[593])).
% 5.44/5.45 tff(595,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[594, 58])).
% 5.44/5.45 tff(596,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[595])).
% 5.44/5.45 tff(597,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[596, 36])).
% 5.44/5.45 tff(598,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[597])).
% 5.44/5.45 tff(599,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[598, 48])).
% 5.44/5.45 tff(600,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[599])).
% 5.44/5.45 tff(601,plain,
% 5.44/5.45 (NSY4!20 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(602,plain,
% 5.44/5.45 (NSY4!20 = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[601, 600, 14])).
% 5.44/5.45 tff(603,plain,
% 5.44/5.45 (pred(NSY4!20) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[602])).
% 5.44/5.45 tff(604,plain,
% 5.44/5.45 (pred(NSY4!20) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[603, 15])).
% 5.44/5.45 tff(605,plain,
% 5.44/5.45 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n3, n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[604, 581])).
% 5.44/5.45 tff(606,plain,
% 5.44/5.45 (sum(pred(NSY4!20), succ(NPY4!22)) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[605, 32])).
% 5.44/5.45 tff(607,plain,
% 5.44/5.45 (pred(pred(X4!53)) = pred(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[549])).
% 5.44/5.45 tff(608,plain,
% 5.44/5.45 (pred(pred(X4!53)) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[607, 25])).
% 5.44/5.45 tff(609,plain,
% 5.44/5.45 (pred(pred(pred(X4!53))) = pred(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[608])).
% 5.44/5.45 tff(610,plain,
% 5.44/5.45 (pred(pred(pred(X4!53))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[609, 24])).
% 5.44/5.45 tff(611,plain,
% 5.44/5.45 (pred(pred(pred(pred(X4!53)))) = pred(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[610])).
% 5.44/5.45 tff(612,plain,
% 5.44/5.45 (pred(pred(pred(pred(X4!53)))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[611, 23])).
% 5.44/5.45 tff(613,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(X4!53))))) = pred(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[612])).
% 5.44/5.45 tff(614,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(X4!53))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[613, 22])).
% 5.44/5.45 tff(615,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[614])).
% 5.44/5.45 tff(616,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[615, 21])).
% 5.44/5.45 tff(617,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[616])).
% 5.44/5.45 tff(618,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[617, 20])).
% 5.44/5.45 tff(619,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[618])).
% 5.44/5.45 tff(620,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[619, 19])).
% 5.44/5.45 tff(621,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[620])).
% 5.44/5.45 tff(622,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[621, 18])).
% 5.44/5.45 tff(623,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[622])).
% 5.44/5.45 tff(624,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[623, 17])).
% 5.44/5.45 tff(625,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[624])).
% 5.44/5.45 tff(626,plain,
% 5.44/5.45 (NPX4!23 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(627,plain,
% 5.44/5.45 (NPX4!23 = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[626, 625, 16])).
% 5.44/5.45 tff(628,plain,
% 5.44/5.45 (succ(NPX4!23) = succ(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[627])).
% 5.44/5.45 tff(629,plain,
% 5.44/5.45 (succ(NPX4!23) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[628, 33])).
% 5.44/5.45 tff(630,plain,
% 5.44/5.45 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n5, n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[629, 606])).
% 5.44/5.45 tff(631,plain,
% 5.44/5.45 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[630, 558])).
% 5.44/5.45 tff(632,plain,
% 5.44/5.45 (succ(succ(X4!53)) = succ(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[441])).
% 5.44/5.45 tff(633,plain,
% 5.44/5.45 (succ(succ(X4!53)) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[632, 30])).
% 5.44/5.45 tff(634,plain,
% 5.44/5.45 (succ(succ(succ(X4!53))) = succ(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[633])).
% 5.44/5.45 tff(635,plain,
% 5.44/5.45 (succ(succ(succ(X4!53))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[634, 39])).
% 5.44/5.45 tff(636,plain,
% 5.44/5.45 (succ(succ(succ(succ(X4!53)))) = succ(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[635])).
% 5.44/5.45 tff(637,plain,
% 5.44/5.45 (succ(succ(succ(succ(X4!53)))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[636, 53])).
% 5.44/5.45 tff(638,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(X4!53))))) = succ(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[637])).
% 5.44/5.45 tff(639,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(X4!53))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[638, 45])).
% 5.44/5.45 tff(640,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[639])).
% 5.44/5.45 tff(641,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[640, 28])).
% 5.44/5.45 tff(642,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[641])).
% 5.44/5.45 tff(643,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[642, 42])).
% 5.44/5.45 tff(644,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[643])).
% 5.44/5.45 tff(645,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[644, 58])).
% 5.44/5.45 tff(646,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[645])).
% 5.44/5.45 tff(647,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[646, 36])).
% 5.44/5.45 tff(648,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[647])).
% 5.44/5.45 tff(649,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[648, 48])).
% 5.44/5.45 tff(650,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[649])).
% 5.44/5.45 tff(651,plain,
% 5.44/5.45 (NSX4!21 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(652,plain,
% 5.44/5.45 (NSX4!21 = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[651, 650, 14])).
% 5.44/5.45 tff(653,plain,
% 5.44/5.45 (pred(NSX4!21) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[652])).
% 5.44/5.45 tff(654,plain,
% 5.44/5.45 (pred(NSX4!21) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[653, 15])).
% 5.44/5.45 tff(655,plain,
% 5.44/5.45 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n3, n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[654, 631])).
% 5.44/5.45 tff(656,plain,
% 5.44/5.45 (Y5!50 = sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(657,plain,
% 5.44/5.45 (Y5!50 = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[656, 655, 557])).
% 5.44/5.45 tff(658,plain,
% 5.44/5.45 (pred(Y5!50) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[657])).
% 5.44/5.45 tff(659,plain,
% 5.44/5.45 (pred(Y5!50) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[658, 16])).
% 5.44/5.45 tff(660,plain,
% 5.44/5.45 (sum(pred(Y5!50), succ(X5!51)) = sum(n4, n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[659, 556])).
% 5.44/5.45 tff(661,plain,
% 5.44/5.45 (sum(pred(Y5!50), succ(X5!51)) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[660, 12])).
% 5.44/5.45 tff(662,plain,
% 5.44/5.45 (succ(Y5!50) = succ(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[657])).
% 5.44/5.45 tff(663,plain,
% 5.44/5.45 (succ(Y5!50) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[662, 30])).
% 5.44/5.45 tff(664,plain,
% 5.44/5.45 (pred(X5!51) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[554])).
% 5.44/5.45 tff(665,plain,
% 5.44/5.45 (pred(X5!51) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[664, 16])).
% 5.44/5.45 tff(666,plain,
% 5.44/5.45 (sum(pred(X5!51), succ(Y5!50)) = sum(n4, n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[665, 663])).
% 5.44/5.45 tff(667,plain,
% 5.44/5.45 (sum(pred(X5!51), succ(Y5!50)) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[666, 12])).
% 5.44/5.45 tff(668,plain,
% 5.44/5.45 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n10, n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[667, 661])).
% 5.44/5.45 tff(669,plain,
% 5.44/5.45 (X6!49 = sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51)))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(670,plain,
% 5.44/5.45 (X6!49 = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[669, 668, 29])).
% 5.44/5.45 tff(671,plain,
% 5.44/5.45 (succ(X6!49) = succ(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[670])).
% 5.44/5.45 tff(672,plain,
% 5.44/5.45 (succ(X6!49) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[671, 28])).
% 5.44/5.45 tff(673,plain,
% 5.44/5.45 (sum(n4, n5) = n9),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(674,plain,
% 5.44/5.45 (sum(n6, n10) = n5),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(675,plain,
% 5.44/5.45 (pred(pred(Y5!50)) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[659])).
% 5.44/5.45 tff(676,plain,
% 5.44/5.45 (pred(pred(Y5!50)) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[675, 15])).
% 5.44/5.45 tff(677,plain,
% 5.44/5.45 (pred(pred(pred(Y5!50))) = pred(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[676])).
% 5.44/5.45 tff(678,plain,
% 5.44/5.45 (pred(pred(pred(Y5!50))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[677, 25])).
% 5.44/5.45 tff(679,plain,
% 5.44/5.45 (pred(pred(pred(pred(Y5!50)))) = pred(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[678])).
% 5.44/5.45 tff(680,plain,
% 5.44/5.45 (pred(pred(pred(pred(Y5!50)))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[679, 24])).
% 5.44/5.45 tff(681,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[680])).
% 5.44/5.45 tff(682,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(Y5!50))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[681, 23])).
% 5.44/5.45 tff(683,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[682])).
% 5.44/5.45 tff(684,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[683, 22])).
% 5.44/5.45 tff(685,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[684])).
% 5.44/5.45 tff(686,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[685, 21])).
% 5.44/5.45 tff(687,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[686])).
% 5.44/5.45 tff(688,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[687, 20])).
% 5.44/5.45 tff(689,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[688])).
% 5.44/5.45 tff(690,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[689, 19])).
% 5.44/5.45 tff(691,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[690])).
% 5.44/5.45 tff(692,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[691, 18])).
% 5.44/5.45 tff(693,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[692])).
% 5.44/5.45 tff(694,plain,
% 5.44/5.45 (NPY5!18 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(695,plain,
% 5.44/5.45 (NPY5!18 = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[694, 693, 17])).
% 5.44/5.45 tff(696,plain,
% 5.44/5.45 (succ(NPY5!18) = succ(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[695])).
% 5.44/5.45 tff(697,plain,
% 5.44/5.45 (succ(NPY5!18) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[696, 30])).
% 5.44/5.45 tff(698,plain,
% 5.44/5.45 (succ(succ(Y5!50)) = succ(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[663])).
% 5.44/5.45 tff(699,plain,
% 5.44/5.45 (succ(succ(Y5!50)) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[698, 39])).
% 5.44/5.45 tff(700,plain,
% 5.44/5.45 (succ(succ(succ(Y5!50))) = succ(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[699])).
% 5.44/5.45 tff(701,plain,
% 5.44/5.45 (succ(succ(succ(Y5!50))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[700, 53])).
% 5.44/5.45 tff(702,plain,
% 5.44/5.45 (succ(succ(succ(succ(Y5!50)))) = succ(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[701])).
% 5.44/5.45 tff(703,plain,
% 5.44/5.45 (succ(succ(succ(succ(Y5!50)))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[702, 45])).
% 5.44/5.45 tff(704,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[703])).
% 5.44/5.45 tff(705,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(Y5!50))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[704, 28])).
% 5.44/5.45 tff(706,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[705])).
% 5.44/5.45 tff(707,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[706, 42])).
% 5.44/5.45 tff(708,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[707])).
% 5.44/5.45 tff(709,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[708, 58])).
% 5.44/5.45 tff(710,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[709])).
% 5.44/5.45 tff(711,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[710, 36])).
% 5.44/5.45 tff(712,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[711])).
% 5.44/5.45 tff(713,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[712, 48])).
% 5.44/5.45 tff(714,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[713])).
% 5.44/5.45 tff(715,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[714, 14])).
% 5.44/5.45 tff(716,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[715])).
% 5.44/5.45 tff(717,plain,
% 5.44/5.45 (NSY5!16 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(718,plain,
% 5.44/5.45 (NSY5!16 = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[717, 716, 33])).
% 5.44/5.45 tff(719,plain,
% 5.44/5.45 (pred(NSY5!16) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[718])).
% 5.44/5.45 tff(720,plain,
% 5.44/5.45 (pred(NSY5!16) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[719, 16])).
% 5.44/5.45 tff(721,plain,
% 5.44/5.45 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n4, n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[720, 697])).
% 5.44/5.45 tff(722,plain,
% 5.44/5.45 (sum(pred(NSY5!16), succ(NPY5!18)) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[721, 12])).
% 5.44/5.45 tff(723,plain,
% 5.44/5.45 (pred(pred(X5!51)) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[665])).
% 5.44/5.45 tff(724,plain,
% 5.44/5.45 (pred(pred(X5!51)) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[723, 15])).
% 5.44/5.45 tff(725,plain,
% 5.44/5.45 (pred(pred(pred(X5!51))) = pred(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[724])).
% 5.44/5.45 tff(726,plain,
% 5.44/5.45 (pred(pred(pred(X5!51))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[725, 25])).
% 5.44/5.45 tff(727,plain,
% 5.44/5.45 (pred(pred(pred(pred(X5!51)))) = pred(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[726])).
% 5.44/5.45 tff(728,plain,
% 5.44/5.45 (pred(pred(pred(pred(X5!51)))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[727, 24])).
% 5.44/5.45 tff(729,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(X5!51))))) = pred(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[728])).
% 5.44/5.45 tff(730,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(X5!51))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[729, 23])).
% 5.44/5.45 tff(731,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[730])).
% 5.44/5.45 tff(732,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[731, 22])).
% 5.44/5.45 tff(733,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[732])).
% 5.44/5.45 tff(734,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[733, 21])).
% 5.44/5.45 tff(735,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[734])).
% 5.44/5.45 tff(736,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[735, 20])).
% 5.44/5.45 tff(737,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[736])).
% 5.44/5.45 tff(738,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[737, 19])).
% 5.44/5.45 tff(739,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[738])).
% 5.44/5.45 tff(740,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[739, 18])).
% 5.44/5.45 tff(741,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[740])).
% 5.44/5.45 tff(742,plain,
% 5.44/5.45 (NPX5!19 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(743,plain,
% 5.44/5.45 (NPX5!19 = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[742, 741, 17])).
% 5.44/5.45 tff(744,plain,
% 5.44/5.45 (succ(NPX5!19) = succ(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[743])).
% 5.44/5.45 tff(745,plain,
% 5.44/5.45 (succ(NPX5!19) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[744, 30])).
% 5.44/5.45 tff(746,plain,
% 5.44/5.45 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n6, n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[745, 722])).
% 5.44/5.45 tff(747,plain,
% 5.44/5.45 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[746, 674])).
% 5.44/5.45 tff(748,plain,
% 5.44/5.45 (succ(succ(X5!51)) = succ(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[556])).
% 5.44/5.45 tff(749,plain,
% 5.44/5.45 (succ(succ(X5!51)) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[748, 39])).
% 5.44/5.45 tff(750,plain,
% 5.44/5.45 (succ(succ(succ(X5!51))) = succ(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[749])).
% 5.44/5.45 tff(751,plain,
% 5.44/5.45 (succ(succ(succ(X5!51))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[750, 53])).
% 5.44/5.45 tff(752,plain,
% 5.44/5.45 (succ(succ(succ(succ(X5!51)))) = succ(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[751])).
% 5.44/5.45 tff(753,plain,
% 5.44/5.45 (succ(succ(succ(succ(X5!51)))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[752, 45])).
% 5.44/5.45 tff(754,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(X5!51))))) = succ(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[753])).
% 5.44/5.45 tff(755,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(X5!51))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[754, 28])).
% 5.44/5.45 tff(756,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[755])).
% 5.44/5.45 tff(757,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[756, 42])).
% 5.44/5.45 tff(758,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[757])).
% 5.44/5.45 tff(759,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[758, 58])).
% 5.44/5.45 tff(760,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[759])).
% 5.44/5.45 tff(761,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[760, 36])).
% 5.44/5.45 tff(762,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[761])).
% 5.44/5.45 tff(763,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[762, 48])).
% 5.44/5.45 tff(764,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[763])).
% 5.44/5.45 tff(765,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[764, 14])).
% 5.44/5.45 tff(766,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[765])).
% 5.44/5.45 tff(767,plain,
% 5.44/5.45 (NSX5!17 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(768,plain,
% 5.44/5.45 (NSX5!17 = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[767, 766, 33])).
% 5.44/5.45 tff(769,plain,
% 5.44/5.45 (pred(NSX5!17) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[768])).
% 5.44/5.45 tff(770,plain,
% 5.44/5.45 (pred(NSX5!17) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[769, 16])).
% 5.44/5.45 tff(771,plain,
% 5.44/5.45 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n4, n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[770, 747])).
% 5.44/5.45 tff(772,plain,
% 5.44/5.45 (Y6!48 = sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(773,plain,
% 5.44/5.45 (Y6!48 = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[772, 771, 673])).
% 5.44/5.45 tff(774,plain,
% 5.44/5.45 (pred(Y6!48) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[773])).
% 5.44/5.45 tff(775,plain,
% 5.44/5.45 (pred(Y6!48) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[774, 20])).
% 5.44/5.45 tff(776,plain,
% 5.44/5.45 (sum(pred(Y6!48), succ(X6!49)) = sum(n8, n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[775, 672])).
% 5.44/5.45 tff(777,plain,
% 5.44/5.45 (sum(pred(Y6!48), succ(X6!49)) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[776, 27])).
% 5.44/5.45 tff(778,plain,
% 5.44/5.45 (succ(Y6!48) = succ(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[773])).
% 5.44/5.45 tff(779,plain,
% 5.44/5.45 (succ(Y6!48) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[778, 28])).
% 5.44/5.45 tff(780,plain,
% 5.44/5.45 (pred(X6!49) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[670])).
% 5.44/5.45 tff(781,plain,
% 5.44/5.45 (pred(X6!49) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[780, 20])).
% 5.44/5.45 tff(782,plain,
% 5.44/5.45 (sum(pred(X6!49), succ(Y6!48)) = sum(n8, n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[781, 779])).
% 5.44/5.45 tff(783,plain,
% 5.44/5.45 (sum(pred(X6!49), succ(Y6!48)) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[782, 27])).
% 5.44/5.45 tff(784,plain,
% 5.44/5.45 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n7, n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[783, 777])).
% 5.44/5.45 tff(785,plain,
% 5.44/5.45 (X7!47 = sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49)))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(786,plain,
% 5.44/5.45 (sum(n3, n4) = n7),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(787,plain,
% 5.44/5.45 (sum(n7, n1) = n8),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(788,plain,
% 5.44/5.45 (sum(n6, n0) = n6),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(789,plain,
% 5.44/5.45 (sum(n7, n3) = n10),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(790,plain,
% 5.44/5.45 (sum(n9, n5) = n3),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(791,plain,
% 5.44/5.45 (sum(n1, n7) = n8),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(792,assumption,(~(X7!47 = Y7!46)), introduced(assumption)).
% 5.44/5.45 tff(793,plain,
% 5.44/5.45 (Y7!46 = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(794,plain,
% 5.44/5.45 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = Y7!46),
% 5.44/5.45 inference(symmetry,[status(thm)],[793])).
% 5.44/5.45 tff(795,plain,
% 5.44/5.45 (sum(n7, n6) = n2),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(796,plain,
% 5.44/5.45 (sum(n9, n8) = n6),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(797,assumption,(Y0!60 = n4), introduced(assumption)).
% 5.44/5.45 tff(798,plain,
% 5.44/5.45 (pred(Y0!60) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[797])).
% 5.44/5.45 tff(799,plain,
% 5.44/5.45 (pred(Y0!60) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[798, 15])).
% 5.44/5.45 tff(800,plain,
% 5.44/5.45 (pred(pred(Y0!60)) = pred(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[799])).
% 5.44/5.45 tff(801,plain,
% 5.44/5.45 (pred(pred(Y0!60)) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[800, 25])).
% 5.44/5.45 tff(802,plain,
% 5.44/5.45 (pred(pred(pred(Y0!60))) = pred(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[801])).
% 5.44/5.45 tff(803,plain,
% 5.44/5.45 (pred(pred(pred(Y0!60))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[802, 24])).
% 5.44/5.45 tff(804,plain,
% 5.44/5.45 (pred(pred(pred(pred(Y0!60)))) = pred(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[803])).
% 5.44/5.45 tff(805,plain,
% 5.44/5.45 (pred(pred(pred(pred(Y0!60)))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[804, 23])).
% 5.44/5.45 tff(806,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[805])).
% 5.44/5.45 tff(807,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(Y0!60))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[806, 22])).
% 5.44/5.45 tff(808,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[807])).
% 5.44/5.45 tff(809,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[808, 21])).
% 5.44/5.45 tff(810,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[809])).
% 5.44/5.45 tff(811,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[810, 20])).
% 5.44/5.45 tff(812,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[811])).
% 5.44/5.45 tff(813,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[812, 19])).
% 5.44/5.45 tff(814,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[813])).
% 5.44/5.45 tff(815,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[814, 18])).
% 5.44/5.45 tff(816,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[815])).
% 5.44/5.45 tff(817,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[816, 17])).
% 5.44/5.45 tff(818,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[817])).
% 5.44/5.45 tff(819,plain,
% 5.44/5.45 (NPY0!38 = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[118, 818, 16])).
% 5.44/5.45 tff(820,plain,
% 5.44/5.45 (succ(NPY0!38) = succ(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[819])).
% 5.44/5.45 tff(821,plain,
% 5.44/5.45 (succ(NPY0!38) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[820, 33])).
% 5.44/5.45 tff(822,plain,
% 5.44/5.45 (succ(Y0!60) = succ(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[797])).
% 5.44/5.45 tff(823,plain,
% 5.44/5.45 (succ(Y0!60) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[822, 33])).
% 5.44/5.45 tff(824,plain,
% 5.44/5.45 (succ(succ(Y0!60)) = succ(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[823])).
% 5.44/5.45 tff(825,plain,
% 5.44/5.45 (succ(succ(Y0!60)) = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[824, 30])).
% 5.44/5.45 tff(826,plain,
% 5.44/5.45 (succ(succ(succ(Y0!60))) = succ(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[825])).
% 5.44/5.45 tff(827,plain,
% 5.44/5.45 (succ(succ(succ(Y0!60))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[826, 39])).
% 5.44/5.45 tff(828,plain,
% 5.44/5.45 (succ(succ(succ(succ(Y0!60)))) = succ(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[827])).
% 5.44/5.45 tff(829,plain,
% 5.44/5.45 (succ(succ(succ(succ(Y0!60)))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[828, 53])).
% 5.44/5.45 tff(830,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[829])).
% 5.44/5.45 tff(831,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(Y0!60))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[830, 45])).
% 5.44/5.45 tff(832,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[831])).
% 5.44/5.45 tff(833,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[832, 28])).
% 5.44/5.45 tff(834,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[833])).
% 5.44/5.45 tff(835,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[834, 42])).
% 5.44/5.45 tff(836,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[835])).
% 5.44/5.45 tff(837,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[836, 58])).
% 5.44/5.45 tff(838,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[837])).
% 5.44/5.45 tff(839,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[838, 36])).
% 5.44/5.45 tff(840,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[839])).
% 5.44/5.45 tff(841,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[840, 48])).
% 5.44/5.45 tff(842,plain,
% 5.44/5.45 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[841])).
% 5.44/5.45 tff(843,plain,
% 5.44/5.45 (NSY0!36 = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[141, 842, 14])).
% 5.44/5.45 tff(844,plain,
% 5.44/5.45 (pred(NSY0!36) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[843])).
% 5.44/5.45 tff(845,plain,
% 5.44/5.45 (pred(NSY0!36) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[844, 15])).
% 5.44/5.45 tff(846,plain,
% 5.44/5.45 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n3, n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[845, 821])).
% 5.44/5.45 tff(847,plain,
% 5.44/5.45 (sum(pred(NSY0!36), succ(NPY0!38)) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[846, 32])).
% 5.44/5.45 tff(848,plain,
% 5.44/5.45 (sum(n5, n4) = n9),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(849,plain,
% 5.44/5.45 (sum(n7, n8) = n4),
% 5.44/5.45 inference(and_elim,[status(thm)],[9])).
% 5.44/5.45 tff(850,assumption,(X0!61 = n6), introduced(assumption)).
% 5.44/5.45 tff(851,plain,
% 5.44/5.45 (pred(X0!61) = pred(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[850])).
% 5.44/5.45 tff(852,plain,
% 5.44/5.45 (pred(X0!61) = n5),
% 5.44/5.45 inference(transitivity,[status(thm)],[851, 17])).
% 5.44/5.45 tff(853,plain,
% 5.44/5.45 (pred(pred(X0!61)) = pred(n5)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[852])).
% 5.44/5.45 tff(854,plain,
% 5.44/5.45 (pred(pred(X0!61)) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[853, 16])).
% 5.44/5.45 tff(855,plain,
% 5.44/5.45 (pred(pred(pred(X0!61))) = pred(n4)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[854])).
% 5.44/5.45 tff(856,plain,
% 5.44/5.45 (pred(pred(pred(X0!61))) = n3),
% 5.44/5.45 inference(transitivity,[status(thm)],[855, 15])).
% 5.44/5.45 tff(857,plain,
% 5.44/5.45 (pred(pred(pred(pred(X0!61)))) = pred(n3)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[856])).
% 5.44/5.45 tff(858,plain,
% 5.44/5.45 (pred(pred(pred(pred(X0!61)))) = n2),
% 5.44/5.45 inference(transitivity,[status(thm)],[857, 25])).
% 5.44/5.45 tff(859,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(X0!61))))) = pred(n2)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[858])).
% 5.44/5.45 tff(860,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(X0!61))))) = n1),
% 5.44/5.45 inference(transitivity,[status(thm)],[859, 24])).
% 5.44/5.45 tff(861,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n1)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[860])).
% 5.44/5.45 tff(862,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n0),
% 5.44/5.45 inference(transitivity,[status(thm)],[861, 23])).
% 5.44/5.45 tff(863,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n0)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[862])).
% 5.44/5.45 tff(864,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n10),
% 5.44/5.45 inference(transitivity,[status(thm)],[863, 22])).
% 5.44/5.45 tff(865,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n10)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[864])).
% 5.44/5.45 tff(866,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n9),
% 5.44/5.45 inference(transitivity,[status(thm)],[865, 21])).
% 5.44/5.45 tff(867,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n9)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[866])).
% 5.44/5.45 tff(868,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n8),
% 5.44/5.45 inference(transitivity,[status(thm)],[867, 20])).
% 5.44/5.45 tff(869,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[868])).
% 5.44/5.45 tff(870,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[869, 19])).
% 5.44/5.45 tff(871,plain,
% 5.44/5.45 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[870])).
% 5.44/5.45 tff(872,plain,
% 5.44/5.45 (NPX0!39 = n6),
% 5.44/5.45 inference(transitivity,[status(thm)],[166, 871, 18])).
% 5.44/5.45 tff(873,plain,
% 5.44/5.45 (succ(NPX0!39) = succ(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[872])).
% 5.44/5.45 tff(874,plain,
% 5.44/5.45 (succ(NPX0!39) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[873, 39])).
% 5.44/5.45 tff(875,plain,
% 5.44/5.45 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n7, n8)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[874, 847])).
% 5.44/5.45 tff(876,plain,
% 5.44/5.45 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n4),
% 5.44/5.45 inference(transitivity,[status(thm)],[875, 849])).
% 5.44/5.45 tff(877,plain,
% 5.44/5.45 (succ(X0!61) = succ(n6)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[850])).
% 5.44/5.45 tff(878,plain,
% 5.44/5.45 (succ(X0!61) = n7),
% 5.44/5.45 inference(transitivity,[status(thm)],[877, 39])).
% 5.44/5.45 tff(879,plain,
% 5.44/5.45 (succ(succ(X0!61)) = succ(n7)),
% 5.44/5.45 inference(monotonicity,[status(thm)],[878])).
% 5.44/5.46 tff(880,plain,
% 5.44/5.46 (succ(succ(X0!61)) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[879, 53])).
% 5.44/5.46 tff(881,plain,
% 5.44/5.46 (succ(succ(succ(X0!61))) = succ(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[880])).
% 5.44/5.46 tff(882,plain,
% 5.44/5.46 (succ(succ(succ(X0!61))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[881, 45])).
% 5.44/5.46 tff(883,plain,
% 5.44/5.46 (succ(succ(succ(succ(X0!61)))) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[882])).
% 5.44/5.46 tff(884,plain,
% 5.44/5.46 (succ(succ(succ(succ(X0!61)))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[883, 28])).
% 5.44/5.46 tff(885,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(X0!61))))) = succ(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[884])).
% 5.44/5.46 tff(886,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(X0!61))))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[885, 42])).
% 5.44/5.46 tff(887,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[886])).
% 5.44/5.46 tff(888,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[887, 58])).
% 5.44/5.46 tff(889,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[888])).
% 5.44/5.46 tff(890,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[889, 36])).
% 5.44/5.46 tff(891,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[890])).
% 5.44/5.46 tff(892,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[891, 48])).
% 5.44/5.46 tff(893,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[892])).
% 5.44/5.46 tff(894,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[893, 14])).
% 5.44/5.46 tff(895,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[894])).
% 5.44/5.46 tff(896,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[895, 33])).
% 5.44/5.46 tff(897,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[896])).
% 5.44/5.46 tff(898,plain,
% 5.44/5.46 (NSX0!37 = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[191, 897, 30])).
% 5.44/5.46 tff(899,plain,
% 5.44/5.46 (pred(NSX0!37) = pred(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[898])).
% 5.44/5.46 tff(900,plain,
% 5.44/5.46 (pred(NSX0!37) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[899, 17])).
% 5.44/5.46 tff(901,plain,
% 5.44/5.46 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n5, n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[900, 876])).
% 5.44/5.46 tff(902,plain,
% 5.44/5.46 (Y1!58 = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[196, 901, 848])).
% 5.44/5.46 tff(903,plain,
% 5.44/5.46 (pred(Y1!58) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[902])).
% 5.44/5.46 tff(904,plain,
% 5.44/5.46 (pred(Y1!58) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[903, 20])).
% 5.44/5.46 tff(905,plain,
% 5.44/5.46 (pred(pred(Y1!58)) = pred(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[904])).
% 5.44/5.46 tff(906,plain,
% 5.44/5.46 (pred(pred(Y1!58)) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[905, 19])).
% 5.44/5.46 tff(907,plain,
% 5.44/5.46 (pred(pred(pred(Y1!58))) = pred(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[906])).
% 5.44/5.46 tff(908,plain,
% 5.44/5.46 (pred(pred(pred(Y1!58))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[907, 18])).
% 5.44/5.46 tff(909,plain,
% 5.44/5.46 (pred(pred(pred(pred(Y1!58)))) = pred(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[908])).
% 5.44/5.46 tff(910,plain,
% 5.44/5.46 (pred(pred(pred(pred(Y1!58)))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[909, 17])).
% 5.44/5.46 tff(911,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[910])).
% 5.44/5.46 tff(912,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(Y1!58))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[911, 16])).
% 5.44/5.46 tff(913,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[912])).
% 5.44/5.46 tff(914,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[913, 15])).
% 5.44/5.46 tff(915,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[914])).
% 5.44/5.46 tff(916,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[915, 25])).
% 5.44/5.46 tff(917,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[916])).
% 5.44/5.46 tff(918,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[917, 24])).
% 5.44/5.46 tff(919,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[918])).
% 5.44/5.46 tff(920,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[919, 23])).
% 5.44/5.46 tff(921,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[920])).
% 5.44/5.46 tff(922,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[921, 22])).
% 5.44/5.46 tff(923,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[922])).
% 5.44/5.46 tff(924,plain,
% 5.44/5.46 (NPY1!34 = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[232, 923, 21])).
% 5.44/5.46 tff(925,plain,
% 5.44/5.46 (succ(NPY1!34) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[924])).
% 5.44/5.46 tff(926,plain,
% 5.44/5.46 (succ(NPY1!34) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[925, 28])).
% 5.44/5.46 tff(927,plain,
% 5.44/5.46 (succ(Y1!58) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[902])).
% 5.44/5.46 tff(928,plain,
% 5.44/5.46 (succ(Y1!58) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[927, 28])).
% 5.44/5.46 tff(929,plain,
% 5.44/5.46 (succ(succ(Y1!58)) = succ(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[928])).
% 5.44/5.46 tff(930,plain,
% 5.44/5.46 (succ(succ(Y1!58)) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[929, 42])).
% 5.44/5.46 tff(931,plain,
% 5.44/5.46 (succ(succ(succ(Y1!58))) = succ(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[930])).
% 5.44/5.46 tff(932,plain,
% 5.44/5.46 (succ(succ(succ(Y1!58))) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[931, 58])).
% 5.44/5.46 tff(933,plain,
% 5.44/5.46 (succ(succ(succ(succ(Y1!58)))) = succ(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[932])).
% 5.44/5.46 tff(934,plain,
% 5.44/5.46 (succ(succ(succ(succ(Y1!58)))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[933, 36])).
% 5.44/5.46 tff(935,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[934])).
% 5.44/5.46 tff(936,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(Y1!58))))) = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[935, 48])).
% 5.44/5.46 tff(937,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[936])).
% 5.44/5.46 tff(938,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[937, 14])).
% 5.44/5.46 tff(939,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[938])).
% 5.44/5.46 tff(940,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[939, 33])).
% 5.44/5.46 tff(941,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[940])).
% 5.44/5.46 tff(942,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[941, 30])).
% 5.44/5.46 tff(943,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[942])).
% 5.44/5.46 tff(944,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[943, 39])).
% 5.44/5.46 tff(945,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[944])).
% 5.44/5.46 tff(946,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[945, 53])).
% 5.44/5.46 tff(947,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[946])).
% 5.44/5.46 tff(948,plain,
% 5.44/5.46 (NSY1!32 = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[255, 947, 45])).
% 5.44/5.46 tff(949,plain,
% 5.44/5.46 (pred(NSY1!32) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[948])).
% 5.44/5.46 tff(950,plain,
% 5.44/5.46 (pred(NSY1!32) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[949, 20])).
% 5.44/5.46 tff(951,plain,
% 5.44/5.46 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n8, n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[950, 926])).
% 5.44/5.46 tff(952,plain,
% 5.44/5.46 (sum(pred(NSY1!32), succ(NPY1!34)) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[951, 27])).
% 5.44/5.46 tff(953,plain,
% 5.44/5.46 (sum(n3, n7) = n10),
% 5.44/5.46 inference(and_elim,[status(thm)],[9])).
% 5.44/5.46 tff(954,plain,
% 5.44/5.46 (sum(pred(Y0!60), succ(X0!61)) = sum(n3, n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[799, 878])).
% 5.44/5.46 tff(955,plain,
% 5.44/5.46 (sum(pred(Y0!60), succ(X0!61)) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[954, 953])).
% 5.44/5.46 tff(956,plain,
% 5.44/5.46 (sum(pred(X0!61), succ(Y0!60)) = sum(n5, n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[852, 823])).
% 5.44/5.46 tff(957,plain,
% 5.44/5.46 (sum(pred(X0!61), succ(Y0!60)) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[956, 43])).
% 5.44/5.46 tff(958,plain,
% 5.44/5.46 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n10, n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[957, 955])).
% 5.44/5.46 tff(959,plain,
% 5.44/5.46 (X1!59 = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[93, 958, 29])).
% 5.44/5.46 tff(960,plain,
% 5.44/5.46 (pred(X1!59) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[959])).
% 5.44/5.46 tff(961,plain,
% 5.44/5.46 (pred(X1!59) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[960, 20])).
% 5.44/5.46 tff(962,plain,
% 5.44/5.46 (pred(pred(X1!59)) = pred(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[961])).
% 5.44/5.46 tff(963,plain,
% 5.44/5.46 (pred(pred(X1!59)) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[962, 19])).
% 5.44/5.46 tff(964,plain,
% 5.44/5.46 (pred(pred(pred(X1!59))) = pred(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[963])).
% 5.44/5.46 tff(965,plain,
% 5.44/5.46 (pred(pred(pred(X1!59))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[964, 18])).
% 5.44/5.46 tff(966,plain,
% 5.44/5.46 (pred(pred(pred(pred(X1!59)))) = pred(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[965])).
% 5.44/5.46 tff(967,plain,
% 5.44/5.46 (pred(pred(pred(pred(X1!59)))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[966, 17])).
% 5.44/5.46 tff(968,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(X1!59))))) = pred(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[967])).
% 5.44/5.46 tff(969,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(X1!59))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[968, 16])).
% 5.44/5.46 tff(970,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[969])).
% 5.44/5.46 tff(971,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[970, 15])).
% 5.44/5.46 tff(972,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[971])).
% 5.44/5.46 tff(973,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[972, 25])).
% 5.44/5.46 tff(974,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[973])).
% 5.44/5.46 tff(975,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[974, 24])).
% 5.44/5.46 tff(976,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[975])).
% 5.44/5.46 tff(977,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[976, 23])).
% 5.44/5.46 tff(978,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[977])).
% 5.44/5.46 tff(979,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[978, 22])).
% 5.44/5.46 tff(980,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[979])).
% 5.44/5.46 tff(981,plain,
% 5.44/5.46 (NPX1!35 = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[280, 980, 21])).
% 5.44/5.46 tff(982,plain,
% 5.44/5.46 (succ(NPX1!35) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[981])).
% 5.44/5.46 tff(983,plain,
% 5.44/5.46 (succ(NPX1!35) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[982, 28])).
% 5.44/5.46 tff(984,plain,
% 5.44/5.46 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n10, n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[983, 952])).
% 5.44/5.46 tff(985,plain,
% 5.44/5.46 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[984, 69])).
% 5.44/5.46 tff(986,plain,
% 5.44/5.46 (succ(X1!59) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[959])).
% 5.44/5.46 tff(987,plain,
% 5.44/5.46 (succ(X1!59) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[986, 28])).
% 5.44/5.46 tff(988,plain,
% 5.44/5.46 (succ(succ(X1!59)) = succ(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[987])).
% 5.44/5.46 tff(989,plain,
% 5.44/5.46 (succ(succ(X1!59)) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[988, 42])).
% 5.44/5.46 tff(990,plain,
% 5.44/5.46 (succ(succ(succ(X1!59))) = succ(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[989])).
% 5.44/5.46 tff(991,plain,
% 5.44/5.46 (succ(succ(succ(X1!59))) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[990, 58])).
% 5.44/5.46 tff(992,plain,
% 5.44/5.46 (succ(succ(succ(succ(X1!59)))) = succ(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[991])).
% 5.44/5.46 tff(993,plain,
% 5.44/5.46 (succ(succ(succ(succ(X1!59)))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[992, 36])).
% 5.44/5.46 tff(994,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(X1!59))))) = succ(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[993])).
% 5.44/5.46 tff(995,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(X1!59))))) = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[994, 48])).
% 5.44/5.46 tff(996,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[995])).
% 5.44/5.46 tff(997,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[996, 14])).
% 5.44/5.46 tff(998,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[997])).
% 5.44/5.46 tff(999,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[998, 33])).
% 5.44/5.46 tff(1000,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[999])).
% 5.44/5.46 tff(1001,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1000, 30])).
% 5.44/5.46 tff(1002,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1001])).
% 5.44/5.46 tff(1003,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1002, 39])).
% 5.44/5.46 tff(1004,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1003])).
% 5.44/5.46 tff(1005,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1004, 53])).
% 5.44/5.46 tff(1006,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1005])).
% 5.44/5.46 tff(1007,plain,
% 5.44/5.46 (NSX1!33 = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[305, 1006, 45])).
% 5.44/5.46 tff(1008,plain,
% 5.44/5.46 (pred(NSX1!33) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1007])).
% 5.44/5.46 tff(1009,plain,
% 5.44/5.46 (pred(NSX1!33) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1008, 20])).
% 5.44/5.46 tff(1010,plain,
% 5.44/5.46 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n8, n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1009, 985])).
% 5.44/5.46 tff(1011,plain,
% 5.44/5.46 (Y2!56 = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[310, 1010, 98])).
% 5.44/5.46 tff(1012,plain,
% 5.44/5.46 (pred(Y2!56) = pred(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1011])).
% 5.44/5.46 tff(1013,plain,
% 5.44/5.46 (pred(Y2!56) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1012, 25])).
% 5.44/5.46 tff(1014,plain,
% 5.44/5.46 (pred(pred(Y2!56)) = pred(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1013])).
% 5.44/5.46 tff(1015,plain,
% 5.44/5.46 (pred(pred(Y2!56)) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[1014, 24])).
% 5.44/5.46 tff(1016,plain,
% 5.44/5.46 (pred(pred(pred(Y2!56))) = pred(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1015])).
% 5.44/5.46 tff(1017,plain,
% 5.44/5.46 (pred(pred(pred(Y2!56))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1016, 23])).
% 5.44/5.46 tff(1018,plain,
% 5.44/5.46 (pred(pred(pred(pred(Y2!56)))) = pred(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1017])).
% 5.44/5.46 tff(1019,plain,
% 5.44/5.46 (pred(pred(pred(pred(Y2!56)))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1018, 22])).
% 5.44/5.46 tff(1020,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1019])).
% 5.44/5.46 tff(1021,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(Y2!56))))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[1020, 21])).
% 5.44/5.46 tff(1022,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1021])).
% 5.44/5.46 tff(1023,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1022, 20])).
% 5.44/5.46 tff(1024,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1023])).
% 5.44/5.46 tff(1025,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1024, 19])).
% 5.44/5.46 tff(1026,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1025])).
% 5.44/5.46 tff(1027,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1026, 18])).
% 5.44/5.46 tff(1028,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1027])).
% 5.44/5.46 tff(1029,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[1028, 17])).
% 5.44/5.46 tff(1030,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1029])).
% 5.44/5.46 tff(1031,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1030, 16])).
% 5.44/5.46 tff(1032,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1031])).
% 5.44/5.46 tff(1033,plain,
% 5.44/5.46 (NPY2!30 = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[347, 1032, 15])).
% 5.44/5.46 tff(1034,plain,
% 5.44/5.46 (succ(NPY2!30) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1033])).
% 5.44/5.46 tff(1035,plain,
% 5.44/5.46 (succ(NPY2!30) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1034, 14])).
% 5.44/5.46 tff(1036,plain,
% 5.44/5.46 (succ(Y2!56) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1011])).
% 5.44/5.46 tff(1037,plain,
% 5.44/5.46 (succ(Y2!56) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1036, 14])).
% 5.44/5.46 tff(1038,plain,
% 5.44/5.46 (succ(succ(Y2!56)) = succ(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1037])).
% 5.44/5.46 tff(1039,plain,
% 5.44/5.46 (succ(succ(Y2!56)) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[1038, 33])).
% 5.44/5.46 tff(1040,plain,
% 5.44/5.46 (succ(succ(succ(Y2!56))) = succ(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1039])).
% 5.44/5.46 tff(1041,plain,
% 5.44/5.46 (succ(succ(succ(Y2!56))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1040, 30])).
% 5.44/5.46 tff(1042,plain,
% 5.44/5.46 (succ(succ(succ(succ(Y2!56)))) = succ(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1041])).
% 5.44/5.46 tff(1043,plain,
% 5.44/5.46 (succ(succ(succ(succ(Y2!56)))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1042, 39])).
% 5.44/5.46 tff(1044,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1043])).
% 5.44/5.46 tff(1045,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(Y2!56))))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1044, 53])).
% 5.44/5.46 tff(1046,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1045])).
% 5.44/5.46 tff(1047,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[1046, 45])).
% 5.44/5.46 tff(1048,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1047])).
% 5.44/5.46 tff(1049,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1048, 28])).
% 5.44/5.46 tff(1050,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1049])).
% 5.44/5.46 tff(1051,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1050, 42])).
% 5.44/5.46 tff(1052,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1051])).
% 5.44/5.46 tff(1053,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[1052, 58])).
% 5.44/5.46 tff(1054,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1053])).
% 5.44/5.46 tff(1055,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1054, 36])).
% 5.44/5.46 tff(1056,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1055])).
% 5.44/5.46 tff(1057,plain,
% 5.44/5.46 (NSY2!28 = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[370, 1056, 48])).
% 5.44/5.46 tff(1058,plain,
% 5.44/5.46 (pred(NSY2!28) = pred(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1057])).
% 5.44/5.46 tff(1059,plain,
% 5.44/5.46 (pred(NSY2!28) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1058, 25])).
% 5.44/5.46 tff(1060,plain,
% 5.44/5.46 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n2, n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1059, 1035])).
% 5.44/5.46 tff(1061,plain,
% 5.44/5.46 (sum(pred(NSY2!28), succ(NPY2!30)) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1060, 13])).
% 5.44/5.46 tff(1062,plain,
% 5.44/5.46 (sum(pred(Y1!58), succ(X1!59)) = sum(n8, n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[904, 987])).
% 5.44/5.46 tff(1063,plain,
% 5.44/5.46 (sum(pred(Y1!58), succ(X1!59)) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1062, 27])).
% 5.44/5.46 tff(1064,plain,
% 5.44/5.46 (sum(pred(X1!59), succ(Y1!58)) = sum(n8, n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[961, 928])).
% 5.44/5.46 tff(1065,plain,
% 5.44/5.46 (sum(pred(X1!59), succ(Y1!58)) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1064, 27])).
% 5.44/5.46 tff(1066,plain,
% 5.44/5.46 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n7, n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1065, 1063])).
% 5.44/5.46 tff(1067,plain,
% 5.44/5.46 (X2!57 = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[209, 1066, 26])).
% 5.44/5.46 tff(1068,plain,
% 5.44/5.46 (pred(X2!57) = pred(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1067])).
% 5.44/5.46 tff(1069,plain,
% 5.44/5.46 (pred(X2!57) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1068, 25])).
% 5.44/5.46 tff(1070,plain,
% 5.44/5.46 (pred(pred(X2!57)) = pred(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1069])).
% 5.44/5.46 tff(1071,plain,
% 5.44/5.46 (pred(pred(X2!57)) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[1070, 24])).
% 5.44/5.46 tff(1072,plain,
% 5.44/5.46 (pred(pred(pred(X2!57))) = pred(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1071])).
% 5.44/5.46 tff(1073,plain,
% 5.44/5.46 (pred(pred(pred(X2!57))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1072, 23])).
% 5.44/5.46 tff(1074,plain,
% 5.44/5.46 (pred(pred(pred(pred(X2!57)))) = pred(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1073])).
% 5.44/5.46 tff(1075,plain,
% 5.44/5.46 (pred(pred(pred(pred(X2!57)))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1074, 22])).
% 5.44/5.46 tff(1076,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(X2!57))))) = pred(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1075])).
% 5.44/5.46 tff(1077,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(X2!57))))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[1076, 21])).
% 5.44/5.46 tff(1078,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1077])).
% 5.44/5.46 tff(1079,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1078, 20])).
% 5.44/5.46 tff(1080,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1079])).
% 5.44/5.46 tff(1081,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1080, 19])).
% 5.44/5.46 tff(1082,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1081])).
% 5.44/5.46 tff(1083,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1082, 18])).
% 5.44/5.46 tff(1084,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1083])).
% 5.44/5.46 tff(1085,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[1084, 17])).
% 5.44/5.46 tff(1086,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1085])).
% 5.44/5.46 tff(1087,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1086, 16])).
% 5.44/5.46 tff(1088,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1087])).
% 5.44/5.46 tff(1089,plain,
% 5.44/5.46 (NPX2!31 = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[395, 1088, 15])).
% 5.44/5.46 tff(1090,plain,
% 5.44/5.46 (succ(NPX2!31) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1089])).
% 5.44/5.46 tff(1091,plain,
% 5.44/5.46 (succ(NPX2!31) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1090, 14])).
% 5.44/5.46 tff(1092,plain,
% 5.44/5.46 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n4, n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1091, 1061])).
% 5.44/5.46 tff(1093,plain,
% 5.44/5.46 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1092, 12])).
% 5.44/5.46 tff(1094,plain,
% 5.44/5.46 (succ(X2!57) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1067])).
% 5.44/5.46 tff(1095,plain,
% 5.44/5.46 (succ(X2!57) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1094, 14])).
% 5.44/5.46 tff(1096,plain,
% 5.44/5.46 (succ(succ(X2!57)) = succ(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1095])).
% 5.44/5.46 tff(1097,plain,
% 5.44/5.46 (succ(succ(X2!57)) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[1096, 33])).
% 5.44/5.46 tff(1098,plain,
% 5.44/5.46 (succ(succ(succ(X2!57))) = succ(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1097])).
% 5.44/5.46 tff(1099,plain,
% 5.44/5.46 (succ(succ(succ(X2!57))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1098, 30])).
% 5.44/5.46 tff(1100,plain,
% 5.44/5.46 (succ(succ(succ(succ(X2!57)))) = succ(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1099])).
% 5.44/5.46 tff(1101,plain,
% 5.44/5.46 (succ(succ(succ(succ(X2!57)))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1100, 39])).
% 5.44/5.46 tff(1102,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(X2!57))))) = succ(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1101])).
% 5.44/5.46 tff(1103,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(X2!57))))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1102, 53])).
% 5.44/5.46 tff(1104,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1103])).
% 5.44/5.46 tff(1105,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[1104, 45])).
% 5.44/5.46 tff(1106,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1105])).
% 5.44/5.46 tff(1107,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1106, 28])).
% 5.44/5.46 tff(1108,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1107])).
% 5.44/5.46 tff(1109,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1108, 42])).
% 5.44/5.46 tff(1110,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1109])).
% 5.44/5.46 tff(1111,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[1110, 58])).
% 5.44/5.46 tff(1112,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1111])).
% 5.44/5.46 tff(1113,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1112, 36])).
% 5.44/5.46 tff(1114,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1113])).
% 5.44/5.46 tff(1115,plain,
% 5.44/5.46 (NSX2!29 = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[420, 1114, 48])).
% 5.44/5.46 tff(1116,plain,
% 5.44/5.46 (pred(NSX2!29) = pred(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1115])).
% 5.44/5.46 tff(1117,plain,
% 5.44/5.46 (pred(NSX2!29) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1116, 25])).
% 5.44/5.46 tff(1118,plain,
% 5.44/5.46 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n2, n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1117, 1093])).
% 5.44/5.46 tff(1119,plain,
% 5.44/5.46 (Y3!54 = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[425, 1118, 327])).
% 5.44/5.46 tff(1120,plain,
% 5.44/5.46 (pred(Y3!54) = pred(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1119])).
% 5.44/5.46 tff(1121,plain,
% 5.44/5.46 (pred(Y3!54) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1120, 23])).
% 5.44/5.46 tff(1122,plain,
% 5.44/5.46 (pred(pred(Y3!54)) = pred(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1121])).
% 5.44/5.46 tff(1123,plain,
% 5.44/5.46 (pred(pred(Y3!54)) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1122, 22])).
% 5.44/5.46 tff(1124,plain,
% 5.44/5.46 (pred(pred(pred(Y3!54))) = pred(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1123])).
% 5.44/5.46 tff(1125,plain,
% 5.44/5.46 (pred(pred(pred(Y3!54))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[1124, 21])).
% 5.44/5.46 tff(1126,plain,
% 5.44/5.46 (pred(pred(pred(pred(Y3!54)))) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1125])).
% 5.44/5.46 tff(1127,plain,
% 5.44/5.46 (pred(pred(pred(pred(Y3!54)))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1126, 20])).
% 5.44/5.46 tff(1128,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1127])).
% 5.44/5.46 tff(1129,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(Y3!54))))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1128, 19])).
% 5.44/5.46 tff(1130,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1129])).
% 5.44/5.46 tff(1131,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1130, 18])).
% 5.44/5.46 tff(1132,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1131])).
% 5.44/5.46 tff(1133,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[1132, 17])).
% 5.44/5.46 tff(1134,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1133])).
% 5.44/5.46 tff(1135,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1134, 16])).
% 5.44/5.46 tff(1136,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1135])).
% 5.44/5.46 tff(1137,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[1136, 15])).
% 5.44/5.46 tff(1138,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1137])).
% 5.44/5.46 tff(1139,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1138, 25])).
% 5.44/5.46 tff(1140,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1139])).
% 5.44/5.46 tff(1141,plain,
% 5.44/5.46 (NPY3!26 = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[462, 1140, 24])).
% 5.44/5.46 tff(1142,plain,
% 5.44/5.46 (succ(NPY3!26) = succ(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1141])).
% 5.44/5.46 tff(1143,plain,
% 5.44/5.46 (succ(NPY3!26) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1142, 36])).
% 5.44/5.46 tff(1144,plain,
% 5.44/5.46 (succ(Y3!54) = succ(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1119])).
% 5.44/5.46 tff(1145,plain,
% 5.44/5.46 (succ(Y3!54) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1144, 36])).
% 5.44/5.46 tff(1146,plain,
% 5.44/5.46 (succ(succ(Y3!54)) = succ(n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1145])).
% 5.44/5.46 tff(1147,plain,
% 5.44/5.46 (succ(succ(Y3!54)) = n3),
% 5.44/5.46 inference(transitivity,[status(thm)],[1146, 48])).
% 5.44/5.46 tff(1148,plain,
% 5.44/5.46 (succ(succ(succ(Y3!54))) = succ(n3)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1147])).
% 5.44/5.46 tff(1149,plain,
% 5.44/5.46 (succ(succ(succ(Y3!54))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1148, 14])).
% 5.44/5.46 tff(1150,plain,
% 5.44/5.46 (succ(succ(succ(succ(Y3!54)))) = succ(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1149])).
% 5.44/5.46 tff(1151,plain,
% 5.44/5.46 (succ(succ(succ(succ(Y3!54)))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[1150, 33])).
% 5.44/5.46 tff(1152,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1151])).
% 5.44/5.46 tff(1153,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(Y3!54))))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1152, 30])).
% 5.44/5.46 tff(1154,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1153])).
% 5.44/5.46 tff(1155,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1154, 39])).
% 5.44/5.46 tff(1156,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1155])).
% 5.44/5.46 tff(1157,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1156, 53])).
% 5.44/5.46 tff(1158,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1157])).
% 5.44/5.46 tff(1159,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[1158, 45])).
% 5.44/5.46 tff(1160,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1159])).
% 5.44/5.46 tff(1161,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1160, 28])).
% 5.44/5.46 tff(1162,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1161])).
% 5.44/5.46 tff(1163,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1162, 42])).
% 5.44/5.46 tff(1164,plain,
% 5.44/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1163])).
% 5.44/5.46 tff(1165,plain,
% 5.44/5.46 (NSY3!24 = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[485, 1164, 58])).
% 5.44/5.46 tff(1166,plain,
% 5.44/5.46 (pred(NSY3!24) = pred(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1165])).
% 5.44/5.46 tff(1167,plain,
% 5.44/5.46 (pred(NSY3!24) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1166, 23])).
% 5.44/5.46 tff(1168,plain,
% 5.44/5.46 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n0, n2)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1167, 1143])).
% 5.44/5.46 tff(1169,plain,
% 5.44/5.46 (sum(pred(NSY3!24), succ(NPY3!26)) = n2),
% 5.44/5.46 inference(transitivity,[status(thm)],[1168, 35])).
% 5.44/5.46 tff(1170,plain,
% 5.44/5.46 (sum(pred(Y2!56), succ(X2!57)) = sum(n2, n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1013, 1095])).
% 5.44/5.46 tff(1171,plain,
% 5.44/5.46 (sum(pred(Y2!56), succ(X2!57)) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1170, 13])).
% 5.44/5.46 tff(1172,plain,
% 5.44/5.46 (sum(pred(X2!57), succ(Y2!56)) = sum(n2, n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1069, 1037])).
% 5.44/5.46 tff(1173,plain,
% 5.44/5.46 (sum(pred(X2!57), succ(Y2!56)) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1172, 13])).
% 5.44/5.46 tff(1174,plain,
% 5.44/5.46 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n6, n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1173, 1171])).
% 5.44/5.46 tff(1175,plain,
% 5.44/5.46 (X3!55 = n1),
% 5.44/5.46 inference(transitivity,[status(thm)],[323, 1174, 37])).
% 5.44/5.46 tff(1176,plain,
% 5.44/5.46 (pred(X3!55) = pred(n1)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1175])).
% 5.44/5.46 tff(1177,plain,
% 5.44/5.46 (pred(X3!55) = n0),
% 5.44/5.46 inference(transitivity,[status(thm)],[1176, 23])).
% 5.44/5.46 tff(1178,plain,
% 5.44/5.46 (pred(pred(X3!55)) = pred(n0)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1177])).
% 5.44/5.46 tff(1179,plain,
% 5.44/5.46 (pred(pred(X3!55)) = n10),
% 5.44/5.46 inference(transitivity,[status(thm)],[1178, 22])).
% 5.44/5.46 tff(1180,plain,
% 5.44/5.46 (pred(pred(pred(X3!55))) = pred(n10)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1179])).
% 5.44/5.46 tff(1181,plain,
% 5.44/5.46 (pred(pred(pred(X3!55))) = n9),
% 5.44/5.46 inference(transitivity,[status(thm)],[1180, 21])).
% 5.44/5.46 tff(1182,plain,
% 5.44/5.46 (pred(pred(pred(pred(X3!55)))) = pred(n9)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1181])).
% 5.44/5.46 tff(1183,plain,
% 5.44/5.46 (pred(pred(pred(pred(X3!55)))) = n8),
% 5.44/5.46 inference(transitivity,[status(thm)],[1182, 20])).
% 5.44/5.46 tff(1184,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(X3!55))))) = pred(n8)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1183])).
% 5.44/5.46 tff(1185,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(X3!55))))) = n7),
% 5.44/5.46 inference(transitivity,[status(thm)],[1184, 19])).
% 5.44/5.46 tff(1186,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n7)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1185])).
% 5.44/5.46 tff(1187,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n6),
% 5.44/5.46 inference(transitivity,[status(thm)],[1186, 18])).
% 5.44/5.46 tff(1188,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n6)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1187])).
% 5.44/5.46 tff(1189,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n5),
% 5.44/5.46 inference(transitivity,[status(thm)],[1188, 17])).
% 5.44/5.46 tff(1190,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n5)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1189])).
% 5.44/5.46 tff(1191,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n4),
% 5.44/5.46 inference(transitivity,[status(thm)],[1190, 16])).
% 5.44/5.46 tff(1192,plain,
% 5.44/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n4)),
% 5.44/5.46 inference(monotonicity,[status(thm)],[1191])).
% 5.53/5.46 tff(1193,plain,
% 5.53/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n3),
% 5.53/5.46 inference(transitivity,[status(thm)],[1192, 15])).
% 5.53/5.46 tff(1194,plain,
% 5.53/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n3)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1193])).
% 5.53/5.46 tff(1195,plain,
% 5.53/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n2),
% 5.53/5.46 inference(transitivity,[status(thm)],[1194, 25])).
% 5.53/5.46 tff(1196,plain,
% 5.53/5.46 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n2)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1195])).
% 5.53/5.46 tff(1197,plain,
% 5.53/5.46 (NPX3!27 = n1),
% 5.53/5.46 inference(transitivity,[status(thm)],[510, 1196, 24])).
% 5.53/5.46 tff(1198,plain,
% 5.53/5.46 (succ(NPX3!27) = succ(n1)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1197])).
% 5.53/5.46 tff(1199,plain,
% 5.53/5.46 (succ(NPX3!27) = n2),
% 5.53/5.46 inference(transitivity,[status(thm)],[1198, 36])).
% 5.53/5.46 tff(1200,plain,
% 5.53/5.46 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n2, n2)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1199, 1169])).
% 5.53/5.46 tff(1201,plain,
% 5.53/5.46 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n4),
% 5.53/5.46 inference(transitivity,[status(thm)],[1200, 34])).
% 5.53/5.46 tff(1202,plain,
% 5.53/5.46 (succ(X3!55) = succ(n1)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1175])).
% 5.53/5.46 tff(1203,plain,
% 5.53/5.46 (succ(X3!55) = n2),
% 5.53/5.46 inference(transitivity,[status(thm)],[1202, 36])).
% 5.53/5.46 tff(1204,plain,
% 5.53/5.46 (succ(succ(X3!55)) = succ(n2)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1203])).
% 5.53/5.46 tff(1205,plain,
% 5.53/5.46 (succ(succ(X3!55)) = n3),
% 5.53/5.46 inference(transitivity,[status(thm)],[1204, 48])).
% 5.53/5.46 tff(1206,plain,
% 5.53/5.46 (succ(succ(succ(X3!55))) = succ(n3)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1205])).
% 5.53/5.46 tff(1207,plain,
% 5.53/5.46 (succ(succ(succ(X3!55))) = n4),
% 5.53/5.46 inference(transitivity,[status(thm)],[1206, 14])).
% 5.53/5.46 tff(1208,plain,
% 5.53/5.46 (succ(succ(succ(succ(X3!55)))) = succ(n4)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1207])).
% 5.53/5.46 tff(1209,plain,
% 5.53/5.46 (succ(succ(succ(succ(X3!55)))) = n5),
% 5.53/5.46 inference(transitivity,[status(thm)],[1208, 33])).
% 5.53/5.46 tff(1210,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(X3!55))))) = succ(n5)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1209])).
% 5.53/5.46 tff(1211,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(X3!55))))) = n6),
% 5.53/5.46 inference(transitivity,[status(thm)],[1210, 30])).
% 5.53/5.46 tff(1212,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n6)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1211])).
% 5.53/5.46 tff(1213,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n7),
% 5.53/5.46 inference(transitivity,[status(thm)],[1212, 39])).
% 5.53/5.46 tff(1214,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n7)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1213])).
% 5.53/5.46 tff(1215,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n8),
% 5.53/5.46 inference(transitivity,[status(thm)],[1214, 53])).
% 5.53/5.46 tff(1216,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n8)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1215])).
% 5.53/5.46 tff(1217,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n9),
% 5.53/5.46 inference(transitivity,[status(thm)],[1216, 45])).
% 5.53/5.46 tff(1218,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n9)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1217])).
% 5.53/5.46 tff(1219,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n10),
% 5.53/5.46 inference(transitivity,[status(thm)],[1218, 28])).
% 5.53/5.46 tff(1220,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n10)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1219])).
% 5.53/5.46 tff(1221,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n0),
% 5.53/5.46 inference(transitivity,[status(thm)],[1220, 42])).
% 5.53/5.46 tff(1222,plain,
% 5.53/5.46 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n0)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1221])).
% 5.53/5.46 tff(1223,plain,
% 5.53/5.46 (NSX3!25 = n1),
% 5.53/5.46 inference(transitivity,[status(thm)],[535, 1222, 58])).
% 5.53/5.46 tff(1224,plain,
% 5.53/5.46 (pred(NSX3!25) = pred(n1)),
% 5.53/5.46 inference(monotonicity,[status(thm)],[1223])).
% 5.53/5.46 tff(1225,plain,
% 5.53/5.46 (pred(NSX3!25) = n0),
% 5.53/5.46 inference(transitivity,[status(thm)],[1224, 23])).
% 5.53/5.47 tff(1226,plain,
% 5.53/5.47 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n0, n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1225, 1201])).
% 5.53/5.47 tff(1227,plain,
% 5.53/5.47 (Y4!52 = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[540, 1226, 442])).
% 5.53/5.47 tff(1228,plain,
% 5.53/5.47 (pred(Y4!52) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1227])).
% 5.53/5.47 tff(1229,plain,
% 5.53/5.47 (pred(Y4!52) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1228, 15])).
% 5.53/5.47 tff(1230,plain,
% 5.53/5.47 (pred(pred(Y4!52)) = pred(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1229])).
% 5.53/5.47 tff(1231,plain,
% 5.53/5.47 (pred(pred(Y4!52)) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1230, 25])).
% 5.53/5.47 tff(1232,plain,
% 5.53/5.47 (pred(pred(pred(Y4!52))) = pred(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1231])).
% 5.53/5.47 tff(1233,plain,
% 5.53/5.47 (pred(pred(pred(Y4!52))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1232, 24])).
% 5.53/5.47 tff(1234,plain,
% 5.53/5.47 (pred(pred(pred(pred(Y4!52)))) = pred(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1233])).
% 5.53/5.47 tff(1235,plain,
% 5.53/5.47 (pred(pred(pred(pred(Y4!52)))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1234, 23])).
% 5.53/5.47 tff(1236,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1235])).
% 5.53/5.47 tff(1237,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(Y4!52))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1236, 22])).
% 5.53/5.47 tff(1238,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1237])).
% 5.53/5.47 tff(1239,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1238, 21])).
% 5.53/5.47 tff(1240,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1239])).
% 5.53/5.47 tff(1241,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1240, 20])).
% 5.53/5.47 tff(1242,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1241])).
% 5.53/5.47 tff(1243,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1242, 19])).
% 5.53/5.47 tff(1244,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1243])).
% 5.53/5.47 tff(1245,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1244, 18])).
% 5.53/5.47 tff(1246,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1245])).
% 5.53/5.47 tff(1247,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1246, 17])).
% 5.53/5.47 tff(1248,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1247])).
% 5.53/5.47 tff(1249,plain,
% 5.53/5.47 (NPY4!22 = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[578, 1248, 16])).
% 5.53/5.47 tff(1250,plain,
% 5.53/5.47 (succ(NPY4!22) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1249])).
% 5.53/5.47 tff(1251,plain,
% 5.53/5.47 (succ(NPY4!22) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1250, 33])).
% 5.53/5.47 tff(1252,plain,
% 5.53/5.47 (succ(Y4!52) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1227])).
% 5.53/5.47 tff(1253,plain,
% 5.53/5.47 (succ(Y4!52) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1252, 33])).
% 5.53/5.47 tff(1254,plain,
% 5.53/5.47 (succ(succ(Y4!52)) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1253])).
% 5.53/5.47 tff(1255,plain,
% 5.53/5.47 (succ(succ(Y4!52)) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1254, 30])).
% 5.53/5.47 tff(1256,plain,
% 5.53/5.47 (succ(succ(succ(Y4!52))) = succ(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1255])).
% 5.53/5.47 tff(1257,plain,
% 5.53/5.47 (succ(succ(succ(Y4!52))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1256, 39])).
% 5.53/5.47 tff(1258,plain,
% 5.53/5.47 (succ(succ(succ(succ(Y4!52)))) = succ(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1257])).
% 5.53/5.47 tff(1259,plain,
% 5.53/5.47 (succ(succ(succ(succ(Y4!52)))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1258, 53])).
% 5.53/5.47 tff(1260,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1259])).
% 5.53/5.47 tff(1261,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(Y4!52))))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1260, 45])).
% 5.53/5.47 tff(1262,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1261])).
% 5.53/5.47 tff(1263,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1262, 28])).
% 5.53/5.47 tff(1264,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1263])).
% 5.53/5.47 tff(1265,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1264, 42])).
% 5.53/5.47 tff(1266,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1265])).
% 5.53/5.47 tff(1267,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1266, 58])).
% 5.53/5.47 tff(1268,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1267])).
% 5.53/5.47 tff(1269,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1268, 36])).
% 5.53/5.47 tff(1270,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1269])).
% 5.53/5.47 tff(1271,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1270, 48])).
% 5.53/5.47 tff(1272,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1271])).
% 5.53/5.47 tff(1273,plain,
% 5.53/5.47 (NSY4!20 = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[601, 1272, 14])).
% 5.53/5.47 tff(1274,plain,
% 5.53/5.47 (pred(NSY4!20) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1273])).
% 5.53/5.47 tff(1275,plain,
% 5.53/5.47 (pred(NSY4!20) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1274, 15])).
% 5.53/5.47 tff(1276,plain,
% 5.53/5.47 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n3, n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1275, 1251])).
% 5.53/5.47 tff(1277,plain,
% 5.53/5.47 (sum(pred(NSY4!20), succ(NPY4!22)) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1276, 32])).
% 5.53/5.47 tff(1278,plain,
% 5.53/5.47 (sum(pred(Y3!54), succ(X3!55)) = sum(n0, n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1121, 1203])).
% 5.53/5.47 tff(1279,plain,
% 5.53/5.47 (sum(pred(Y3!54), succ(X3!55)) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1278, 35])).
% 5.53/5.47 tff(1280,plain,
% 5.53/5.47 (sum(pred(X3!55), succ(Y3!54)) = sum(n0, n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1177, 1145])).
% 5.53/5.47 tff(1281,plain,
% 5.53/5.47 (sum(pred(X3!55), succ(Y3!54)) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1280, 35])).
% 5.53/5.47 tff(1282,plain,
% 5.53/5.47 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n2, n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1281, 1279])).
% 5.53/5.47 tff(1283,plain,
% 5.53/5.47 (X4!53 = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[438, 1282, 34])).
% 5.53/5.47 tff(1284,plain,
% 5.53/5.47 (pred(X4!53) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1283])).
% 5.53/5.47 tff(1285,plain,
% 5.53/5.47 (pred(X4!53) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1284, 15])).
% 5.53/5.47 tff(1286,plain,
% 5.53/5.47 (pred(pred(X4!53)) = pred(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1285])).
% 5.53/5.47 tff(1287,plain,
% 5.53/5.47 (pred(pred(X4!53)) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1286, 25])).
% 5.53/5.47 tff(1288,plain,
% 5.53/5.47 (pred(pred(pred(X4!53))) = pred(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1287])).
% 5.53/5.47 tff(1289,plain,
% 5.53/5.47 (pred(pred(pred(X4!53))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1288, 24])).
% 5.53/5.47 tff(1290,plain,
% 5.53/5.47 (pred(pred(pred(pred(X4!53)))) = pred(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1289])).
% 5.53/5.47 tff(1291,plain,
% 5.53/5.47 (pred(pred(pred(pred(X4!53)))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1290, 23])).
% 5.53/5.47 tff(1292,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(X4!53))))) = pred(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1291])).
% 5.53/5.47 tff(1293,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(X4!53))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1292, 22])).
% 5.53/5.47 tff(1294,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1293])).
% 5.53/5.47 tff(1295,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1294, 21])).
% 5.53/5.47 tff(1296,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1295])).
% 5.53/5.47 tff(1297,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1296, 20])).
% 5.53/5.47 tff(1298,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1297])).
% 5.53/5.47 tff(1299,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1298, 19])).
% 5.53/5.47 tff(1300,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1299])).
% 5.53/5.47 tff(1301,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1300, 18])).
% 5.53/5.47 tff(1302,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1301])).
% 5.53/5.47 tff(1303,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1302, 17])).
% 5.53/5.47 tff(1304,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1303])).
% 5.53/5.47 tff(1305,plain,
% 5.53/5.47 (NPX4!23 = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[626, 1304, 16])).
% 5.53/5.47 tff(1306,plain,
% 5.53/5.47 (succ(NPX4!23) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1305])).
% 5.53/5.47 tff(1307,plain,
% 5.53/5.47 (succ(NPX4!23) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1306, 33])).
% 5.53/5.47 tff(1308,plain,
% 5.53/5.47 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n5, n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1307, 1277])).
% 5.53/5.47 tff(1309,plain,
% 5.53/5.47 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1308, 558])).
% 5.53/5.47 tff(1310,plain,
% 5.53/5.47 (succ(X4!53) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1283])).
% 5.53/5.47 tff(1311,plain,
% 5.53/5.47 (succ(X4!53) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1310, 33])).
% 5.53/5.47 tff(1312,plain,
% 5.53/5.47 (succ(succ(X4!53)) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1311])).
% 5.53/5.47 tff(1313,plain,
% 5.53/5.47 (succ(succ(X4!53)) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1312, 30])).
% 5.53/5.47 tff(1314,plain,
% 5.53/5.47 (succ(succ(succ(X4!53))) = succ(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1313])).
% 5.53/5.47 tff(1315,plain,
% 5.53/5.47 (succ(succ(succ(X4!53))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1314, 39])).
% 5.53/5.47 tff(1316,plain,
% 5.53/5.47 (succ(succ(succ(succ(X4!53)))) = succ(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1315])).
% 5.53/5.47 tff(1317,plain,
% 5.53/5.47 (succ(succ(succ(succ(X4!53)))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1316, 53])).
% 5.53/5.47 tff(1318,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(X4!53))))) = succ(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1317])).
% 5.53/5.47 tff(1319,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(X4!53))))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1318, 45])).
% 5.53/5.47 tff(1320,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1319])).
% 5.53/5.47 tff(1321,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1320, 28])).
% 5.53/5.47 tff(1322,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1321])).
% 5.53/5.47 tff(1323,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1322, 42])).
% 5.53/5.47 tff(1324,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1323])).
% 5.53/5.47 tff(1325,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1324, 58])).
% 5.53/5.47 tff(1326,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1325])).
% 5.53/5.47 tff(1327,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1326, 36])).
% 5.53/5.47 tff(1328,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1327])).
% 5.53/5.47 tff(1329,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1328, 48])).
% 5.53/5.47 tff(1330,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1329])).
% 5.53/5.47 tff(1331,plain,
% 5.53/5.47 (NSX4!21 = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[651, 1330, 14])).
% 5.53/5.47 tff(1332,plain,
% 5.53/5.47 (pred(NSX4!21) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1331])).
% 5.53/5.47 tff(1333,plain,
% 5.53/5.47 (pred(NSX4!21) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1332, 15])).
% 5.53/5.47 tff(1334,plain,
% 5.53/5.47 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n3, n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1333, 1309])).
% 5.53/5.47 tff(1335,plain,
% 5.53/5.47 (Y5!50 = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[656, 1334, 557])).
% 5.53/5.47 tff(1336,plain,
% 5.53/5.47 (pred(Y5!50) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1335])).
% 5.53/5.47 tff(1337,plain,
% 5.53/5.47 (pred(Y5!50) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1336, 16])).
% 5.53/5.47 tff(1338,plain,
% 5.53/5.47 (pred(pred(Y5!50)) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1337])).
% 5.53/5.47 tff(1339,plain,
% 5.53/5.47 (pred(pred(Y5!50)) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1338, 15])).
% 5.53/5.47 tff(1340,plain,
% 5.53/5.47 (pred(pred(pred(Y5!50))) = pred(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1339])).
% 5.53/5.47 tff(1341,plain,
% 5.53/5.47 (pred(pred(pred(Y5!50))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1340, 25])).
% 5.53/5.47 tff(1342,plain,
% 5.53/5.47 (pred(pred(pred(pred(Y5!50)))) = pred(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1341])).
% 5.53/5.47 tff(1343,plain,
% 5.53/5.47 (pred(pred(pred(pred(Y5!50)))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1342, 24])).
% 5.53/5.47 tff(1344,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1343])).
% 5.53/5.47 tff(1345,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(Y5!50))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1344, 23])).
% 5.53/5.47 tff(1346,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1345])).
% 5.53/5.47 tff(1347,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1346, 22])).
% 5.53/5.47 tff(1348,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1347])).
% 5.53/5.47 tff(1349,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1348, 21])).
% 5.53/5.47 tff(1350,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1349])).
% 5.53/5.47 tff(1351,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1350, 20])).
% 5.53/5.47 tff(1352,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1351])).
% 5.53/5.47 tff(1353,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1352, 19])).
% 5.53/5.47 tff(1354,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1353])).
% 5.53/5.47 tff(1355,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1354, 18])).
% 5.53/5.47 tff(1356,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1355])).
% 5.53/5.47 tff(1357,plain,
% 5.53/5.47 (NPY5!18 = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[694, 1356, 17])).
% 5.53/5.47 tff(1358,plain,
% 5.53/5.47 (succ(NPY5!18) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1357])).
% 5.53/5.47 tff(1359,plain,
% 5.53/5.47 (succ(NPY5!18) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1358, 30])).
% 5.53/5.47 tff(1360,plain,
% 5.53/5.47 (succ(Y5!50) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1335])).
% 5.53/5.47 tff(1361,plain,
% 5.53/5.47 (succ(Y5!50) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1360, 30])).
% 5.53/5.47 tff(1362,plain,
% 5.53/5.47 (succ(succ(Y5!50)) = succ(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1361])).
% 5.53/5.47 tff(1363,plain,
% 5.53/5.47 (succ(succ(Y5!50)) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1362, 39])).
% 5.53/5.47 tff(1364,plain,
% 5.53/5.47 (succ(succ(succ(Y5!50))) = succ(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1363])).
% 5.53/5.47 tff(1365,plain,
% 5.53/5.47 (succ(succ(succ(Y5!50))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1364, 53])).
% 5.53/5.47 tff(1366,plain,
% 5.53/5.47 (succ(succ(succ(succ(Y5!50)))) = succ(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1365])).
% 5.53/5.47 tff(1367,plain,
% 5.53/5.47 (succ(succ(succ(succ(Y5!50)))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1366, 45])).
% 5.53/5.47 tff(1368,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1367])).
% 5.53/5.47 tff(1369,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(Y5!50))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1368, 28])).
% 5.53/5.47 tff(1370,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1369])).
% 5.53/5.47 tff(1371,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1370, 42])).
% 5.53/5.47 tff(1372,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1371])).
% 5.53/5.47 tff(1373,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1372, 58])).
% 5.53/5.47 tff(1374,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1373])).
% 5.53/5.47 tff(1375,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1374, 36])).
% 5.53/5.47 tff(1376,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1375])).
% 5.53/5.47 tff(1377,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1376, 48])).
% 5.53/5.47 tff(1378,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1377])).
% 5.53/5.47 tff(1379,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1378, 14])).
% 5.53/5.47 tff(1380,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1379])).
% 5.53/5.47 tff(1381,plain,
% 5.53/5.47 (NSY5!16 = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[717, 1380, 33])).
% 5.53/5.47 tff(1382,plain,
% 5.53/5.47 (pred(NSY5!16) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1381])).
% 5.53/5.47 tff(1383,plain,
% 5.53/5.47 (pred(NSY5!16) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1382, 16])).
% 5.53/5.47 tff(1384,plain,
% 5.53/5.47 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n4, n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1383, 1359])).
% 5.53/5.47 tff(1385,plain,
% 5.53/5.47 (sum(pred(NSY5!16), succ(NPY5!18)) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1384, 12])).
% 5.53/5.47 tff(1386,plain,
% 5.53/5.47 (sum(pred(Y4!52), succ(X4!53)) = sum(n3, n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1229, 1311])).
% 5.53/5.47 tff(1387,plain,
% 5.53/5.47 (sum(pred(Y4!52), succ(X4!53)) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1386, 32])).
% 5.53/5.47 tff(1388,plain,
% 5.53/5.47 (sum(pred(X4!53), succ(Y4!52)) = sum(n3, n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1285, 1253])).
% 5.53/5.47 tff(1389,plain,
% 5.53/5.47 (sum(pred(X4!53), succ(Y4!52)) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1388, 32])).
% 5.53/5.47 tff(1390,plain,
% 5.53/5.47 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n8, n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1389, 1387])).
% 5.53/5.47 tff(1391,plain,
% 5.53/5.47 (X5!51 = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[553, 1390, 31])).
% 5.53/5.47 tff(1392,plain,
% 5.53/5.47 (pred(X5!51) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1391])).
% 5.53/5.47 tff(1393,plain,
% 5.53/5.47 (pred(X5!51) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1392, 16])).
% 5.53/5.47 tff(1394,plain,
% 5.53/5.47 (pred(pred(X5!51)) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1393])).
% 5.53/5.47 tff(1395,plain,
% 5.53/5.47 (pred(pred(X5!51)) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1394, 15])).
% 5.53/5.47 tff(1396,plain,
% 5.53/5.47 (pred(pred(pred(X5!51))) = pred(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1395])).
% 5.53/5.47 tff(1397,plain,
% 5.53/5.47 (pred(pred(pred(X5!51))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1396, 25])).
% 5.53/5.47 tff(1398,plain,
% 5.53/5.47 (pred(pred(pred(pred(X5!51)))) = pred(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1397])).
% 5.53/5.47 tff(1399,plain,
% 5.53/5.47 (pred(pred(pred(pred(X5!51)))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1398, 24])).
% 5.53/5.47 tff(1400,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(X5!51))))) = pred(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1399])).
% 5.53/5.47 tff(1401,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(X5!51))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1400, 23])).
% 5.53/5.47 tff(1402,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1401])).
% 5.53/5.47 tff(1403,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1402, 22])).
% 5.53/5.47 tff(1404,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1403])).
% 5.53/5.47 tff(1405,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1404, 21])).
% 5.53/5.47 tff(1406,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1405])).
% 5.53/5.47 tff(1407,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1406, 20])).
% 5.53/5.47 tff(1408,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1407])).
% 5.53/5.47 tff(1409,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1408, 19])).
% 5.53/5.47 tff(1410,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1409])).
% 5.53/5.47 tff(1411,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1410, 18])).
% 5.53/5.47 tff(1412,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1411])).
% 5.53/5.47 tff(1413,plain,
% 5.53/5.47 (NPX5!19 = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[742, 1412, 17])).
% 5.53/5.47 tff(1414,plain,
% 5.53/5.47 (succ(NPX5!19) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1413])).
% 5.53/5.47 tff(1415,plain,
% 5.53/5.47 (succ(NPX5!19) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1414, 30])).
% 5.53/5.47 tff(1416,plain,
% 5.53/5.47 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n6, n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1415, 1385])).
% 5.53/5.47 tff(1417,plain,
% 5.53/5.47 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1416, 674])).
% 5.53/5.47 tff(1418,plain,
% 5.53/5.47 (succ(X5!51) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1391])).
% 5.53/5.47 tff(1419,plain,
% 5.53/5.47 (succ(X5!51) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1418, 30])).
% 5.53/5.47 tff(1420,plain,
% 5.53/5.47 (succ(succ(X5!51)) = succ(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1419])).
% 5.53/5.47 tff(1421,plain,
% 5.53/5.47 (succ(succ(X5!51)) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1420, 39])).
% 5.53/5.47 tff(1422,plain,
% 5.53/5.47 (succ(succ(succ(X5!51))) = succ(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1421])).
% 5.53/5.47 tff(1423,plain,
% 5.53/5.47 (succ(succ(succ(X5!51))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1422, 53])).
% 5.53/5.47 tff(1424,plain,
% 5.53/5.47 (succ(succ(succ(succ(X5!51)))) = succ(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1423])).
% 5.53/5.47 tff(1425,plain,
% 5.53/5.47 (succ(succ(succ(succ(X5!51)))) = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1424, 45])).
% 5.53/5.47 tff(1426,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(X5!51))))) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1425])).
% 5.53/5.47 tff(1427,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(X5!51))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1426, 28])).
% 5.53/5.47 tff(1428,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1427])).
% 5.53/5.47 tff(1429,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1428, 42])).
% 5.53/5.47 tff(1430,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1429])).
% 5.53/5.47 tff(1431,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1430, 58])).
% 5.53/5.47 tff(1432,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1431])).
% 5.53/5.47 tff(1433,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1432, 36])).
% 5.53/5.47 tff(1434,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1433])).
% 5.53/5.47 tff(1435,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1434, 48])).
% 5.53/5.47 tff(1436,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1435])).
% 5.53/5.47 tff(1437,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1436, 14])).
% 5.53/5.47 tff(1438,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1437])).
% 5.53/5.47 tff(1439,plain,
% 5.53/5.47 (NSX5!17 = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[767, 1438, 33])).
% 5.53/5.47 tff(1440,plain,
% 5.53/5.47 (pred(NSX5!17) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1439])).
% 5.53/5.47 tff(1441,plain,
% 5.53/5.47 (pred(NSX5!17) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1440, 16])).
% 5.53/5.47 tff(1442,plain,
% 5.53/5.47 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n4, n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1441, 1417])).
% 5.53/5.47 tff(1443,plain,
% 5.53/5.47 (Y6!48 = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[772, 1442, 673])).
% 5.53/5.47 tff(1444,plain,
% 5.53/5.47 (pred(Y6!48) = pred(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1443])).
% 5.53/5.47 tff(1445,plain,
% 5.53/5.47 (pred(Y6!48) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1444, 20])).
% 5.53/5.47 tff(1446,plain,
% 5.53/5.47 (pred(pred(Y6!48)) = pred(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1445])).
% 5.53/5.47 tff(1447,plain,
% 5.53/5.47 (pred(pred(Y6!48)) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1446, 19])).
% 5.53/5.47 tff(1448,plain,
% 5.53/5.47 (pred(pred(pred(Y6!48))) = pred(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1447])).
% 5.53/5.47 tff(1449,plain,
% 5.53/5.47 (pred(pred(pred(Y6!48))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1448, 18])).
% 5.53/5.47 tff(1450,plain,
% 5.53/5.47 (pred(pred(pred(pred(Y6!48)))) = pred(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1449])).
% 5.53/5.47 tff(1451,plain,
% 5.53/5.47 (pred(pred(pred(pred(Y6!48)))) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1450, 17])).
% 5.53/5.47 tff(1452,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1451])).
% 5.53/5.47 tff(1453,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(Y6!48))))) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1452, 16])).
% 5.53/5.47 tff(1454,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1453])).
% 5.53/5.47 tff(1455,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1454, 15])).
% 5.53/5.47 tff(1456,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1455])).
% 5.53/5.47 tff(1457,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1456, 25])).
% 5.53/5.47 tff(1458,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1457])).
% 5.53/5.47 tff(1459,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1458, 24])).
% 5.53/5.47 tff(1460,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1459])).
% 5.53/5.47 tff(1461,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1460, 23])).
% 5.53/5.47 tff(1462,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1461])).
% 5.53/5.47 tff(1463,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1462, 22])).
% 5.53/5.47 tff(1464,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1463])).
% 5.53/5.47 tff(1465,plain,
% 5.53/5.47 (NPY6!14 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))))),
% 5.53/5.47 inference(and_elim,[status(thm)],[9])).
% 5.53/5.47 tff(1466,plain,
% 5.53/5.47 (NPY6!14 = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1465, 1464, 21])).
% 5.53/5.47 tff(1467,plain,
% 5.53/5.47 (succ(NPY6!14) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1466])).
% 5.53/5.47 tff(1468,plain,
% 5.53/5.47 (succ(NPY6!14) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1467, 28])).
% 5.53/5.47 tff(1469,plain,
% 5.53/5.47 (succ(Y6!48) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1443])).
% 5.53/5.47 tff(1470,plain,
% 5.53/5.47 (succ(Y6!48) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1469, 28])).
% 5.53/5.47 tff(1471,plain,
% 5.53/5.47 (succ(succ(Y6!48)) = succ(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1470])).
% 5.53/5.47 tff(1472,plain,
% 5.53/5.47 (succ(succ(Y6!48)) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1471, 42])).
% 5.53/5.47 tff(1473,plain,
% 5.53/5.47 (succ(succ(succ(Y6!48))) = succ(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1472])).
% 5.53/5.47 tff(1474,plain,
% 5.53/5.47 (succ(succ(succ(Y6!48))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1473, 58])).
% 5.53/5.47 tff(1475,plain,
% 5.53/5.47 (succ(succ(succ(succ(Y6!48)))) = succ(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1474])).
% 5.53/5.47 tff(1476,plain,
% 5.53/5.47 (succ(succ(succ(succ(Y6!48)))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1475, 36])).
% 5.53/5.47 tff(1477,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1476])).
% 5.53/5.47 tff(1478,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(Y6!48))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1477, 48])).
% 5.53/5.47 tff(1479,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1478])).
% 5.53/5.47 tff(1480,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1479, 14])).
% 5.53/5.47 tff(1481,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1480])).
% 5.53/5.47 tff(1482,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1481, 33])).
% 5.53/5.47 tff(1483,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1482])).
% 5.53/5.47 tff(1484,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1483, 30])).
% 5.53/5.47 tff(1485,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1484])).
% 5.53/5.47 tff(1486,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1485, 39])).
% 5.53/5.47 tff(1487,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1486])).
% 5.53/5.47 tff(1488,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1487, 53])).
% 5.53/5.47 tff(1489,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1488])).
% 5.53/5.47 tff(1490,plain,
% 5.53/5.47 (NSY6!12 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))))),
% 5.53/5.47 inference(and_elim,[status(thm)],[9])).
% 5.53/5.47 tff(1491,plain,
% 5.53/5.47 (NSY6!12 = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1490, 1489, 45])).
% 5.53/5.47 tff(1492,plain,
% 5.53/5.47 (pred(NSY6!12) = pred(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1491])).
% 5.53/5.47 tff(1493,plain,
% 5.53/5.47 (pred(NSY6!12) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1492, 20])).
% 5.53/5.47 tff(1494,plain,
% 5.53/5.47 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n8, n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1493, 1468])).
% 5.53/5.47 tff(1495,plain,
% 5.53/5.47 (sum(pred(NSY6!12), succ(NPY6!14)) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1494, 27])).
% 5.53/5.47 tff(1496,plain,
% 5.53/5.47 (sum(pred(Y5!50), succ(X5!51)) = sum(n4, n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1337, 1419])).
% 5.53/5.47 tff(1497,plain,
% 5.53/5.47 (sum(pred(Y5!50), succ(X5!51)) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1496, 12])).
% 5.53/5.47 tff(1498,plain,
% 5.53/5.47 (sum(pred(X5!51), succ(Y5!50)) = sum(n4, n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1393, 1361])).
% 5.53/5.47 tff(1499,plain,
% 5.53/5.47 (sum(pred(X5!51), succ(Y5!50)) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1498, 12])).
% 5.53/5.47 tff(1500,plain,
% 5.53/5.47 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n10, n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1499, 1497])).
% 5.53/5.47 tff(1501,plain,
% 5.53/5.47 (X6!49 = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[669, 1500, 29])).
% 5.53/5.47 tff(1502,plain,
% 5.53/5.47 (pred(X6!49) = pred(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1501])).
% 5.53/5.47 tff(1503,plain,
% 5.53/5.47 (pred(X6!49) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1502, 20])).
% 5.53/5.47 tff(1504,plain,
% 5.53/5.47 (pred(pred(X6!49)) = pred(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1503])).
% 5.53/5.47 tff(1505,plain,
% 5.53/5.47 (pred(pred(X6!49)) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1504, 19])).
% 5.53/5.47 tff(1506,plain,
% 5.53/5.47 (pred(pred(pred(X6!49))) = pred(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1505])).
% 5.53/5.47 tff(1507,plain,
% 5.53/5.47 (pred(pred(pred(X6!49))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1506, 18])).
% 5.53/5.47 tff(1508,plain,
% 5.53/5.47 (pred(pred(pred(pred(X6!49)))) = pred(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1507])).
% 5.53/5.47 tff(1509,plain,
% 5.53/5.47 (pred(pred(pred(pred(X6!49)))) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1508, 17])).
% 5.53/5.47 tff(1510,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(X6!49))))) = pred(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1509])).
% 5.53/5.47 tff(1511,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(X6!49))))) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1510, 16])).
% 5.53/5.47 tff(1512,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1511])).
% 5.53/5.47 tff(1513,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1512, 15])).
% 5.53/5.47 tff(1514,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1513])).
% 5.53/5.47 tff(1515,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1514, 25])).
% 5.53/5.47 tff(1516,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1515])).
% 5.53/5.47 tff(1517,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1516, 24])).
% 5.53/5.47 tff(1518,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1517])).
% 5.53/5.47 tff(1519,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1518, 23])).
% 5.53/5.47 tff(1520,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1519])).
% 5.53/5.47 tff(1521,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1520, 22])).
% 5.53/5.47 tff(1522,plain,
% 5.53/5.47 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1521])).
% 5.53/5.47 tff(1523,plain,
% 5.53/5.47 (NPX6!15 = pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))))),
% 5.53/5.47 inference(and_elim,[status(thm)],[9])).
% 5.53/5.47 tff(1524,plain,
% 5.53/5.47 (NPX6!15 = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1523, 1522, 21])).
% 5.53/5.47 tff(1525,plain,
% 5.53/5.47 (succ(NPX6!15) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1524])).
% 5.53/5.47 tff(1526,plain,
% 5.53/5.47 (succ(NPX6!15) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1525, 28])).
% 5.53/5.47 tff(1527,plain,
% 5.53/5.47 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n10, n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1526, 1495])).
% 5.53/5.47 tff(1528,plain,
% 5.53/5.47 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1527, 69])).
% 5.53/5.47 tff(1529,plain,
% 5.53/5.47 (succ(X6!49) = succ(n9)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1501])).
% 5.53/5.47 tff(1530,plain,
% 5.53/5.47 (succ(X6!49) = n10),
% 5.53/5.47 inference(transitivity,[status(thm)],[1529, 28])).
% 5.53/5.47 tff(1531,plain,
% 5.53/5.47 (succ(succ(X6!49)) = succ(n10)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1530])).
% 5.53/5.47 tff(1532,plain,
% 5.53/5.47 (succ(succ(X6!49)) = n0),
% 5.53/5.47 inference(transitivity,[status(thm)],[1531, 42])).
% 5.53/5.47 tff(1533,plain,
% 5.53/5.47 (succ(succ(succ(X6!49))) = succ(n0)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1532])).
% 5.53/5.47 tff(1534,plain,
% 5.53/5.47 (succ(succ(succ(X6!49))) = n1),
% 5.53/5.47 inference(transitivity,[status(thm)],[1533, 58])).
% 5.53/5.47 tff(1535,plain,
% 5.53/5.47 (succ(succ(succ(succ(X6!49)))) = succ(n1)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1534])).
% 5.53/5.47 tff(1536,plain,
% 5.53/5.47 (succ(succ(succ(succ(X6!49)))) = n2),
% 5.53/5.47 inference(transitivity,[status(thm)],[1535, 36])).
% 5.53/5.47 tff(1537,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(X6!49))))) = succ(n2)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1536])).
% 5.53/5.47 tff(1538,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(X6!49))))) = n3),
% 5.53/5.47 inference(transitivity,[status(thm)],[1537, 48])).
% 5.53/5.47 tff(1539,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n3)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1538])).
% 5.53/5.47 tff(1540,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n4),
% 5.53/5.47 inference(transitivity,[status(thm)],[1539, 14])).
% 5.53/5.47 tff(1541,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n4)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1540])).
% 5.53/5.47 tff(1542,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n5),
% 5.53/5.47 inference(transitivity,[status(thm)],[1541, 33])).
% 5.53/5.47 tff(1543,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n5)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1542])).
% 5.53/5.47 tff(1544,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n6),
% 5.53/5.47 inference(transitivity,[status(thm)],[1543, 30])).
% 5.53/5.47 tff(1545,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n6)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1544])).
% 5.53/5.47 tff(1546,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n7),
% 5.53/5.47 inference(transitivity,[status(thm)],[1545, 39])).
% 5.53/5.47 tff(1547,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n7)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1546])).
% 5.53/5.47 tff(1548,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n8),
% 5.53/5.47 inference(transitivity,[status(thm)],[1547, 53])).
% 5.53/5.47 tff(1549,plain,
% 5.53/5.47 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n8)),
% 5.53/5.47 inference(monotonicity,[status(thm)],[1548])).
% 5.53/5.47 tff(1550,plain,
% 5.53/5.47 (NSX6!13 = succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))))),
% 5.53/5.47 inference(and_elim,[status(thm)],[9])).
% 5.53/5.47 tff(1551,plain,
% 5.53/5.47 (NSX6!13 = n9),
% 5.53/5.47 inference(transitivity,[status(thm)],[1550, 1549, 45])).
% 5.53/5.47 tff(1552,plain,
% 5.53/5.47 (pred(NSX6!13) = pred(n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1551])).
% 5.53/5.48 tff(1553,plain,
% 5.53/5.48 (pred(NSX6!13) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1552, 20])).
% 5.53/5.48 tff(1554,plain,
% 5.53/5.48 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n8, n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1553, 1528])).
% 5.53/5.48 tff(1555,plain,
% 5.53/5.48 (sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.53/5.48 inference(symmetry,[status(thm)],[1554])).
% 5.53/5.48 tff(1556,plain,
% 5.53/5.48 (n3 = sum(n8, n6)),
% 5.53/5.48 inference(symmetry,[status(thm)],[98])).
% 5.53/5.48 tff(1557,plain,
% 5.53/5.48 (sum(pred(Y6!48), succ(X6!49)) = sum(n8, n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1445, 1530])).
% 5.53/5.48 tff(1558,plain,
% 5.53/5.48 (sum(pred(Y6!48), succ(X6!49)) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1557, 27])).
% 5.53/5.48 tff(1559,plain,
% 5.53/5.48 (sum(pred(X6!49), succ(Y6!48)) = sum(n8, n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1503, 1470])).
% 5.53/5.48 tff(1560,plain,
% 5.53/5.48 (sum(pred(X6!49), succ(Y6!48)) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1559, 27])).
% 5.53/5.48 tff(1561,plain,
% 5.53/5.48 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n7, n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1560, 1558])).
% 5.53/5.48 tff(1562,plain,
% 5.53/5.48 (X7!47 = sum(n8, n6)),
% 5.53/5.48 inference(transitivity,[status(thm)],[785, 1561, 26, 1556])).
% 5.53/5.48 tff(1563,plain,
% 5.53/5.48 ((X7!47 = Y7!46) <=> (sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))))),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1562, 793])).
% 5.53/5.48 tff(1564,plain,
% 5.53/5.48 ((~(X7!47 = Y7!46)) <=> (~(sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))))),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1563])).
% 5.53/5.48 tff(1565,plain,
% 5.53/5.48 (~(sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))))),
% 5.53/5.48 inference(modus_ponens,[status(thm)],[792, 1564])).
% 5.53/5.48 tff(1566,plain,
% 5.53/5.48 ($false),
% 5.53/5.48 inference(unit_resolution,[status(thm)],[1565, 1555])).
% 5.53/5.48 tff(1567,plain,((~(X0!61 = n6)) | (~(Y0!60 = n4)) | (X7!47 = Y7!46)), inference(lemma,lemma(discharge,[]))).
% 5.53/5.48 tff(1568,plain,
% 5.53/5.48 (~(X0!61 = n6)),
% 5.53/5.48 inference(unit_resolution,[status(thm)],[1567, 797, 792])).
% 5.53/5.48 tff(1569,plain,
% 5.53/5.48 (sum(n6, n5) = n0),
% 5.53/5.48 inference(and_elim,[status(thm)],[9])).
% 5.53/5.48 tff(1570,plain,
% 5.53/5.48 (sum(n6, n9) = n4),
% 5.53/5.48 inference(and_elim,[status(thm)],[9])).
% 5.53/5.48 tff(1571,plain,
% 5.53/5.48 (sum(n8, n1) = n9),
% 5.53/5.48 inference(and_elim,[status(thm)],[9])).
% 5.53/5.48 tff(1572,assumption,(Y0!60 = n6), introduced(assumption)).
% 5.53/5.48 tff(1573,plain,
% 5.53/5.48 (pred(Y0!60) = pred(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1572])).
% 5.53/5.48 tff(1574,plain,
% 5.53/5.48 (pred(Y0!60) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1573, 17])).
% 5.53/5.48 tff(1575,plain,
% 5.53/5.48 (pred(pred(Y0!60)) = pred(n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1574])).
% 5.53/5.48 tff(1576,plain,
% 5.53/5.48 (pred(pred(Y0!60)) = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[1575, 16])).
% 5.53/5.48 tff(1577,plain,
% 5.53/5.48 (pred(pred(pred(Y0!60))) = pred(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1576])).
% 5.53/5.48 tff(1578,plain,
% 5.53/5.48 (pred(pred(pred(Y0!60))) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1577, 15])).
% 5.53/5.48 tff(1579,plain,
% 5.53/5.48 (pred(pred(pred(pred(Y0!60)))) = pred(n3)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1578])).
% 5.53/5.48 tff(1580,plain,
% 5.53/5.48 (pred(pred(pred(pred(Y0!60)))) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1579, 25])).
% 5.53/5.48 tff(1581,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1580])).
% 5.53/5.48 tff(1582,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(Y0!60))))) = n1),
% 5.53/5.48 inference(transitivity,[status(thm)],[1581, 24])).
% 5.53/5.48 tff(1583,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n1)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1582])).
% 5.53/5.48 tff(1584,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n0),
% 5.53/5.48 inference(transitivity,[status(thm)],[1583, 23])).
% 5.53/5.48 tff(1585,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n0)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1584])).
% 5.53/5.48 tff(1586,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n10),
% 5.53/5.48 inference(transitivity,[status(thm)],[1585, 22])).
% 5.53/5.48 tff(1587,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1586])).
% 5.53/5.48 tff(1588,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n9),
% 5.53/5.48 inference(transitivity,[status(thm)],[1587, 21])).
% 5.53/5.48 tff(1589,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1588])).
% 5.53/5.48 tff(1590,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1589, 20])).
% 5.53/5.48 tff(1591,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1590])).
% 5.53/5.48 tff(1592,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1591, 19])).
% 5.53/5.48 tff(1593,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1592])).
% 5.53/5.48 tff(1594,plain,
% 5.53/5.48 (NPY0!38 = n6),
% 5.53/5.48 inference(transitivity,[status(thm)],[118, 1593, 18])).
% 5.53/5.48 tff(1595,plain,
% 5.53/5.48 (succ(NPY0!38) = succ(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1594])).
% 5.53/5.48 tff(1596,plain,
% 5.53/5.48 (succ(NPY0!38) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1595, 39])).
% 5.53/5.48 tff(1597,plain,
% 5.53/5.48 (succ(Y0!60) = succ(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1572])).
% 5.53/5.48 tff(1598,plain,
% 5.53/5.48 (succ(Y0!60) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1597, 39])).
% 5.53/5.48 tff(1599,plain,
% 5.53/5.48 (succ(succ(Y0!60)) = succ(n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1598])).
% 5.53/5.48 tff(1600,plain,
% 5.53/5.48 (succ(succ(Y0!60)) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1599, 53])).
% 5.53/5.48 tff(1601,plain,
% 5.53/5.48 (succ(succ(succ(Y0!60))) = succ(n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1600])).
% 5.53/5.48 tff(1602,plain,
% 5.53/5.48 (succ(succ(succ(Y0!60))) = n9),
% 5.53/5.48 inference(transitivity,[status(thm)],[1601, 45])).
% 5.53/5.48 tff(1603,plain,
% 5.53/5.48 (succ(succ(succ(succ(Y0!60)))) = succ(n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1602])).
% 5.53/5.48 tff(1604,plain,
% 5.53/5.48 (succ(succ(succ(succ(Y0!60)))) = n10),
% 5.53/5.48 inference(transitivity,[status(thm)],[1603, 28])).
% 5.53/5.48 tff(1605,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1604])).
% 5.53/5.48 tff(1606,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(Y0!60))))) = n0),
% 5.53/5.48 inference(transitivity,[status(thm)],[1605, 42])).
% 5.53/5.48 tff(1607,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n0)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1606])).
% 5.53/5.48 tff(1608,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n1),
% 5.53/5.48 inference(transitivity,[status(thm)],[1607, 58])).
% 5.53/5.48 tff(1609,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n1)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1608])).
% 5.53/5.48 tff(1610,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1609, 36])).
% 5.53/5.48 tff(1611,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1610])).
% 5.53/5.48 tff(1612,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1611, 48])).
% 5.53/5.48 tff(1613,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n3)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1612])).
% 5.53/5.48 tff(1614,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[1613, 14])).
% 5.53/5.48 tff(1615,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1614])).
% 5.53/5.48 tff(1616,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1615, 33])).
% 5.53/5.48 tff(1617,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1616])).
% 5.53/5.48 tff(1618,plain,
% 5.53/5.48 (NSY0!36 = n6),
% 5.53/5.48 inference(transitivity,[status(thm)],[141, 1617, 30])).
% 5.53/5.48 tff(1619,plain,
% 5.53/5.48 (pred(NSY0!36) = pred(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1618])).
% 5.53/5.48 tff(1620,plain,
% 5.53/5.48 (pred(NSY0!36) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1619, 17])).
% 5.53/5.48 tff(1621,plain,
% 5.53/5.48 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n5, n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1620, 1596])).
% 5.53/5.48 tff(1622,plain,
% 5.53/5.48 (sum(pred(NSY0!36), succ(NPY0!38)) = n1),
% 5.53/5.48 inference(transitivity,[status(thm)],[1621, 50])).
% 5.53/5.48 tff(1623,plain,
% 5.53/5.48 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n8, n1)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[169, 1622])).
% 5.53/5.48 tff(1624,plain,
% 5.53/5.48 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n9),
% 5.53/5.48 inference(transitivity,[status(thm)],[1623, 1571])).
% 5.53/5.48 tff(1625,plain,
% 5.53/5.48 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n6, n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[194, 1624])).
% 5.53/5.48 tff(1626,plain,
% 5.53/5.48 (Y1!58 = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[196, 1625, 1570])).
% 5.53/5.48 tff(1627,plain,
% 5.53/5.48 (pred(Y1!58) = pred(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1626])).
% 5.53/5.48 tff(1628,plain,
% 5.53/5.48 (pred(Y1!58) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1627, 15])).
% 5.53/5.48 tff(1629,plain,
% 5.53/5.48 (pred(pred(Y1!58)) = pred(n3)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1628])).
% 5.53/5.48 tff(1630,plain,
% 5.53/5.48 (pred(pred(Y1!58)) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1629, 25])).
% 5.53/5.48 tff(1631,plain,
% 5.53/5.48 (pred(pred(pred(Y1!58))) = pred(n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1630])).
% 5.53/5.48 tff(1632,plain,
% 5.53/5.48 (pred(pred(pred(Y1!58))) = n1),
% 5.53/5.48 inference(transitivity,[status(thm)],[1631, 24])).
% 5.53/5.48 tff(1633,plain,
% 5.53/5.48 (pred(pred(pred(pred(Y1!58)))) = pred(n1)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1632])).
% 5.53/5.48 tff(1634,plain,
% 5.53/5.48 (pred(pred(pred(pred(Y1!58)))) = n0),
% 5.53/5.48 inference(transitivity,[status(thm)],[1633, 23])).
% 5.53/5.48 tff(1635,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n0)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1634])).
% 5.53/5.48 tff(1636,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(Y1!58))))) = n10),
% 5.53/5.48 inference(transitivity,[status(thm)],[1635, 22])).
% 5.53/5.48 tff(1637,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1636])).
% 5.53/5.48 tff(1638,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n9),
% 5.53/5.48 inference(transitivity,[status(thm)],[1637, 21])).
% 5.53/5.48 tff(1639,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1638])).
% 5.53/5.48 tff(1640,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1639, 20])).
% 5.53/5.48 tff(1641,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1640])).
% 5.53/5.48 tff(1642,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1641, 19])).
% 5.53/5.48 tff(1643,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1642])).
% 5.53/5.48 tff(1644,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n6),
% 5.53/5.48 inference(transitivity,[status(thm)],[1643, 18])).
% 5.53/5.48 tff(1645,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1644])).
% 5.53/5.48 tff(1646,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1645, 17])).
% 5.53/5.48 tff(1647,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1646])).
% 5.53/5.48 tff(1648,plain,
% 5.53/5.48 (NPY1!34 = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[232, 1647, 16])).
% 5.53/5.48 tff(1649,plain,
% 5.53/5.48 (succ(NPY1!34) = succ(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1648])).
% 5.53/5.48 tff(1650,plain,
% 5.53/5.48 (succ(NPY1!34) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1649, 33])).
% 5.53/5.48 tff(1651,plain,
% 5.53/5.48 (succ(Y1!58) = succ(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1626])).
% 5.53/5.48 tff(1652,plain,
% 5.53/5.48 (succ(Y1!58) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1651, 33])).
% 5.53/5.48 tff(1653,plain,
% 5.53/5.48 (succ(succ(Y1!58)) = succ(n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1652])).
% 5.53/5.48 tff(1654,plain,
% 5.53/5.48 (succ(succ(Y1!58)) = n6),
% 5.53/5.48 inference(transitivity,[status(thm)],[1653, 30])).
% 5.53/5.48 tff(1655,plain,
% 5.53/5.48 (succ(succ(succ(Y1!58))) = succ(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1654])).
% 5.53/5.48 tff(1656,plain,
% 5.53/5.48 (succ(succ(succ(Y1!58))) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1655, 39])).
% 5.53/5.48 tff(1657,plain,
% 5.53/5.48 (succ(succ(succ(succ(Y1!58)))) = succ(n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1656])).
% 5.53/5.48 tff(1658,plain,
% 5.53/5.48 (succ(succ(succ(succ(Y1!58)))) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1657, 53])).
% 5.53/5.48 tff(1659,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1658])).
% 5.53/5.48 tff(1660,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(Y1!58))))) = n9),
% 5.53/5.48 inference(transitivity,[status(thm)],[1659, 45])).
% 5.53/5.48 tff(1661,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1660])).
% 5.53/5.48 tff(1662,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n10),
% 5.53/5.48 inference(transitivity,[status(thm)],[1661, 28])).
% 5.53/5.48 tff(1663,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1662])).
% 5.53/5.48 tff(1664,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n0),
% 5.53/5.48 inference(transitivity,[status(thm)],[1663, 42])).
% 5.53/5.48 tff(1665,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n0)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1664])).
% 5.53/5.48 tff(1666,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n1),
% 5.53/5.48 inference(transitivity,[status(thm)],[1665, 58])).
% 5.53/5.48 tff(1667,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n1)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1666])).
% 5.53/5.48 tff(1668,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1667, 36])).
% 5.53/5.48 tff(1669,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1668])).
% 5.53/5.48 tff(1670,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1669, 48])).
% 5.53/5.48 tff(1671,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n3)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1670])).
% 5.53/5.48 tff(1672,plain,
% 5.53/5.48 (NSY1!32 = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[255, 1671, 14])).
% 5.53/5.48 tff(1673,plain,
% 5.53/5.48 (pred(NSY1!32) = pred(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1672])).
% 5.53/5.48 tff(1674,plain,
% 5.53/5.48 (pred(NSY1!32) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1673, 15])).
% 5.53/5.48 tff(1675,plain,
% 5.53/5.48 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n3, n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1674, 1650])).
% 5.53/5.48 tff(1676,plain,
% 5.53/5.48 (sum(pred(NSY1!32), succ(NPY1!34)) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1675, 32])).
% 5.53/5.48 tff(1677,plain,
% 5.53/5.48 (sum(pred(Y0!60), succ(X0!61)) = sum(n5, n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1574, 75])).
% 5.53/5.48 tff(1678,plain,
% 5.53/5.48 (sum(pred(Y0!60), succ(X0!61)) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1677, 558])).
% 5.53/5.48 tff(1679,plain,
% 5.53/5.48 (sum(pred(X0!61), succ(Y0!60)) = sum(n6, n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[89, 1598])).
% 5.53/5.48 tff(1680,plain,
% 5.53/5.48 (sum(pred(X0!61), succ(Y0!60)) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1679, 38])).
% 5.53/5.48 tff(1681,plain,
% 5.53/5.48 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n2, n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1680, 1678])).
% 5.53/5.48 tff(1682,plain,
% 5.53/5.48 (X1!59 = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[93, 1681, 34])).
% 5.53/5.48 tff(1683,plain,
% 5.53/5.48 (pred(X1!59) = pred(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1682])).
% 5.53/5.48 tff(1684,plain,
% 5.53/5.48 (pred(X1!59) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1683, 15])).
% 5.53/5.48 tff(1685,plain,
% 5.53/5.48 (pred(pred(X1!59)) = pred(n3)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1684])).
% 5.53/5.48 tff(1686,plain,
% 5.53/5.48 (pred(pred(X1!59)) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1685, 25])).
% 5.53/5.48 tff(1687,plain,
% 5.53/5.48 (pred(pred(pred(X1!59))) = pred(n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1686])).
% 5.53/5.48 tff(1688,plain,
% 5.53/5.48 (pred(pred(pred(X1!59))) = n1),
% 5.53/5.48 inference(transitivity,[status(thm)],[1687, 24])).
% 5.53/5.48 tff(1689,plain,
% 5.53/5.48 (pred(pred(pred(pred(X1!59)))) = pred(n1)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1688])).
% 5.53/5.48 tff(1690,plain,
% 5.53/5.48 (pred(pred(pred(pred(X1!59)))) = n0),
% 5.53/5.48 inference(transitivity,[status(thm)],[1689, 23])).
% 5.53/5.48 tff(1691,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(X1!59))))) = pred(n0)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1690])).
% 5.53/5.48 tff(1692,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(X1!59))))) = n10),
% 5.53/5.48 inference(transitivity,[status(thm)],[1691, 22])).
% 5.53/5.48 tff(1693,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1692])).
% 5.53/5.48 tff(1694,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n9),
% 5.53/5.48 inference(transitivity,[status(thm)],[1693, 21])).
% 5.53/5.48 tff(1695,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1694])).
% 5.53/5.48 tff(1696,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1695, 20])).
% 5.53/5.48 tff(1697,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1696])).
% 5.53/5.48 tff(1698,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1697, 19])).
% 5.53/5.48 tff(1699,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1698])).
% 5.53/5.48 tff(1700,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n6),
% 5.53/5.48 inference(transitivity,[status(thm)],[1699, 18])).
% 5.53/5.48 tff(1701,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1700])).
% 5.53/5.48 tff(1702,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1701, 17])).
% 5.53/5.48 tff(1703,plain,
% 5.53/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1702])).
% 5.53/5.48 tff(1704,plain,
% 5.53/5.48 (NPX1!35 = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[280, 1703, 16])).
% 5.53/5.48 tff(1705,plain,
% 5.53/5.48 (succ(NPX1!35) = succ(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1704])).
% 5.53/5.48 tff(1706,plain,
% 5.53/5.48 (succ(NPX1!35) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1705, 33])).
% 5.53/5.48 tff(1707,plain,
% 5.53/5.48 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n5, n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1706, 1676])).
% 5.53/5.48 tff(1708,plain,
% 5.53/5.48 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1707, 558])).
% 5.53/5.48 tff(1709,plain,
% 5.53/5.48 (succ(X1!59) = succ(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1682])).
% 5.53/5.48 tff(1710,plain,
% 5.53/5.48 (succ(X1!59) = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[1709, 33])).
% 5.53/5.48 tff(1711,plain,
% 5.53/5.48 (succ(succ(X1!59)) = succ(n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1710])).
% 5.53/5.48 tff(1712,plain,
% 5.53/5.48 (succ(succ(X1!59)) = n6),
% 5.53/5.48 inference(transitivity,[status(thm)],[1711, 30])).
% 5.53/5.48 tff(1713,plain,
% 5.53/5.48 (succ(succ(succ(X1!59))) = succ(n6)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1712])).
% 5.53/5.48 tff(1714,plain,
% 5.53/5.48 (succ(succ(succ(X1!59))) = n7),
% 5.53/5.48 inference(transitivity,[status(thm)],[1713, 39])).
% 5.53/5.48 tff(1715,plain,
% 5.53/5.48 (succ(succ(succ(succ(X1!59)))) = succ(n7)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1714])).
% 5.53/5.48 tff(1716,plain,
% 5.53/5.48 (succ(succ(succ(succ(X1!59)))) = n8),
% 5.53/5.48 inference(transitivity,[status(thm)],[1715, 53])).
% 5.53/5.48 tff(1717,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(X1!59))))) = succ(n8)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1716])).
% 5.53/5.48 tff(1718,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(X1!59))))) = n9),
% 5.53/5.48 inference(transitivity,[status(thm)],[1717, 45])).
% 5.53/5.48 tff(1719,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n9)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1718])).
% 5.53/5.48 tff(1720,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n10),
% 5.53/5.48 inference(transitivity,[status(thm)],[1719, 28])).
% 5.53/5.48 tff(1721,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n10)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1720])).
% 5.53/5.48 tff(1722,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n0),
% 5.53/5.48 inference(transitivity,[status(thm)],[1721, 42])).
% 5.53/5.48 tff(1723,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n0)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1722])).
% 5.53/5.48 tff(1724,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n1),
% 5.53/5.48 inference(transitivity,[status(thm)],[1723, 58])).
% 5.53/5.48 tff(1725,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n1)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1724])).
% 5.53/5.48 tff(1726,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n2),
% 5.53/5.48 inference(transitivity,[status(thm)],[1725, 36])).
% 5.53/5.48 tff(1727,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1726])).
% 5.53/5.48 tff(1728,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1727, 48])).
% 5.53/5.48 tff(1729,plain,
% 5.53/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n3)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1728])).
% 5.53/5.48 tff(1730,plain,
% 5.53/5.48 (NSX1!33 = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[305, 1729, 14])).
% 5.53/5.48 tff(1731,plain,
% 5.53/5.48 (pred(NSX1!33) = pred(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1730])).
% 5.53/5.48 tff(1732,plain,
% 5.53/5.48 (pred(NSX1!33) = n3),
% 5.53/5.48 inference(transitivity,[status(thm)],[1731, 15])).
% 5.53/5.48 tff(1733,plain,
% 5.53/5.48 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n3, n2)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1732, 1708])).
% 5.53/5.48 tff(1734,plain,
% 5.53/5.48 (Y2!56 = n5),
% 5.53/5.48 inference(transitivity,[status(thm)],[310, 1733, 557])).
% 5.53/5.48 tff(1735,plain,
% 5.53/5.48 (pred(Y2!56) = pred(n5)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1734])).
% 5.53/5.48 tff(1736,plain,
% 5.53/5.48 (pred(Y2!56) = n4),
% 5.53/5.48 inference(transitivity,[status(thm)],[1735, 16])).
% 5.53/5.48 tff(1737,plain,
% 5.53/5.48 (pred(pred(Y2!56)) = pred(n4)),
% 5.53/5.48 inference(monotonicity,[status(thm)],[1736])).
% 5.55/5.48 tff(1738,plain,
% 5.55/5.48 (pred(pred(Y2!56)) = n3),
% 5.55/5.48 inference(transitivity,[status(thm)],[1737, 15])).
% 5.55/5.48 tff(1739,plain,
% 5.55/5.48 (pred(pred(pred(Y2!56))) = pred(n3)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1738])).
% 5.55/5.48 tff(1740,plain,
% 5.55/5.48 (pred(pred(pred(Y2!56))) = n2),
% 5.55/5.48 inference(transitivity,[status(thm)],[1739, 25])).
% 5.55/5.48 tff(1741,plain,
% 5.55/5.48 (pred(pred(pred(pred(Y2!56)))) = pred(n2)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1740])).
% 5.55/5.48 tff(1742,plain,
% 5.55/5.48 (pred(pred(pred(pred(Y2!56)))) = n1),
% 5.55/5.48 inference(transitivity,[status(thm)],[1741, 24])).
% 5.55/5.48 tff(1743,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n1)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1742])).
% 5.55/5.48 tff(1744,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(Y2!56))))) = n0),
% 5.55/5.48 inference(transitivity,[status(thm)],[1743, 23])).
% 5.55/5.48 tff(1745,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n0)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1744])).
% 5.55/5.48 tff(1746,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n10),
% 5.55/5.48 inference(transitivity,[status(thm)],[1745, 22])).
% 5.55/5.48 tff(1747,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n10)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1746])).
% 5.55/5.48 tff(1748,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n9),
% 5.55/5.48 inference(transitivity,[status(thm)],[1747, 21])).
% 5.55/5.48 tff(1749,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n9)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1748])).
% 5.55/5.48 tff(1750,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n8),
% 5.55/5.48 inference(transitivity,[status(thm)],[1749, 20])).
% 5.55/5.48 tff(1751,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n8)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1750])).
% 5.55/5.48 tff(1752,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n7),
% 5.55/5.48 inference(transitivity,[status(thm)],[1751, 19])).
% 5.55/5.48 tff(1753,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n7)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1752])).
% 5.55/5.48 tff(1754,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n6),
% 5.55/5.48 inference(transitivity,[status(thm)],[1753, 18])).
% 5.55/5.48 tff(1755,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n6)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1754])).
% 5.55/5.48 tff(1756,plain,
% 5.55/5.48 (NPY2!30 = n5),
% 5.55/5.48 inference(transitivity,[status(thm)],[347, 1755, 17])).
% 5.55/5.48 tff(1757,plain,
% 5.55/5.48 (succ(NPY2!30) = succ(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1756])).
% 5.55/5.48 tff(1758,plain,
% 5.55/5.48 (succ(NPY2!30) = n6),
% 5.55/5.48 inference(transitivity,[status(thm)],[1757, 30])).
% 5.55/5.48 tff(1759,plain,
% 5.55/5.48 (succ(Y2!56) = succ(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1734])).
% 5.55/5.48 tff(1760,plain,
% 5.55/5.48 (succ(Y2!56) = n6),
% 5.55/5.48 inference(transitivity,[status(thm)],[1759, 30])).
% 5.55/5.48 tff(1761,plain,
% 5.55/5.48 (succ(succ(Y2!56)) = succ(n6)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1760])).
% 5.55/5.48 tff(1762,plain,
% 5.55/5.48 (succ(succ(Y2!56)) = n7),
% 5.55/5.48 inference(transitivity,[status(thm)],[1761, 39])).
% 5.55/5.48 tff(1763,plain,
% 5.55/5.48 (succ(succ(succ(Y2!56))) = succ(n7)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1762])).
% 5.55/5.48 tff(1764,plain,
% 5.55/5.48 (succ(succ(succ(Y2!56))) = n8),
% 5.55/5.48 inference(transitivity,[status(thm)],[1763, 53])).
% 5.55/5.48 tff(1765,plain,
% 5.55/5.48 (succ(succ(succ(succ(Y2!56)))) = succ(n8)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1764])).
% 5.55/5.48 tff(1766,plain,
% 5.55/5.48 (succ(succ(succ(succ(Y2!56)))) = n9),
% 5.55/5.48 inference(transitivity,[status(thm)],[1765, 45])).
% 5.55/5.48 tff(1767,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n9)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1766])).
% 5.55/5.48 tff(1768,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(Y2!56))))) = n10),
% 5.55/5.48 inference(transitivity,[status(thm)],[1767, 28])).
% 5.55/5.48 tff(1769,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n10)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1768])).
% 5.55/5.48 tff(1770,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n0),
% 5.55/5.48 inference(transitivity,[status(thm)],[1769, 42])).
% 5.55/5.48 tff(1771,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n0)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1770])).
% 5.55/5.48 tff(1772,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n1),
% 5.55/5.48 inference(transitivity,[status(thm)],[1771, 58])).
% 5.55/5.48 tff(1773,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n1)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1772])).
% 5.55/5.48 tff(1774,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n2),
% 5.55/5.48 inference(transitivity,[status(thm)],[1773, 36])).
% 5.55/5.48 tff(1775,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n2)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1774])).
% 5.55/5.48 tff(1776,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n3),
% 5.55/5.48 inference(transitivity,[status(thm)],[1775, 48])).
% 5.55/5.48 tff(1777,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n3)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1776])).
% 5.55/5.48 tff(1778,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n4),
% 5.55/5.48 inference(transitivity,[status(thm)],[1777, 14])).
% 5.55/5.48 tff(1779,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n4)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1778])).
% 5.55/5.48 tff(1780,plain,
% 5.55/5.48 (NSY2!28 = n5),
% 5.55/5.48 inference(transitivity,[status(thm)],[370, 1779, 33])).
% 5.55/5.48 tff(1781,plain,
% 5.55/5.48 (pred(NSY2!28) = pred(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1780])).
% 5.55/5.48 tff(1782,plain,
% 5.55/5.48 (pred(NSY2!28) = n4),
% 5.55/5.48 inference(transitivity,[status(thm)],[1781, 16])).
% 5.55/5.48 tff(1783,plain,
% 5.55/5.48 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n4, n6)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1782, 1758])).
% 5.55/5.48 tff(1784,plain,
% 5.55/5.48 (sum(pred(NSY2!28), succ(NPY2!30)) = n10),
% 5.55/5.48 inference(transitivity,[status(thm)],[1783, 12])).
% 5.55/5.48 tff(1785,plain,
% 5.55/5.48 (sum(pred(Y1!58), succ(X1!59)) = sum(n3, n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1628, 1710])).
% 5.55/5.48 tff(1786,plain,
% 5.55/5.48 (sum(pred(Y1!58), succ(X1!59)) = n8),
% 5.55/5.48 inference(transitivity,[status(thm)],[1785, 32])).
% 5.55/5.48 tff(1787,plain,
% 5.55/5.48 (sum(pred(X1!59), succ(Y1!58)) = sum(n3, n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1684, 1652])).
% 5.55/5.48 tff(1788,plain,
% 5.55/5.48 (sum(pred(X1!59), succ(Y1!58)) = n8),
% 5.55/5.48 inference(transitivity,[status(thm)],[1787, 32])).
% 5.55/5.48 tff(1789,plain,
% 5.55/5.48 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n8, n8)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1788, 1786])).
% 5.55/5.48 tff(1790,plain,
% 5.55/5.48 (X2!57 = n5),
% 5.55/5.48 inference(transitivity,[status(thm)],[209, 1789, 31])).
% 5.55/5.48 tff(1791,plain,
% 5.55/5.48 (pred(X2!57) = pred(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1790])).
% 5.55/5.48 tff(1792,plain,
% 5.55/5.48 (pred(X2!57) = n4),
% 5.55/5.48 inference(transitivity,[status(thm)],[1791, 16])).
% 5.55/5.48 tff(1793,plain,
% 5.55/5.48 (pred(pred(X2!57)) = pred(n4)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1792])).
% 5.55/5.48 tff(1794,plain,
% 5.55/5.48 (pred(pred(X2!57)) = n3),
% 5.55/5.48 inference(transitivity,[status(thm)],[1793, 15])).
% 5.55/5.48 tff(1795,plain,
% 5.55/5.48 (pred(pred(pred(X2!57))) = pred(n3)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1794])).
% 5.55/5.48 tff(1796,plain,
% 5.55/5.48 (pred(pred(pred(X2!57))) = n2),
% 5.55/5.48 inference(transitivity,[status(thm)],[1795, 25])).
% 5.55/5.48 tff(1797,plain,
% 5.55/5.48 (pred(pred(pred(pred(X2!57)))) = pred(n2)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1796])).
% 5.55/5.48 tff(1798,plain,
% 5.55/5.48 (pred(pred(pred(pred(X2!57)))) = n1),
% 5.55/5.48 inference(transitivity,[status(thm)],[1797, 24])).
% 5.55/5.48 tff(1799,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(X2!57))))) = pred(n1)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1798])).
% 5.55/5.48 tff(1800,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(X2!57))))) = n0),
% 5.55/5.48 inference(transitivity,[status(thm)],[1799, 23])).
% 5.55/5.48 tff(1801,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n0)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1800])).
% 5.55/5.48 tff(1802,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n10),
% 5.55/5.48 inference(transitivity,[status(thm)],[1801, 22])).
% 5.55/5.48 tff(1803,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n10)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1802])).
% 5.55/5.48 tff(1804,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n9),
% 5.55/5.48 inference(transitivity,[status(thm)],[1803, 21])).
% 5.55/5.48 tff(1805,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n9)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1804])).
% 5.55/5.48 tff(1806,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n8),
% 5.55/5.48 inference(transitivity,[status(thm)],[1805, 20])).
% 5.55/5.48 tff(1807,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n8)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1806])).
% 5.55/5.48 tff(1808,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n7),
% 5.55/5.48 inference(transitivity,[status(thm)],[1807, 19])).
% 5.55/5.48 tff(1809,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n7)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1808])).
% 5.55/5.48 tff(1810,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n6),
% 5.55/5.48 inference(transitivity,[status(thm)],[1809, 18])).
% 5.55/5.48 tff(1811,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n6)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1810])).
% 5.55/5.48 tff(1812,plain,
% 5.55/5.48 (NPX2!31 = n5),
% 5.55/5.48 inference(transitivity,[status(thm)],[395, 1811, 17])).
% 5.55/5.48 tff(1813,plain,
% 5.55/5.48 (succ(NPX2!31) = succ(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1812])).
% 5.55/5.48 tff(1814,plain,
% 5.55/5.48 (succ(NPX2!31) = n6),
% 5.55/5.48 inference(transitivity,[status(thm)],[1813, 30])).
% 5.55/5.48 tff(1815,plain,
% 5.55/5.48 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n6, n10)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1814, 1784])).
% 5.55/5.48 tff(1816,plain,
% 5.55/5.48 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n5),
% 5.55/5.48 inference(transitivity,[status(thm)],[1815, 674])).
% 5.55/5.48 tff(1817,plain,
% 5.55/5.48 (succ(X2!57) = succ(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1790])).
% 5.55/5.48 tff(1818,plain,
% 5.55/5.48 (succ(X2!57) = n6),
% 5.55/5.48 inference(transitivity,[status(thm)],[1817, 30])).
% 5.55/5.48 tff(1819,plain,
% 5.55/5.48 (succ(succ(X2!57)) = succ(n6)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1818])).
% 5.55/5.48 tff(1820,plain,
% 5.55/5.48 (succ(succ(X2!57)) = n7),
% 5.55/5.48 inference(transitivity,[status(thm)],[1819, 39])).
% 5.55/5.48 tff(1821,plain,
% 5.55/5.48 (succ(succ(succ(X2!57))) = succ(n7)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1820])).
% 5.55/5.48 tff(1822,plain,
% 5.55/5.48 (succ(succ(succ(X2!57))) = n8),
% 5.55/5.48 inference(transitivity,[status(thm)],[1821, 53])).
% 5.55/5.48 tff(1823,plain,
% 5.55/5.48 (succ(succ(succ(succ(X2!57)))) = succ(n8)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1822])).
% 5.55/5.48 tff(1824,plain,
% 5.55/5.48 (succ(succ(succ(succ(X2!57)))) = n9),
% 5.55/5.48 inference(transitivity,[status(thm)],[1823, 45])).
% 5.55/5.48 tff(1825,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(X2!57))))) = succ(n9)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1824])).
% 5.55/5.48 tff(1826,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(X2!57))))) = n10),
% 5.55/5.48 inference(transitivity,[status(thm)],[1825, 28])).
% 5.55/5.48 tff(1827,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n10)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1826])).
% 5.55/5.48 tff(1828,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n0),
% 5.55/5.48 inference(transitivity,[status(thm)],[1827, 42])).
% 5.55/5.48 tff(1829,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n0)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1828])).
% 5.55/5.48 tff(1830,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n1),
% 5.55/5.48 inference(transitivity,[status(thm)],[1829, 58])).
% 5.55/5.48 tff(1831,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n1)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1830])).
% 5.55/5.48 tff(1832,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n2),
% 5.55/5.48 inference(transitivity,[status(thm)],[1831, 36])).
% 5.55/5.48 tff(1833,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n2)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1832])).
% 5.55/5.48 tff(1834,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n3),
% 5.55/5.48 inference(transitivity,[status(thm)],[1833, 48])).
% 5.55/5.48 tff(1835,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n3)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1834])).
% 5.55/5.48 tff(1836,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n4),
% 5.55/5.48 inference(transitivity,[status(thm)],[1835, 14])).
% 5.55/5.48 tff(1837,plain,
% 5.55/5.48 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n4)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1836])).
% 5.55/5.48 tff(1838,plain,
% 5.55/5.48 (NSX2!29 = n5),
% 5.55/5.48 inference(transitivity,[status(thm)],[420, 1837, 33])).
% 5.55/5.48 tff(1839,plain,
% 5.55/5.48 (pred(NSX2!29) = pred(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1838])).
% 5.55/5.48 tff(1840,plain,
% 5.55/5.48 (pred(NSX2!29) = n4),
% 5.55/5.48 inference(transitivity,[status(thm)],[1839, 16])).
% 5.55/5.48 tff(1841,plain,
% 5.55/5.48 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n4, n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1840, 1816])).
% 5.55/5.48 tff(1842,plain,
% 5.55/5.48 (Y3!54 = n9),
% 5.55/5.48 inference(transitivity,[status(thm)],[425, 1841, 673])).
% 5.55/5.48 tff(1843,plain,
% 5.55/5.48 (pred(Y3!54) = pred(n9)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1842])).
% 5.55/5.48 tff(1844,plain,
% 5.55/5.48 (pred(Y3!54) = n8),
% 5.55/5.48 inference(transitivity,[status(thm)],[1843, 20])).
% 5.55/5.48 tff(1845,plain,
% 5.55/5.48 (pred(pred(Y3!54)) = pred(n8)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1844])).
% 5.55/5.48 tff(1846,plain,
% 5.55/5.48 (pred(pred(Y3!54)) = n7),
% 5.55/5.48 inference(transitivity,[status(thm)],[1845, 19])).
% 5.55/5.48 tff(1847,plain,
% 5.55/5.48 (pred(pred(pred(Y3!54))) = pred(n7)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1846])).
% 5.55/5.48 tff(1848,plain,
% 5.55/5.48 (pred(pred(pred(Y3!54))) = n6),
% 5.55/5.48 inference(transitivity,[status(thm)],[1847, 18])).
% 5.55/5.48 tff(1849,plain,
% 5.55/5.48 (pred(pred(pred(pred(Y3!54)))) = pred(n6)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1848])).
% 5.55/5.48 tff(1850,plain,
% 5.55/5.48 (pred(pred(pred(pred(Y3!54)))) = n5),
% 5.55/5.48 inference(transitivity,[status(thm)],[1849, 17])).
% 5.55/5.48 tff(1851,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n5)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1850])).
% 5.55/5.48 tff(1852,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(Y3!54))))) = n4),
% 5.55/5.48 inference(transitivity,[status(thm)],[1851, 16])).
% 5.55/5.48 tff(1853,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n4)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1852])).
% 5.55/5.48 tff(1854,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n3),
% 5.55/5.48 inference(transitivity,[status(thm)],[1853, 15])).
% 5.55/5.48 tff(1855,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n3)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1854])).
% 5.55/5.48 tff(1856,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n2),
% 5.55/5.48 inference(transitivity,[status(thm)],[1855, 25])).
% 5.55/5.48 tff(1857,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n2)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1856])).
% 5.55/5.48 tff(1858,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n1),
% 5.55/5.48 inference(transitivity,[status(thm)],[1857, 24])).
% 5.55/5.48 tff(1859,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n1)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1858])).
% 5.55/5.48 tff(1860,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n0),
% 5.55/5.48 inference(transitivity,[status(thm)],[1859, 23])).
% 5.55/5.48 tff(1861,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n0)),
% 5.55/5.48 inference(monotonicity,[status(thm)],[1860])).
% 5.55/5.48 tff(1862,plain,
% 5.55/5.48 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n10),
% 5.55/5.48 inference(transitivity,[status(thm)],[1861, 22])).
% 5.55/5.49 tff(1863,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1862])).
% 5.55/5.49 tff(1864,plain,
% 5.55/5.49 (NPY3!26 = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[462, 1863, 21])).
% 5.55/5.49 tff(1865,plain,
% 5.55/5.49 (succ(NPY3!26) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1864])).
% 5.55/5.49 tff(1866,plain,
% 5.55/5.49 (succ(NPY3!26) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1865, 28])).
% 5.55/5.49 tff(1867,plain,
% 5.55/5.49 (succ(Y3!54) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1842])).
% 5.55/5.49 tff(1868,plain,
% 5.55/5.49 (succ(Y3!54) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1867, 28])).
% 5.55/5.49 tff(1869,plain,
% 5.55/5.49 (succ(succ(Y3!54)) = succ(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1868])).
% 5.55/5.49 tff(1870,plain,
% 5.55/5.49 (succ(succ(Y3!54)) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[1869, 42])).
% 5.55/5.49 tff(1871,plain,
% 5.55/5.49 (succ(succ(succ(Y3!54))) = succ(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1870])).
% 5.55/5.49 tff(1872,plain,
% 5.55/5.49 (succ(succ(succ(Y3!54))) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[1871, 58])).
% 5.55/5.49 tff(1873,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y3!54)))) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1872])).
% 5.55/5.49 tff(1874,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y3!54)))) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[1873, 36])).
% 5.55/5.49 tff(1875,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1874])).
% 5.55/5.49 tff(1876,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y3!54))))) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[1875, 48])).
% 5.55/5.49 tff(1877,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1876])).
% 5.55/5.49 tff(1878,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[1877, 14])).
% 5.55/5.49 tff(1879,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1878])).
% 5.55/5.49 tff(1880,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[1879, 33])).
% 5.55/5.49 tff(1881,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1880])).
% 5.55/5.49 tff(1882,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[1881, 30])).
% 5.55/5.49 tff(1883,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1882])).
% 5.55/5.49 tff(1884,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[1883, 39])).
% 5.55/5.49 tff(1885,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1884])).
% 5.55/5.49 tff(1886,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[1885, 53])).
% 5.55/5.49 tff(1887,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1886])).
% 5.55/5.49 tff(1888,plain,
% 5.55/5.49 (NSY3!24 = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[485, 1887, 45])).
% 5.55/5.49 tff(1889,plain,
% 5.55/5.49 (pred(NSY3!24) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1888])).
% 5.55/5.49 tff(1890,plain,
% 5.55/5.49 (pred(NSY3!24) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[1889, 20])).
% 5.55/5.49 tff(1891,plain,
% 5.55/5.49 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n8, n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1890, 1866])).
% 5.55/5.49 tff(1892,plain,
% 5.55/5.49 (sum(pred(NSY3!24), succ(NPY3!26)) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[1891, 27])).
% 5.55/5.49 tff(1893,plain,
% 5.55/5.49 (sum(pred(Y2!56), succ(X2!57)) = sum(n4, n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1736, 1818])).
% 5.55/5.49 tff(1894,plain,
% 5.55/5.49 (sum(pred(Y2!56), succ(X2!57)) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1893, 12])).
% 5.55/5.49 tff(1895,plain,
% 5.55/5.49 (sum(pred(X2!57), succ(Y2!56)) = sum(n4, n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1792, 1760])).
% 5.55/5.49 tff(1896,plain,
% 5.55/5.49 (sum(pred(X2!57), succ(Y2!56)) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1895, 12])).
% 5.55/5.49 tff(1897,plain,
% 5.55/5.49 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n10, n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1896, 1894])).
% 5.55/5.49 tff(1898,plain,
% 5.55/5.49 (X3!55 = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[323, 1897, 29])).
% 5.55/5.49 tff(1899,plain,
% 5.55/5.49 (pred(X3!55) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1898])).
% 5.55/5.49 tff(1900,plain,
% 5.55/5.49 (pred(X3!55) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[1899, 20])).
% 5.55/5.49 tff(1901,plain,
% 5.55/5.49 (pred(pred(X3!55)) = pred(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1900])).
% 5.55/5.49 tff(1902,plain,
% 5.55/5.49 (pred(pred(X3!55)) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[1901, 19])).
% 5.55/5.49 tff(1903,plain,
% 5.55/5.49 (pred(pred(pred(X3!55))) = pred(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1902])).
% 5.55/5.49 tff(1904,plain,
% 5.55/5.49 (pred(pred(pred(X3!55))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[1903, 18])).
% 5.55/5.49 tff(1905,plain,
% 5.55/5.49 (pred(pred(pred(pred(X3!55)))) = pred(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1904])).
% 5.55/5.49 tff(1906,plain,
% 5.55/5.49 (pred(pred(pred(pred(X3!55)))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[1905, 17])).
% 5.55/5.49 tff(1907,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(X3!55))))) = pred(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1906])).
% 5.55/5.49 tff(1908,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(X3!55))))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[1907, 16])).
% 5.55/5.49 tff(1909,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1908])).
% 5.55/5.49 tff(1910,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[1909, 15])).
% 5.55/5.49 tff(1911,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1910])).
% 5.55/5.49 tff(1912,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[1911, 25])).
% 5.55/5.49 tff(1913,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1912])).
% 5.55/5.49 tff(1914,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[1913, 24])).
% 5.55/5.49 tff(1915,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1914])).
% 5.55/5.49 tff(1916,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[1915, 23])).
% 5.55/5.49 tff(1917,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1916])).
% 5.55/5.49 tff(1918,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1917, 22])).
% 5.55/5.49 tff(1919,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1918])).
% 5.55/5.49 tff(1920,plain,
% 5.55/5.49 (NPX3!27 = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[510, 1919, 21])).
% 5.55/5.49 tff(1921,plain,
% 5.55/5.49 (succ(NPX3!27) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1920])).
% 5.55/5.49 tff(1922,plain,
% 5.55/5.49 (succ(NPX3!27) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1921, 28])).
% 5.55/5.49 tff(1923,plain,
% 5.55/5.49 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n10, n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1922, 1892])).
% 5.55/5.49 tff(1924,plain,
% 5.55/5.49 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[1923, 69])).
% 5.55/5.49 tff(1925,plain,
% 5.55/5.49 (succ(X3!55) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1898])).
% 5.55/5.49 tff(1926,plain,
% 5.55/5.49 (succ(X3!55) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1925, 28])).
% 5.55/5.49 tff(1927,plain,
% 5.55/5.49 (succ(succ(X3!55)) = succ(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1926])).
% 5.55/5.49 tff(1928,plain,
% 5.55/5.49 (succ(succ(X3!55)) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[1927, 42])).
% 5.55/5.49 tff(1929,plain,
% 5.55/5.49 (succ(succ(succ(X3!55))) = succ(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1928])).
% 5.55/5.49 tff(1930,plain,
% 5.55/5.49 (succ(succ(succ(X3!55))) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[1929, 58])).
% 5.55/5.49 tff(1931,plain,
% 5.55/5.49 (succ(succ(succ(succ(X3!55)))) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1930])).
% 5.55/5.49 tff(1932,plain,
% 5.55/5.49 (succ(succ(succ(succ(X3!55)))) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[1931, 36])).
% 5.55/5.49 tff(1933,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(X3!55))))) = succ(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1932])).
% 5.55/5.49 tff(1934,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(X3!55))))) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[1933, 48])).
% 5.55/5.49 tff(1935,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1934])).
% 5.55/5.49 tff(1936,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[1935, 14])).
% 5.55/5.49 tff(1937,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1936])).
% 5.55/5.49 tff(1938,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[1937, 33])).
% 5.55/5.49 tff(1939,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1938])).
% 5.55/5.49 tff(1940,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[1939, 30])).
% 5.55/5.49 tff(1941,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1940])).
% 5.55/5.49 tff(1942,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[1941, 39])).
% 5.55/5.49 tff(1943,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1942])).
% 5.55/5.49 tff(1944,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[1943, 53])).
% 5.55/5.49 tff(1945,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1944])).
% 5.55/5.49 tff(1946,plain,
% 5.55/5.49 (NSX3!25 = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[535, 1945, 45])).
% 5.55/5.49 tff(1947,plain,
% 5.55/5.49 (pred(NSX3!25) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1946])).
% 5.55/5.49 tff(1948,plain,
% 5.55/5.49 (pred(NSX3!25) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[1947, 20])).
% 5.55/5.49 tff(1949,plain,
% 5.55/5.49 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n8, n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1948, 1924])).
% 5.55/5.49 tff(1950,plain,
% 5.55/5.49 (Y4!52 = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[540, 1949, 98])).
% 5.55/5.49 tff(1951,plain,
% 5.55/5.49 (pred(Y4!52) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1950])).
% 5.55/5.49 tff(1952,plain,
% 5.55/5.49 (pred(Y4!52) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[1951, 25])).
% 5.55/5.49 tff(1953,plain,
% 5.55/5.49 (pred(pred(Y4!52)) = pred(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1952])).
% 5.55/5.49 tff(1954,plain,
% 5.55/5.49 (pred(pred(Y4!52)) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[1953, 24])).
% 5.55/5.49 tff(1955,plain,
% 5.55/5.49 (pred(pred(pred(Y4!52))) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1954])).
% 5.55/5.49 tff(1956,plain,
% 5.55/5.49 (pred(pred(pred(Y4!52))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[1955, 23])).
% 5.55/5.49 tff(1957,plain,
% 5.55/5.49 (pred(pred(pred(pred(Y4!52)))) = pred(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1956])).
% 5.55/5.49 tff(1958,plain,
% 5.55/5.49 (pred(pred(pred(pred(Y4!52)))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1957, 22])).
% 5.55/5.49 tff(1959,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1958])).
% 5.55/5.49 tff(1960,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(Y4!52))))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[1959, 21])).
% 5.55/5.49 tff(1961,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1960])).
% 5.55/5.49 tff(1962,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[1961, 20])).
% 5.55/5.49 tff(1963,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1962])).
% 5.55/5.49 tff(1964,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[1963, 19])).
% 5.55/5.49 tff(1965,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1964])).
% 5.55/5.49 tff(1966,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[1965, 18])).
% 5.55/5.49 tff(1967,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1966])).
% 5.55/5.49 tff(1968,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[1967, 17])).
% 5.55/5.49 tff(1969,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1968])).
% 5.55/5.49 tff(1970,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[1969, 16])).
% 5.55/5.49 tff(1971,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1970])).
% 5.55/5.49 tff(1972,plain,
% 5.55/5.49 (NPY4!22 = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[578, 1971, 15])).
% 5.55/5.49 tff(1973,plain,
% 5.55/5.49 (succ(NPY4!22) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1972])).
% 5.55/5.49 tff(1974,plain,
% 5.55/5.49 (succ(NPY4!22) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[1973, 14])).
% 5.55/5.49 tff(1975,plain,
% 5.55/5.49 (succ(Y4!52) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1950])).
% 5.55/5.49 tff(1976,plain,
% 5.55/5.49 (succ(Y4!52) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[1975, 14])).
% 5.55/5.49 tff(1977,plain,
% 5.55/5.49 (succ(succ(Y4!52)) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1976])).
% 5.55/5.49 tff(1978,plain,
% 5.55/5.49 (succ(succ(Y4!52)) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[1977, 33])).
% 5.55/5.49 tff(1979,plain,
% 5.55/5.49 (succ(succ(succ(Y4!52))) = succ(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1978])).
% 5.55/5.49 tff(1980,plain,
% 5.55/5.49 (succ(succ(succ(Y4!52))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[1979, 30])).
% 5.55/5.49 tff(1981,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y4!52)))) = succ(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1980])).
% 5.55/5.49 tff(1982,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y4!52)))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[1981, 39])).
% 5.55/5.49 tff(1983,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1982])).
% 5.55/5.49 tff(1984,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y4!52))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[1983, 53])).
% 5.55/5.49 tff(1985,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1984])).
% 5.55/5.49 tff(1986,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[1985, 45])).
% 5.55/5.49 tff(1987,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1986])).
% 5.55/5.49 tff(1988,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[1987, 28])).
% 5.55/5.49 tff(1989,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1988])).
% 5.55/5.49 tff(1990,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[1989, 42])).
% 5.55/5.49 tff(1991,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1990])).
% 5.55/5.49 tff(1992,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[1991, 58])).
% 5.55/5.49 tff(1993,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1992])).
% 5.55/5.49 tff(1994,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[1993, 36])).
% 5.55/5.49 tff(1995,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1994])).
% 5.55/5.49 tff(1996,plain,
% 5.55/5.49 (NSY4!20 = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[601, 1995, 48])).
% 5.55/5.49 tff(1997,plain,
% 5.55/5.49 (pred(NSY4!20) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1996])).
% 5.55/5.49 tff(1998,plain,
% 5.55/5.49 (pred(NSY4!20) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[1997, 25])).
% 5.55/5.49 tff(1999,plain,
% 5.55/5.49 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n2, n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1998, 1974])).
% 5.55/5.49 tff(2000,plain,
% 5.55/5.49 (sum(pred(NSY4!20), succ(NPY4!22)) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[1999, 13])).
% 5.55/5.49 tff(2001,plain,
% 5.55/5.49 (sum(pred(Y3!54), succ(X3!55)) = sum(n8, n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1844, 1926])).
% 5.55/5.49 tff(2002,plain,
% 5.55/5.49 (sum(pred(Y3!54), succ(X3!55)) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2001, 27])).
% 5.55/5.49 tff(2003,plain,
% 5.55/5.49 (sum(pred(X3!55), succ(Y3!54)) = sum(n8, n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1900, 1868])).
% 5.55/5.49 tff(2004,plain,
% 5.55/5.49 (sum(pred(X3!55), succ(Y3!54)) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2003, 27])).
% 5.55/5.49 tff(2005,plain,
% 5.55/5.49 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n7, n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2004, 2002])).
% 5.55/5.49 tff(2006,plain,
% 5.55/5.49 (X4!53 = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[438, 2005, 26])).
% 5.55/5.49 tff(2007,plain,
% 5.55/5.49 (pred(X4!53) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2006])).
% 5.55/5.49 tff(2008,plain,
% 5.55/5.49 (pred(X4!53) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2007, 25])).
% 5.55/5.49 tff(2009,plain,
% 5.55/5.49 (pred(pred(X4!53)) = pred(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2008])).
% 5.55/5.49 tff(2010,plain,
% 5.55/5.49 (pred(pred(X4!53)) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[2009, 24])).
% 5.55/5.49 tff(2011,plain,
% 5.55/5.49 (pred(pred(pred(X4!53))) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2010])).
% 5.55/5.49 tff(2012,plain,
% 5.55/5.49 (pred(pred(pred(X4!53))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2011, 23])).
% 5.55/5.49 tff(2013,plain,
% 5.55/5.49 (pred(pred(pred(pred(X4!53)))) = pred(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2012])).
% 5.55/5.49 tff(2014,plain,
% 5.55/5.49 (pred(pred(pred(pred(X4!53)))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2013, 22])).
% 5.55/5.49 tff(2015,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(X4!53))))) = pred(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2014])).
% 5.55/5.49 tff(2016,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(X4!53))))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[2015, 21])).
% 5.55/5.49 tff(2017,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2016])).
% 5.55/5.49 tff(2018,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2017, 20])).
% 5.55/5.49 tff(2019,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2018])).
% 5.55/5.49 tff(2020,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2019, 19])).
% 5.55/5.49 tff(2021,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2020])).
% 5.55/5.49 tff(2022,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2021, 18])).
% 5.55/5.49 tff(2023,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2022])).
% 5.55/5.49 tff(2024,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2023, 17])).
% 5.55/5.49 tff(2025,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2024])).
% 5.55/5.49 tff(2026,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2025, 16])).
% 5.55/5.49 tff(2027,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2026])).
% 5.55/5.49 tff(2028,plain,
% 5.55/5.49 (NPX4!23 = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[626, 2027, 15])).
% 5.55/5.49 tff(2029,plain,
% 5.55/5.49 (succ(NPX4!23) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2028])).
% 5.55/5.49 tff(2030,plain,
% 5.55/5.49 (succ(NPX4!23) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2029, 14])).
% 5.55/5.49 tff(2031,plain,
% 5.55/5.49 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n4, n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2030, 2000])).
% 5.55/5.49 tff(2032,plain,
% 5.55/5.49 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2031, 12])).
% 5.55/5.49 tff(2033,plain,
% 5.55/5.49 (succ(X4!53) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2006])).
% 5.55/5.49 tff(2034,plain,
% 5.55/5.49 (succ(X4!53) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2033, 14])).
% 5.55/5.49 tff(2035,plain,
% 5.55/5.49 (succ(succ(X4!53)) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2034])).
% 5.55/5.49 tff(2036,plain,
% 5.55/5.49 (succ(succ(X4!53)) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2035, 33])).
% 5.55/5.49 tff(2037,plain,
% 5.55/5.49 (succ(succ(succ(X4!53))) = succ(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2036])).
% 5.55/5.49 tff(2038,plain,
% 5.55/5.49 (succ(succ(succ(X4!53))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2037, 30])).
% 5.55/5.49 tff(2039,plain,
% 5.55/5.49 (succ(succ(succ(succ(X4!53)))) = succ(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2038])).
% 5.55/5.49 tff(2040,plain,
% 5.55/5.49 (succ(succ(succ(succ(X4!53)))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2039, 39])).
% 5.55/5.49 tff(2041,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(X4!53))))) = succ(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2040])).
% 5.55/5.49 tff(2042,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(X4!53))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2041, 53])).
% 5.55/5.49 tff(2043,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2042])).
% 5.55/5.49 tff(2044,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[2043, 45])).
% 5.55/5.49 tff(2045,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2044])).
% 5.55/5.49 tff(2046,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2045, 28])).
% 5.55/5.49 tff(2047,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2046])).
% 5.55/5.49 tff(2048,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2047, 42])).
% 5.55/5.49 tff(2049,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2048])).
% 5.55/5.49 tff(2050,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[2049, 58])).
% 5.55/5.49 tff(2051,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2050])).
% 5.55/5.49 tff(2052,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2051, 36])).
% 5.55/5.49 tff(2053,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2052])).
% 5.55/5.49 tff(2054,plain,
% 5.55/5.49 (NSX4!21 = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[651, 2053, 48])).
% 5.55/5.49 tff(2055,plain,
% 5.55/5.49 (pred(NSX4!21) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2054])).
% 5.55/5.49 tff(2056,plain,
% 5.55/5.49 (pred(NSX4!21) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2055, 25])).
% 5.55/5.49 tff(2057,plain,
% 5.55/5.49 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n2, n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2056, 2032])).
% 5.55/5.49 tff(2058,plain,
% 5.55/5.49 (Y5!50 = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[656, 2057, 327])).
% 5.55/5.49 tff(2059,plain,
% 5.55/5.49 (pred(Y5!50) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2058])).
% 5.55/5.49 tff(2060,plain,
% 5.55/5.49 (pred(Y5!50) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2059, 23])).
% 5.55/5.49 tff(2061,plain,
% 5.55/5.49 (pred(pred(Y5!50)) = pred(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2060])).
% 5.55/5.49 tff(2062,plain,
% 5.55/5.49 (pred(pred(Y5!50)) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2061, 22])).
% 5.55/5.49 tff(2063,plain,
% 5.55/5.49 (pred(pred(pred(Y5!50))) = pred(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2062])).
% 5.55/5.49 tff(2064,plain,
% 5.55/5.49 (pred(pred(pred(Y5!50))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[2063, 21])).
% 5.55/5.49 tff(2065,plain,
% 5.55/5.49 (pred(pred(pred(pred(Y5!50)))) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2064])).
% 5.55/5.49 tff(2066,plain,
% 5.55/5.49 (pred(pred(pred(pred(Y5!50)))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2065, 20])).
% 5.55/5.49 tff(2067,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2066])).
% 5.55/5.49 tff(2068,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(Y5!50))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2067, 19])).
% 5.55/5.49 tff(2069,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2068])).
% 5.55/5.49 tff(2070,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2069, 18])).
% 5.55/5.49 tff(2071,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2070])).
% 5.55/5.49 tff(2072,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2071, 17])).
% 5.55/5.49 tff(2073,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2072])).
% 5.55/5.49 tff(2074,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2073, 16])).
% 5.55/5.49 tff(2075,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2074])).
% 5.55/5.49 tff(2076,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[2075, 15])).
% 5.55/5.49 tff(2077,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2076])).
% 5.55/5.49 tff(2078,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2077, 25])).
% 5.55/5.49 tff(2079,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2078])).
% 5.55/5.49 tff(2080,plain,
% 5.55/5.49 (NPY5!18 = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[694, 2079, 24])).
% 5.55/5.49 tff(2081,plain,
% 5.55/5.49 (succ(NPY5!18) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2080])).
% 5.55/5.49 tff(2082,plain,
% 5.55/5.49 (succ(NPY5!18) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2081, 36])).
% 5.55/5.49 tff(2083,plain,
% 5.55/5.49 (succ(Y5!50) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2058])).
% 5.55/5.49 tff(2084,plain,
% 5.55/5.49 (succ(Y5!50) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2083, 36])).
% 5.55/5.49 tff(2085,plain,
% 5.55/5.49 (succ(succ(Y5!50)) = succ(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2084])).
% 5.55/5.49 tff(2086,plain,
% 5.55/5.49 (succ(succ(Y5!50)) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[2085, 48])).
% 5.55/5.49 tff(2087,plain,
% 5.55/5.49 (succ(succ(succ(Y5!50))) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2086])).
% 5.55/5.49 tff(2088,plain,
% 5.55/5.49 (succ(succ(succ(Y5!50))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2087, 14])).
% 5.55/5.49 tff(2089,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y5!50)))) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2088])).
% 5.55/5.49 tff(2090,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y5!50)))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2089, 33])).
% 5.55/5.49 tff(2091,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2090])).
% 5.55/5.49 tff(2092,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y5!50))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2091, 30])).
% 5.55/5.49 tff(2093,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2092])).
% 5.55/5.49 tff(2094,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2093, 39])).
% 5.55/5.49 tff(2095,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2094])).
% 5.55/5.49 tff(2096,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2095, 53])).
% 5.55/5.49 tff(2097,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2096])).
% 5.55/5.49 tff(2098,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[2097, 45])).
% 5.55/5.49 tff(2099,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2098])).
% 5.55/5.49 tff(2100,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2099, 28])).
% 5.55/5.49 tff(2101,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2100])).
% 5.55/5.49 tff(2102,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2101, 42])).
% 5.55/5.49 tff(2103,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2102])).
% 5.55/5.49 tff(2104,plain,
% 5.55/5.49 (NSY5!16 = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[717, 2103, 58])).
% 5.55/5.49 tff(2105,plain,
% 5.55/5.49 (pred(NSY5!16) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2104])).
% 5.55/5.49 tff(2106,plain,
% 5.55/5.49 (pred(NSY5!16) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2105, 23])).
% 5.55/5.49 tff(2107,plain,
% 5.55/5.49 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n0, n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2106, 2082])).
% 5.55/5.49 tff(2108,plain,
% 5.55/5.49 (sum(pred(NSY5!16), succ(NPY5!18)) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2107, 35])).
% 5.55/5.49 tff(2109,plain,
% 5.55/5.49 (sum(pred(Y4!52), succ(X4!53)) = sum(n2, n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[1952, 2034])).
% 5.55/5.49 tff(2110,plain,
% 5.55/5.49 (sum(pred(Y4!52), succ(X4!53)) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2109, 13])).
% 5.55/5.49 tff(2111,plain,
% 5.55/5.49 (sum(pred(X4!53), succ(Y4!52)) = sum(n2, n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2008, 1976])).
% 5.55/5.49 tff(2112,plain,
% 5.55/5.49 (sum(pred(X4!53), succ(Y4!52)) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2111, 13])).
% 5.55/5.49 tff(2113,plain,
% 5.55/5.49 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n6, n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2112, 2110])).
% 5.55/5.49 tff(2114,plain,
% 5.55/5.49 (X5!51 = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[553, 2113, 37])).
% 5.55/5.49 tff(2115,plain,
% 5.55/5.49 (pred(X5!51) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2114])).
% 5.55/5.49 tff(2116,plain,
% 5.55/5.49 (pred(X5!51) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2115, 23])).
% 5.55/5.49 tff(2117,plain,
% 5.55/5.49 (pred(pred(X5!51)) = pred(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2116])).
% 5.55/5.49 tff(2118,plain,
% 5.55/5.49 (pred(pred(X5!51)) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2117, 22])).
% 5.55/5.49 tff(2119,plain,
% 5.55/5.49 (pred(pred(pred(X5!51))) = pred(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2118])).
% 5.55/5.49 tff(2120,plain,
% 5.55/5.49 (pred(pred(pred(X5!51))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[2119, 21])).
% 5.55/5.49 tff(2121,plain,
% 5.55/5.49 (pred(pred(pred(pred(X5!51)))) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2120])).
% 5.55/5.49 tff(2122,plain,
% 5.55/5.49 (pred(pred(pred(pred(X5!51)))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2121, 20])).
% 5.55/5.49 tff(2123,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(X5!51))))) = pred(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2122])).
% 5.55/5.49 tff(2124,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(X5!51))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2123, 19])).
% 5.55/5.49 tff(2125,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2124])).
% 5.55/5.49 tff(2126,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2125, 18])).
% 5.55/5.49 tff(2127,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2126])).
% 5.55/5.49 tff(2128,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2127, 17])).
% 5.55/5.49 tff(2129,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2128])).
% 5.55/5.49 tff(2130,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2129, 16])).
% 5.55/5.49 tff(2131,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2130])).
% 5.55/5.49 tff(2132,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[2131, 15])).
% 5.55/5.49 tff(2133,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2132])).
% 5.55/5.49 tff(2134,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2133, 25])).
% 5.55/5.49 tff(2135,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2134])).
% 5.55/5.49 tff(2136,plain,
% 5.55/5.49 (NPX5!19 = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[742, 2135, 24])).
% 5.55/5.49 tff(2137,plain,
% 5.55/5.49 (succ(NPX5!19) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2136])).
% 5.55/5.49 tff(2138,plain,
% 5.55/5.49 (succ(NPX5!19) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2137, 36])).
% 5.55/5.49 tff(2139,plain,
% 5.55/5.49 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n2, n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2138, 2108])).
% 5.55/5.49 tff(2140,plain,
% 5.55/5.49 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2139, 34])).
% 5.55/5.49 tff(2141,plain,
% 5.55/5.49 (succ(X5!51) = succ(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2114])).
% 5.55/5.49 tff(2142,plain,
% 5.55/5.49 (succ(X5!51) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2141, 36])).
% 5.55/5.49 tff(2143,plain,
% 5.55/5.49 (succ(succ(X5!51)) = succ(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2142])).
% 5.55/5.49 tff(2144,plain,
% 5.55/5.49 (succ(succ(X5!51)) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[2143, 48])).
% 5.55/5.49 tff(2145,plain,
% 5.55/5.49 (succ(succ(succ(X5!51))) = succ(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2144])).
% 5.55/5.49 tff(2146,plain,
% 5.55/5.49 (succ(succ(succ(X5!51))) = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[2145, 14])).
% 5.55/5.49 tff(2147,plain,
% 5.55/5.49 (succ(succ(succ(succ(X5!51)))) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2146])).
% 5.55/5.49 tff(2148,plain,
% 5.55/5.49 (succ(succ(succ(succ(X5!51)))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2147, 33])).
% 5.55/5.49 tff(2149,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(X5!51))))) = succ(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2148])).
% 5.55/5.49 tff(2150,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(X5!51))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2149, 30])).
% 5.55/5.49 tff(2151,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2150])).
% 5.55/5.49 tff(2152,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2151, 39])).
% 5.55/5.49 tff(2153,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2152])).
% 5.55/5.49 tff(2154,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2153, 53])).
% 5.55/5.49 tff(2155,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2154])).
% 5.55/5.49 tff(2156,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[2155, 45])).
% 5.55/5.49 tff(2157,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2156])).
% 5.55/5.49 tff(2158,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2157, 28])).
% 5.55/5.49 tff(2159,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2158])).
% 5.55/5.49 tff(2160,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2159, 42])).
% 5.55/5.49 tff(2161,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2160])).
% 5.55/5.49 tff(2162,plain,
% 5.55/5.49 (NSX5!17 = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[767, 2161, 58])).
% 5.55/5.49 tff(2163,plain,
% 5.55/5.49 (pred(NSX5!17) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2162])).
% 5.55/5.49 tff(2164,plain,
% 5.55/5.49 (pred(NSX5!17) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2163, 23])).
% 5.55/5.49 tff(2165,plain,
% 5.55/5.49 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n0, n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2164, 2140])).
% 5.55/5.49 tff(2166,plain,
% 5.55/5.49 (Y6!48 = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[772, 2165, 442])).
% 5.55/5.49 tff(2167,plain,
% 5.55/5.49 (pred(Y6!48) = pred(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2166])).
% 5.55/5.49 tff(2168,plain,
% 5.55/5.49 (pred(Y6!48) = n3),
% 5.55/5.49 inference(transitivity,[status(thm)],[2167, 15])).
% 5.55/5.49 tff(2169,plain,
% 5.55/5.49 (pred(pred(Y6!48)) = pred(n3)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2168])).
% 5.55/5.49 tff(2170,plain,
% 5.55/5.49 (pred(pred(Y6!48)) = n2),
% 5.55/5.49 inference(transitivity,[status(thm)],[2169, 25])).
% 5.55/5.49 tff(2171,plain,
% 5.55/5.49 (pred(pred(pred(Y6!48))) = pred(n2)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2170])).
% 5.55/5.49 tff(2172,plain,
% 5.55/5.49 (pred(pred(pred(Y6!48))) = n1),
% 5.55/5.49 inference(transitivity,[status(thm)],[2171, 24])).
% 5.55/5.49 tff(2173,plain,
% 5.55/5.49 (pred(pred(pred(pred(Y6!48)))) = pred(n1)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2172])).
% 5.55/5.49 tff(2174,plain,
% 5.55/5.49 (pred(pred(pred(pred(Y6!48)))) = n0),
% 5.55/5.49 inference(transitivity,[status(thm)],[2173, 23])).
% 5.55/5.49 tff(2175,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n0)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2174])).
% 5.55/5.49 tff(2176,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(Y6!48))))) = n10),
% 5.55/5.49 inference(transitivity,[status(thm)],[2175, 22])).
% 5.55/5.49 tff(2177,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n10)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2176])).
% 5.55/5.49 tff(2178,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n9),
% 5.55/5.49 inference(transitivity,[status(thm)],[2177, 21])).
% 5.55/5.49 tff(2179,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n9)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2178])).
% 5.55/5.49 tff(2180,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2179, 20])).
% 5.55/5.49 tff(2181,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2180])).
% 5.55/5.49 tff(2182,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2181, 19])).
% 5.55/5.49 tff(2183,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2182])).
% 5.55/5.49 tff(2184,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2183, 18])).
% 5.55/5.49 tff(2185,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2184])).
% 5.55/5.49 tff(2186,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2185, 17])).
% 5.55/5.49 tff(2187,plain,
% 5.55/5.49 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2186])).
% 5.55/5.49 tff(2188,plain,
% 5.55/5.49 (NPY6!14 = n4),
% 5.55/5.49 inference(transitivity,[status(thm)],[1465, 2187, 16])).
% 5.55/5.49 tff(2189,plain,
% 5.55/5.49 (succ(NPY6!14) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2188])).
% 5.55/5.49 tff(2190,plain,
% 5.55/5.49 (succ(NPY6!14) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2189, 33])).
% 5.55/5.49 tff(2191,plain,
% 5.55/5.49 (succ(Y6!48) = succ(n4)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2166])).
% 5.55/5.49 tff(2192,plain,
% 5.55/5.49 (succ(Y6!48) = n5),
% 5.55/5.49 inference(transitivity,[status(thm)],[2191, 33])).
% 5.55/5.49 tff(2193,plain,
% 5.55/5.49 (succ(succ(Y6!48)) = succ(n5)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2192])).
% 5.55/5.49 tff(2194,plain,
% 5.55/5.49 (succ(succ(Y6!48)) = n6),
% 5.55/5.49 inference(transitivity,[status(thm)],[2193, 30])).
% 5.55/5.49 tff(2195,plain,
% 5.55/5.49 (succ(succ(succ(Y6!48))) = succ(n6)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2194])).
% 5.55/5.49 tff(2196,plain,
% 5.55/5.49 (succ(succ(succ(Y6!48))) = n7),
% 5.55/5.49 inference(transitivity,[status(thm)],[2195, 39])).
% 5.55/5.49 tff(2197,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y6!48)))) = succ(n7)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2196])).
% 5.55/5.49 tff(2198,plain,
% 5.55/5.49 (succ(succ(succ(succ(Y6!48)))) = n8),
% 5.55/5.49 inference(transitivity,[status(thm)],[2197, 53])).
% 5.55/5.49 tff(2199,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n8)),
% 5.55/5.49 inference(monotonicity,[status(thm)],[2198])).
% 5.55/5.49 tff(2200,plain,
% 5.55/5.49 (succ(succ(succ(succ(succ(Y6!48))))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2199, 45])).
% 5.55/5.50 tff(2201,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2200])).
% 5.55/5.50 tff(2202,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2201, 28])).
% 5.55/5.50 tff(2203,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2202])).
% 5.55/5.50 tff(2204,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2203, 42])).
% 5.55/5.50 tff(2205,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2204])).
% 5.55/5.50 tff(2206,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2205, 58])).
% 5.55/5.50 tff(2207,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2206])).
% 5.55/5.50 tff(2208,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2207, 36])).
% 5.55/5.50 tff(2209,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2208])).
% 5.55/5.50 tff(2210,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2209, 48])).
% 5.55/5.50 tff(2211,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2210])).
% 5.55/5.50 tff(2212,plain,
% 5.55/5.50 (NSY6!12 = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[1490, 2211, 14])).
% 5.55/5.50 tff(2213,plain,
% 5.55/5.50 (pred(NSY6!12) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2212])).
% 5.55/5.50 tff(2214,plain,
% 5.55/5.50 (pred(NSY6!12) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2213, 15])).
% 5.55/5.50 tff(2215,plain,
% 5.55/5.50 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n3, n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2214, 2190])).
% 5.55/5.50 tff(2216,plain,
% 5.55/5.50 (sum(pred(NSY6!12), succ(NPY6!14)) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2215, 32])).
% 5.55/5.50 tff(2217,plain,
% 5.55/5.50 (sum(pred(Y5!50), succ(X5!51)) = sum(n0, n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2060, 2142])).
% 5.55/5.50 tff(2218,plain,
% 5.55/5.50 (sum(pred(Y5!50), succ(X5!51)) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2217, 35])).
% 5.55/5.50 tff(2219,plain,
% 5.55/5.50 (sum(pred(X5!51), succ(Y5!50)) = sum(n0, n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2116, 2084])).
% 5.55/5.50 tff(2220,plain,
% 5.55/5.50 (sum(pred(X5!51), succ(Y5!50)) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2219, 35])).
% 5.55/5.50 tff(2221,plain,
% 5.55/5.50 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n2, n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2220, 2218])).
% 5.55/5.50 tff(2222,plain,
% 5.55/5.50 (X6!49 = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[669, 2221, 34])).
% 5.55/5.50 tff(2223,plain,
% 5.55/5.50 (pred(X6!49) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2222])).
% 5.55/5.50 tff(2224,plain,
% 5.55/5.50 (pred(X6!49) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2223, 15])).
% 5.55/5.50 tff(2225,plain,
% 5.55/5.50 (pred(pred(X6!49)) = pred(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2224])).
% 5.55/5.50 tff(2226,plain,
% 5.55/5.50 (pred(pred(X6!49)) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2225, 25])).
% 5.55/5.50 tff(2227,plain,
% 5.55/5.50 (pred(pred(pred(X6!49))) = pred(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2226])).
% 5.55/5.50 tff(2228,plain,
% 5.55/5.50 (pred(pred(pred(X6!49))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2227, 24])).
% 5.55/5.50 tff(2229,plain,
% 5.55/5.50 (pred(pred(pred(pred(X6!49)))) = pred(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2228])).
% 5.55/5.50 tff(2230,plain,
% 5.55/5.50 (pred(pred(pred(pred(X6!49)))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2229, 23])).
% 5.55/5.50 tff(2231,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(X6!49))))) = pred(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2230])).
% 5.55/5.50 tff(2232,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(X6!49))))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2231, 22])).
% 5.55/5.50 tff(2233,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2232])).
% 5.55/5.50 tff(2234,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2233, 21])).
% 5.55/5.50 tff(2235,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2234])).
% 5.55/5.50 tff(2236,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2235, 20])).
% 5.55/5.50 tff(2237,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2236])).
% 5.55/5.50 tff(2238,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2237, 19])).
% 5.55/5.50 tff(2239,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2238])).
% 5.55/5.50 tff(2240,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2239, 18])).
% 5.55/5.50 tff(2241,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2240])).
% 5.55/5.50 tff(2242,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2241, 17])).
% 5.55/5.50 tff(2243,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2242])).
% 5.55/5.50 tff(2244,plain,
% 5.55/5.50 (NPX6!15 = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[1523, 2243, 16])).
% 5.55/5.50 tff(2245,plain,
% 5.55/5.50 (succ(NPX6!15) = succ(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2244])).
% 5.55/5.50 tff(2246,plain,
% 5.55/5.50 (succ(NPX6!15) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2245, 33])).
% 5.55/5.50 tff(2247,plain,
% 5.55/5.50 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n5, n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2246, 2216])).
% 5.55/5.50 tff(2248,plain,
% 5.55/5.50 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2247, 558])).
% 5.55/5.50 tff(2249,plain,
% 5.55/5.50 (succ(X6!49) = succ(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2222])).
% 5.55/5.50 tff(2250,plain,
% 5.55/5.50 (succ(X6!49) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2249, 33])).
% 5.55/5.50 tff(2251,plain,
% 5.55/5.50 (succ(succ(X6!49)) = succ(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2250])).
% 5.55/5.50 tff(2252,plain,
% 5.55/5.50 (succ(succ(X6!49)) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2251, 30])).
% 5.55/5.50 tff(2253,plain,
% 5.55/5.50 (succ(succ(succ(X6!49))) = succ(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2252])).
% 5.55/5.50 tff(2254,plain,
% 5.55/5.50 (succ(succ(succ(X6!49))) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2253, 39])).
% 5.55/5.50 tff(2255,plain,
% 5.55/5.50 (succ(succ(succ(succ(X6!49)))) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2254])).
% 5.55/5.50 tff(2256,plain,
% 5.55/5.50 (succ(succ(succ(succ(X6!49)))) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2255, 53])).
% 5.55/5.50 tff(2257,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(X6!49))))) = succ(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2256])).
% 5.55/5.50 tff(2258,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(X6!49))))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2257, 45])).
% 5.55/5.50 tff(2259,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2258])).
% 5.55/5.50 tff(2260,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2259, 28])).
% 5.55/5.50 tff(2261,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2260])).
% 5.55/5.50 tff(2262,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2261, 42])).
% 5.55/5.50 tff(2263,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2262])).
% 5.55/5.50 tff(2264,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2263, 58])).
% 5.55/5.50 tff(2265,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2264])).
% 5.55/5.50 tff(2266,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2265, 36])).
% 5.55/5.50 tff(2267,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2266])).
% 5.55/5.50 tff(2268,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2267, 48])).
% 5.55/5.50 tff(2269,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2268])).
% 5.55/5.50 tff(2270,plain,
% 5.55/5.50 (NSX6!13 = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[1550, 2269, 14])).
% 5.55/5.50 tff(2271,plain,
% 5.55/5.50 (pred(NSX6!13) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2270])).
% 5.55/5.50 tff(2272,plain,
% 5.55/5.50 (pred(NSX6!13) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2271, 15])).
% 5.55/5.50 tff(2273,plain,
% 5.55/5.50 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n3, n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2272, 2248])).
% 5.55/5.50 tff(2274,plain,
% 5.55/5.50 (sum(n3, n2) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.55/5.50 inference(symmetry,[status(thm)],[2273])).
% 5.55/5.50 tff(2275,plain,
% 5.55/5.50 (n5 = sum(n3, n2)),
% 5.55/5.50 inference(symmetry,[status(thm)],[557])).
% 5.55/5.50 tff(2276,plain,
% 5.55/5.50 (sum(pred(Y6!48), succ(X6!49)) = sum(n3, n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2168, 2250])).
% 5.55/5.50 tff(2277,plain,
% 5.55/5.50 (sum(pred(Y6!48), succ(X6!49)) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2276, 32])).
% 5.55/5.50 tff(2278,plain,
% 5.55/5.50 (sum(pred(X6!49), succ(Y6!48)) = sum(n3, n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2224, 2192])).
% 5.55/5.50 tff(2279,plain,
% 5.55/5.50 (sum(pred(X6!49), succ(Y6!48)) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2278, 32])).
% 5.55/5.50 tff(2280,plain,
% 5.55/5.50 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n8, n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2279, 2277])).
% 5.55/5.50 tff(2281,plain,
% 5.55/5.50 (X7!47 = Y7!46),
% 5.55/5.50 inference(transitivity,[status(thm)],[785, 2280, 31, 2275, 2274, 794])).
% 5.55/5.50 tff(2282,plain,
% 5.55/5.50 ($false),
% 5.55/5.50 inference(unit_resolution,[status(thm)],[792, 2281])).
% 5.55/5.50 tff(2283,plain,((~(Y0!60 = n6)) | (X7!47 = Y7!46) | (~(X0!61 = n7))), inference(lemma,lemma(discharge,[]))).
% 5.55/5.50 tff(2284,plain,
% 5.55/5.50 (~(Y0!60 = n6)),
% 5.55/5.50 inference(unit_resolution,[status(thm)],[2283, 73, 792])).
% 5.55/5.50 tff(2285,assumption,(Y0!60 = n7), introduced(assumption)).
% 5.55/5.50 tff(2286,plain,
% 5.55/5.50 (pred(Y0!60) = pred(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2285])).
% 5.55/5.50 tff(2287,plain,
% 5.55/5.50 (pred(Y0!60) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2286, 18])).
% 5.55/5.50 tff(2288,plain,
% 5.55/5.50 (pred(pred(Y0!60)) = pred(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2287])).
% 5.55/5.50 tff(2289,plain,
% 5.55/5.50 (pred(pred(Y0!60)) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2288, 17])).
% 5.55/5.50 tff(2290,plain,
% 5.55/5.50 (pred(pred(pred(Y0!60))) = pred(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2289])).
% 5.55/5.50 tff(2291,plain,
% 5.55/5.50 (pred(pred(pred(Y0!60))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2290, 16])).
% 5.55/5.50 tff(2292,plain,
% 5.55/5.50 (pred(pred(pred(pred(Y0!60)))) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2291])).
% 5.55/5.50 tff(2293,plain,
% 5.55/5.50 (pred(pred(pred(pred(Y0!60)))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2292, 15])).
% 5.55/5.50 tff(2294,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2293])).
% 5.55/5.50 tff(2295,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(Y0!60))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2294, 25])).
% 5.55/5.50 tff(2296,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2295])).
% 5.55/5.50 tff(2297,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2296, 24])).
% 5.55/5.50 tff(2298,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2297])).
% 5.55/5.50 tff(2299,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2298, 23])).
% 5.55/5.50 tff(2300,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2299])).
% 5.55/5.50 tff(2301,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2300, 22])).
% 5.55/5.50 tff(2302,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2301])).
% 5.55/5.50 tff(2303,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2302, 21])).
% 5.55/5.50 tff(2304,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2303])).
% 5.55/5.50 tff(2305,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2304, 20])).
% 5.55/5.50 tff(2306,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2305])).
% 5.55/5.50 tff(2307,plain,
% 5.55/5.50 (NPY0!38 = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[118, 2306, 19])).
% 5.55/5.50 tff(2308,plain,
% 5.55/5.50 (succ(NPY0!38) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2307])).
% 5.55/5.50 tff(2309,plain,
% 5.55/5.50 (succ(NPY0!38) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2308, 53])).
% 5.55/5.50 tff(2310,plain,
% 5.55/5.50 (succ(Y0!60) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2285])).
% 5.55/5.50 tff(2311,plain,
% 5.55/5.50 (succ(Y0!60) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2310, 53])).
% 5.55/5.50 tff(2312,plain,
% 5.55/5.50 (succ(succ(Y0!60)) = succ(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2311])).
% 5.55/5.50 tff(2313,plain,
% 5.55/5.50 (succ(succ(Y0!60)) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2312, 45])).
% 5.55/5.50 tff(2314,plain,
% 5.55/5.50 (succ(succ(succ(Y0!60))) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2313])).
% 5.55/5.50 tff(2315,plain,
% 5.55/5.50 (succ(succ(succ(Y0!60))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2314, 28])).
% 5.55/5.50 tff(2316,plain,
% 5.55/5.50 (succ(succ(succ(succ(Y0!60)))) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2315])).
% 5.55/5.50 tff(2317,plain,
% 5.55/5.50 (succ(succ(succ(succ(Y0!60)))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2316, 42])).
% 5.55/5.50 tff(2318,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2317])).
% 5.55/5.50 tff(2319,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(Y0!60))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2318, 58])).
% 5.55/5.50 tff(2320,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2319])).
% 5.55/5.50 tff(2321,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2320, 36])).
% 5.55/5.50 tff(2322,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2321])).
% 5.55/5.50 tff(2323,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2322, 48])).
% 5.55/5.50 tff(2324,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2323])).
% 5.55/5.50 tff(2325,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2324, 14])).
% 5.55/5.50 tff(2326,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2325])).
% 5.55/5.50 tff(2327,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2326, 33])).
% 5.55/5.50 tff(2328,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2327])).
% 5.55/5.50 tff(2329,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2328, 30])).
% 5.55/5.50 tff(2330,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2329])).
% 5.55/5.50 tff(2331,plain,
% 5.55/5.50 (NSY0!36 = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[141, 2330, 39])).
% 5.55/5.50 tff(2332,plain,
% 5.55/5.50 (pred(NSY0!36) = pred(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2331])).
% 5.55/5.50 tff(2333,plain,
% 5.55/5.50 (pred(NSY0!36) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2332, 18])).
% 5.55/5.50 tff(2334,plain,
% 5.55/5.50 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n6, n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2333, 2309])).
% 5.55/5.50 tff(2335,plain,
% 5.55/5.50 (sum(pred(NSY0!36), succ(NPY0!38)) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2334, 52])).
% 5.55/5.50 tff(2336,plain,
% 5.55/5.50 (sum(n8, n2) = n10),
% 5.55/5.50 inference(and_elim,[status(thm)],[9])).
% 5.55/5.50 tff(2337,plain,
% 5.55/5.50 (sum(n10, n3) = n2),
% 5.55/5.50 inference(and_elim,[status(thm)],[9])).
% 5.55/5.50 tff(2338,assumption,(X0!61 = n9), introduced(assumption)).
% 5.55/5.50 tff(2339,plain,
% 5.55/5.50 (pred(X0!61) = pred(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2338])).
% 5.55/5.50 tff(2340,plain,
% 5.55/5.50 (pred(X0!61) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2339, 20])).
% 5.55/5.50 tff(2341,plain,
% 5.55/5.50 (pred(pred(X0!61)) = pred(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2340])).
% 5.55/5.50 tff(2342,plain,
% 5.55/5.50 (pred(pred(X0!61)) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2341, 19])).
% 5.55/5.50 tff(2343,plain,
% 5.55/5.50 (pred(pred(pred(X0!61))) = pred(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2342])).
% 5.55/5.50 tff(2344,plain,
% 5.55/5.50 (pred(pred(pred(X0!61))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2343, 18])).
% 5.55/5.50 tff(2345,plain,
% 5.55/5.50 (pred(pred(pred(pred(X0!61)))) = pred(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2344])).
% 5.55/5.50 tff(2346,plain,
% 5.55/5.50 (pred(pred(pred(pred(X0!61)))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2345, 17])).
% 5.55/5.50 tff(2347,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(X0!61))))) = pred(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2346])).
% 5.55/5.50 tff(2348,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(X0!61))))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2347, 16])).
% 5.55/5.50 tff(2349,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2348])).
% 5.55/5.50 tff(2350,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2349, 15])).
% 5.55/5.50 tff(2351,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2350])).
% 5.55/5.50 tff(2352,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2351, 25])).
% 5.55/5.50 tff(2353,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2352])).
% 5.55/5.50 tff(2354,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2353, 24])).
% 5.55/5.50 tff(2355,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2354])).
% 5.55/5.50 tff(2356,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2355, 23])).
% 5.55/5.50 tff(2357,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2356])).
% 5.55/5.50 tff(2358,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2357, 22])).
% 5.55/5.50 tff(2359,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2358])).
% 5.55/5.50 tff(2360,plain,
% 5.55/5.50 (NPX0!39 = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[166, 2359, 21])).
% 5.55/5.50 tff(2361,plain,
% 5.55/5.50 (succ(NPX0!39) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2360])).
% 5.55/5.50 tff(2362,plain,
% 5.55/5.50 (succ(NPX0!39) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2361, 28])).
% 5.55/5.50 tff(2363,plain,
% 5.55/5.50 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n10, n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2362, 2335])).
% 5.55/5.50 tff(2364,plain,
% 5.55/5.50 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2363, 2337])).
% 5.55/5.50 tff(2365,plain,
% 5.55/5.50 (succ(X0!61) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2338])).
% 5.55/5.50 tff(2366,plain,
% 5.55/5.50 (succ(X0!61) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2365, 28])).
% 5.55/5.50 tff(2367,plain,
% 5.55/5.50 (succ(succ(X0!61)) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2366])).
% 5.55/5.50 tff(2368,plain,
% 5.55/5.50 (succ(succ(X0!61)) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2367, 42])).
% 5.55/5.50 tff(2369,plain,
% 5.55/5.50 (succ(succ(succ(X0!61))) = succ(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2368])).
% 5.55/5.50 tff(2370,plain,
% 5.55/5.50 (succ(succ(succ(X0!61))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2369, 58])).
% 5.55/5.50 tff(2371,plain,
% 5.55/5.50 (succ(succ(succ(succ(X0!61)))) = succ(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2370])).
% 5.55/5.50 tff(2372,plain,
% 5.55/5.50 (succ(succ(succ(succ(X0!61)))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2371, 36])).
% 5.55/5.50 tff(2373,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(X0!61))))) = succ(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2372])).
% 5.55/5.50 tff(2374,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(X0!61))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2373, 48])).
% 5.55/5.50 tff(2375,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2374])).
% 5.55/5.50 tff(2376,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2375, 14])).
% 5.55/5.50 tff(2377,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2376])).
% 5.55/5.50 tff(2378,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2377, 33])).
% 5.55/5.50 tff(2379,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2378])).
% 5.55/5.50 tff(2380,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2379, 30])).
% 5.55/5.50 tff(2381,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2380])).
% 5.55/5.50 tff(2382,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2381, 39])).
% 5.55/5.50 tff(2383,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2382])).
% 5.55/5.50 tff(2384,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2383, 53])).
% 5.55/5.50 tff(2385,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2384])).
% 5.55/5.50 tff(2386,plain,
% 5.55/5.50 (NSX0!37 = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[191, 2385, 45])).
% 5.55/5.50 tff(2387,plain,
% 5.55/5.50 (pred(NSX0!37) = pred(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2386])).
% 5.55/5.50 tff(2388,plain,
% 5.55/5.50 (pred(NSX0!37) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2387, 20])).
% 5.55/5.50 tff(2389,plain,
% 5.55/5.50 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n8, n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2388, 2364])).
% 5.55/5.50 tff(2390,plain,
% 5.55/5.50 (Y1!58 = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[196, 2389, 2336])).
% 5.55/5.50 tff(2391,plain,
% 5.55/5.50 (pred(Y1!58) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2390])).
% 5.55/5.50 tff(2392,plain,
% 5.55/5.50 (pred(Y1!58) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2391, 21])).
% 5.55/5.50 tff(2393,plain,
% 5.55/5.50 (pred(pred(Y1!58)) = pred(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2392])).
% 5.55/5.50 tff(2394,plain,
% 5.55/5.50 (pred(pred(Y1!58)) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2393, 20])).
% 5.55/5.50 tff(2395,plain,
% 5.55/5.50 (pred(pred(pred(Y1!58))) = pred(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2394])).
% 5.55/5.50 tff(2396,plain,
% 5.55/5.50 (pred(pred(pred(Y1!58))) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2395, 19])).
% 5.55/5.50 tff(2397,plain,
% 5.55/5.50 (pred(pred(pred(pred(Y1!58)))) = pred(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2396])).
% 5.55/5.50 tff(2398,plain,
% 5.55/5.50 (pred(pred(pred(pred(Y1!58)))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2397, 18])).
% 5.55/5.50 tff(2399,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2398])).
% 5.55/5.50 tff(2400,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(Y1!58))))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2399, 17])).
% 5.55/5.50 tff(2401,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2400])).
% 5.55/5.50 tff(2402,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2401, 16])).
% 5.55/5.50 tff(2403,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2402])).
% 5.55/5.50 tff(2404,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2403, 15])).
% 5.55/5.50 tff(2405,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2404])).
% 5.55/5.50 tff(2406,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2405, 25])).
% 5.55/5.50 tff(2407,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2406])).
% 5.55/5.50 tff(2408,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2407, 24])).
% 5.55/5.50 tff(2409,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2408])).
% 5.55/5.50 tff(2410,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2409, 23])).
% 5.55/5.50 tff(2411,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2410])).
% 5.55/5.50 tff(2412,plain,
% 5.55/5.50 (NPY1!34 = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[232, 2411, 22])).
% 5.55/5.50 tff(2413,plain,
% 5.55/5.50 (succ(NPY1!34) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2412])).
% 5.55/5.50 tff(2414,plain,
% 5.55/5.50 (succ(NPY1!34) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2413, 42])).
% 5.55/5.50 tff(2415,plain,
% 5.55/5.50 (succ(Y1!58) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2390])).
% 5.55/5.50 tff(2416,plain,
% 5.55/5.50 (succ(Y1!58) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2415, 42])).
% 5.55/5.50 tff(2417,plain,
% 5.55/5.50 (succ(succ(Y1!58)) = succ(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2416])).
% 5.55/5.50 tff(2418,plain,
% 5.55/5.50 (succ(succ(Y1!58)) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2417, 58])).
% 5.55/5.50 tff(2419,plain,
% 5.55/5.50 (succ(succ(succ(Y1!58))) = succ(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2418])).
% 5.55/5.50 tff(2420,plain,
% 5.55/5.50 (succ(succ(succ(Y1!58))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2419, 36])).
% 5.55/5.50 tff(2421,plain,
% 5.55/5.50 (succ(succ(succ(succ(Y1!58)))) = succ(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2420])).
% 5.55/5.50 tff(2422,plain,
% 5.55/5.50 (succ(succ(succ(succ(Y1!58)))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2421, 48])).
% 5.55/5.50 tff(2423,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2422])).
% 5.55/5.50 tff(2424,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(Y1!58))))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2423, 14])).
% 5.55/5.50 tff(2425,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2424])).
% 5.55/5.50 tff(2426,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2425, 33])).
% 5.55/5.50 tff(2427,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2426])).
% 5.55/5.50 tff(2428,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2427, 30])).
% 5.55/5.50 tff(2429,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2428])).
% 5.55/5.50 tff(2430,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2429, 39])).
% 5.55/5.50 tff(2431,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2430])).
% 5.55/5.50 tff(2432,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2431, 53])).
% 5.55/5.50 tff(2433,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2432])).
% 5.55/5.50 tff(2434,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2433, 45])).
% 5.55/5.50 tff(2435,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2434])).
% 5.55/5.50 tff(2436,plain,
% 5.55/5.50 (NSY1!32 = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[255, 2435, 28])).
% 5.55/5.50 tff(2437,plain,
% 5.55/5.50 (pred(NSY1!32) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2436])).
% 5.55/5.50 tff(2438,plain,
% 5.55/5.50 (pred(NSY1!32) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2437, 21])).
% 5.55/5.50 tff(2439,plain,
% 5.55/5.50 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n9, n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2438, 2414])).
% 5.55/5.50 tff(2440,plain,
% 5.55/5.50 (sum(pred(NSY1!32), succ(NPY1!34)) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2439, 41])).
% 5.55/5.50 tff(2441,plain,
% 5.55/5.50 (sum(pred(Y0!60), succ(X0!61)) = sum(n6, n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2287, 2366])).
% 5.55/5.50 tff(2442,plain,
% 5.55/5.50 (sum(pred(Y0!60), succ(X0!61)) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2441, 674])).
% 5.55/5.50 tff(2443,plain,
% 5.55/5.50 (sum(pred(X0!61), succ(Y0!60)) = sum(n8, n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2340, 2311])).
% 5.55/5.50 tff(2444,plain,
% 5.55/5.50 (sum(pred(X0!61), succ(Y0!60)) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2443, 31])).
% 5.55/5.50 tff(2445,plain,
% 5.55/5.50 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n5, n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2444, 2442])).
% 5.55/5.50 tff(2446,plain,
% 5.55/5.50 (X1!59 = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[93, 2445, 43])).
% 5.55/5.50 tff(2447,plain,
% 5.55/5.50 (pred(X1!59) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2446])).
% 5.55/5.50 tff(2448,plain,
% 5.55/5.50 (pred(X1!59) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2447, 21])).
% 5.55/5.50 tff(2449,plain,
% 5.55/5.50 (pred(pred(X1!59)) = pred(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2448])).
% 5.55/5.50 tff(2450,plain,
% 5.55/5.50 (pred(pred(X1!59)) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2449, 20])).
% 5.55/5.50 tff(2451,plain,
% 5.55/5.50 (pred(pred(pred(X1!59))) = pred(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2450])).
% 5.55/5.50 tff(2452,plain,
% 5.55/5.50 (pred(pred(pred(X1!59))) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2451, 19])).
% 5.55/5.50 tff(2453,plain,
% 5.55/5.50 (pred(pred(pred(pred(X1!59)))) = pred(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2452])).
% 5.55/5.50 tff(2454,plain,
% 5.55/5.50 (pred(pred(pred(pred(X1!59)))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2453, 18])).
% 5.55/5.50 tff(2455,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(X1!59))))) = pred(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2454])).
% 5.55/5.50 tff(2456,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(X1!59))))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2455, 17])).
% 5.55/5.50 tff(2457,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2456])).
% 5.55/5.50 tff(2458,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2457, 16])).
% 5.55/5.50 tff(2459,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2458])).
% 5.55/5.50 tff(2460,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2459, 15])).
% 5.55/5.50 tff(2461,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2460])).
% 5.55/5.50 tff(2462,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2461, 25])).
% 5.55/5.50 tff(2463,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2462])).
% 5.55/5.50 tff(2464,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2463, 24])).
% 5.55/5.50 tff(2465,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2464])).
% 5.55/5.50 tff(2466,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2465, 23])).
% 5.55/5.50 tff(2467,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2466])).
% 5.55/5.50 tff(2468,plain,
% 5.55/5.50 (NPX1!35 = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[280, 2467, 22])).
% 5.55/5.50 tff(2469,plain,
% 5.55/5.50 (succ(NPX1!35) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2468])).
% 5.55/5.50 tff(2470,plain,
% 5.55/5.50 (succ(NPX1!35) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2469, 42])).
% 5.55/5.50 tff(2471,plain,
% 5.55/5.50 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n0, n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2470, 2440])).
% 5.55/5.50 tff(2472,plain,
% 5.55/5.50 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2471, 40])).
% 5.55/5.50 tff(2473,plain,
% 5.55/5.50 (succ(X1!59) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2446])).
% 5.55/5.50 tff(2474,plain,
% 5.55/5.50 (succ(X1!59) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2473, 42])).
% 5.55/5.50 tff(2475,plain,
% 5.55/5.50 (succ(succ(X1!59)) = succ(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2474])).
% 5.55/5.50 tff(2476,plain,
% 5.55/5.50 (succ(succ(X1!59)) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2475, 58])).
% 5.55/5.50 tff(2477,plain,
% 5.55/5.50 (succ(succ(succ(X1!59))) = succ(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2476])).
% 5.55/5.50 tff(2478,plain,
% 5.55/5.50 (succ(succ(succ(X1!59))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2477, 36])).
% 5.55/5.50 tff(2479,plain,
% 5.55/5.50 (succ(succ(succ(succ(X1!59)))) = succ(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2478])).
% 5.55/5.50 tff(2480,plain,
% 5.55/5.50 (succ(succ(succ(succ(X1!59)))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2479, 48])).
% 5.55/5.50 tff(2481,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(X1!59))))) = succ(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2480])).
% 5.55/5.50 tff(2482,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(X1!59))))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2481, 14])).
% 5.55/5.50 tff(2483,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2482])).
% 5.55/5.50 tff(2484,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2483, 33])).
% 5.55/5.50 tff(2485,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2484])).
% 5.55/5.50 tff(2486,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2485, 30])).
% 5.55/5.50 tff(2487,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2486])).
% 5.55/5.50 tff(2488,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[2487, 39])).
% 5.55/5.50 tff(2489,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2488])).
% 5.55/5.50 tff(2490,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2489, 53])).
% 5.55/5.50 tff(2491,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2490])).
% 5.55/5.50 tff(2492,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2491, 45])).
% 5.55/5.50 tff(2493,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2492])).
% 5.55/5.50 tff(2494,plain,
% 5.55/5.50 (NSX1!33 = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[305, 2493, 28])).
% 5.55/5.50 tff(2495,plain,
% 5.55/5.50 (pred(NSX1!33) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2494])).
% 5.55/5.50 tff(2496,plain,
% 5.55/5.50 (pred(NSX1!33) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2495, 21])).
% 5.55/5.50 tff(2497,plain,
% 5.55/5.50 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n9, n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2496, 2472])).
% 5.55/5.50 tff(2498,plain,
% 5.55/5.50 (Y2!56 = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[310, 2497, 54])).
% 5.55/5.50 tff(2499,plain,
% 5.55/5.50 (pred(Y2!56) = pred(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2498])).
% 5.55/5.50 tff(2500,plain,
% 5.55/5.50 (pred(Y2!56) = n6),
% 5.55/5.50 inference(transitivity,[status(thm)],[2499, 18])).
% 5.55/5.50 tff(2501,plain,
% 5.55/5.50 (pred(pred(Y2!56)) = pred(n6)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2500])).
% 5.55/5.50 tff(2502,plain,
% 5.55/5.50 (pred(pred(Y2!56)) = n5),
% 5.55/5.50 inference(transitivity,[status(thm)],[2501, 17])).
% 5.55/5.50 tff(2503,plain,
% 5.55/5.50 (pred(pred(pred(Y2!56))) = pred(n5)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2502])).
% 5.55/5.50 tff(2504,plain,
% 5.55/5.50 (pred(pred(pred(Y2!56))) = n4),
% 5.55/5.50 inference(transitivity,[status(thm)],[2503, 16])).
% 5.55/5.50 tff(2505,plain,
% 5.55/5.50 (pred(pred(pred(pred(Y2!56)))) = pred(n4)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2504])).
% 5.55/5.50 tff(2506,plain,
% 5.55/5.50 (pred(pred(pred(pred(Y2!56)))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2505, 15])).
% 5.55/5.50 tff(2507,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n3)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2506])).
% 5.55/5.50 tff(2508,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(Y2!56))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2507, 25])).
% 5.55/5.50 tff(2509,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2508])).
% 5.55/5.50 tff(2510,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2509, 24])).
% 5.55/5.50 tff(2511,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2510])).
% 5.55/5.50 tff(2512,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2511, 23])).
% 5.55/5.50 tff(2513,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2512])).
% 5.55/5.50 tff(2514,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2513, 22])).
% 5.55/5.50 tff(2515,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2514])).
% 5.55/5.50 tff(2516,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2515, 21])).
% 5.55/5.50 tff(2517,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2516])).
% 5.55/5.50 tff(2518,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2517, 20])).
% 5.55/5.50 tff(2519,plain,
% 5.55/5.50 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2518])).
% 5.55/5.50 tff(2520,plain,
% 5.55/5.50 (NPY2!30 = n7),
% 5.55/5.50 inference(transitivity,[status(thm)],[347, 2519, 19])).
% 5.55/5.50 tff(2521,plain,
% 5.55/5.50 (succ(NPY2!30) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2520])).
% 5.55/5.50 tff(2522,plain,
% 5.55/5.50 (succ(NPY2!30) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2521, 53])).
% 5.55/5.50 tff(2523,plain,
% 5.55/5.50 (succ(Y2!56) = succ(n7)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2498])).
% 5.55/5.50 tff(2524,plain,
% 5.55/5.50 (succ(Y2!56) = n8),
% 5.55/5.50 inference(transitivity,[status(thm)],[2523, 53])).
% 5.55/5.50 tff(2525,plain,
% 5.55/5.50 (succ(succ(Y2!56)) = succ(n8)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2524])).
% 5.55/5.50 tff(2526,plain,
% 5.55/5.50 (succ(succ(Y2!56)) = n9),
% 5.55/5.50 inference(transitivity,[status(thm)],[2525, 45])).
% 5.55/5.50 tff(2527,plain,
% 5.55/5.50 (succ(succ(succ(Y2!56))) = succ(n9)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2526])).
% 5.55/5.50 tff(2528,plain,
% 5.55/5.50 (succ(succ(succ(Y2!56))) = n10),
% 5.55/5.50 inference(transitivity,[status(thm)],[2527, 28])).
% 5.55/5.50 tff(2529,plain,
% 5.55/5.50 (succ(succ(succ(succ(Y2!56)))) = succ(n10)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2528])).
% 5.55/5.50 tff(2530,plain,
% 5.55/5.50 (succ(succ(succ(succ(Y2!56)))) = n0),
% 5.55/5.50 inference(transitivity,[status(thm)],[2529, 42])).
% 5.55/5.50 tff(2531,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n0)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2530])).
% 5.55/5.50 tff(2532,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(Y2!56))))) = n1),
% 5.55/5.50 inference(transitivity,[status(thm)],[2531, 58])).
% 5.55/5.50 tff(2533,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n1)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2532])).
% 5.55/5.50 tff(2534,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n2),
% 5.55/5.50 inference(transitivity,[status(thm)],[2533, 36])).
% 5.55/5.50 tff(2535,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n2)),
% 5.55/5.50 inference(monotonicity,[status(thm)],[2534])).
% 5.55/5.50 tff(2536,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n3),
% 5.55/5.50 inference(transitivity,[status(thm)],[2535, 48])).
% 5.55/5.50 tff(2537,plain,
% 5.55/5.50 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2536])).
% 5.55/5.51 tff(2538,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2537, 14])).
% 5.55/5.51 tff(2539,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2538])).
% 5.55/5.51 tff(2540,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2539, 33])).
% 5.55/5.51 tff(2541,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2540])).
% 5.55/5.51 tff(2542,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[2541, 30])).
% 5.55/5.51 tff(2543,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2542])).
% 5.55/5.51 tff(2544,plain,
% 5.55/5.51 (NSY2!28 = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[370, 2543, 39])).
% 5.55/5.51 tff(2545,plain,
% 5.55/5.51 (pred(NSY2!28) = pred(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2544])).
% 5.55/5.51 tff(2546,plain,
% 5.55/5.51 (pred(NSY2!28) = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[2545, 18])).
% 5.55/5.51 tff(2547,plain,
% 5.55/5.51 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n6, n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2546, 2522])).
% 5.55/5.51 tff(2548,plain,
% 5.55/5.51 (sum(pred(NSY2!28), succ(NPY2!30)) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2547, 52])).
% 5.55/5.51 tff(2549,plain,
% 5.55/5.51 (sum(pred(Y1!58), succ(X1!59)) = sum(n9, n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2392, 2474])).
% 5.55/5.51 tff(2550,plain,
% 5.55/5.51 (sum(pred(Y1!58), succ(X1!59)) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2549, 41])).
% 5.55/5.51 tff(2551,plain,
% 5.55/5.51 (sum(pred(X1!59), succ(Y1!58)) = sum(n9, n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2448, 2416])).
% 5.55/5.51 tff(2552,plain,
% 5.55/5.51 (sum(pred(X1!59), succ(Y1!58)) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2551, 41])).
% 5.55/5.51 tff(2553,plain,
% 5.55/5.51 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n9, n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2552, 2550])).
% 5.55/5.51 tff(2554,plain,
% 5.55/5.51 (X2!57 = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[209, 2553, 54])).
% 5.55/5.51 tff(2555,plain,
% 5.55/5.51 (pred(X2!57) = pred(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2554])).
% 5.55/5.51 tff(2556,plain,
% 5.55/5.51 (pred(X2!57) = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[2555, 18])).
% 5.55/5.51 tff(2557,plain,
% 5.55/5.51 (pred(pred(X2!57)) = pred(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2556])).
% 5.55/5.51 tff(2558,plain,
% 5.55/5.51 (pred(pred(X2!57)) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2557, 17])).
% 5.55/5.51 tff(2559,plain,
% 5.55/5.51 (pred(pred(pred(X2!57))) = pred(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2558])).
% 5.55/5.51 tff(2560,plain,
% 5.55/5.51 (pred(pred(pred(X2!57))) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2559, 16])).
% 5.55/5.51 tff(2561,plain,
% 5.55/5.51 (pred(pred(pred(pred(X2!57)))) = pred(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2560])).
% 5.55/5.51 tff(2562,plain,
% 5.55/5.51 (pred(pred(pred(pred(X2!57)))) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2561, 15])).
% 5.55/5.51 tff(2563,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(X2!57))))) = pred(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2562])).
% 5.55/5.51 tff(2564,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(X2!57))))) = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[2563, 25])).
% 5.55/5.51 tff(2565,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2564])).
% 5.55/5.51 tff(2566,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2565, 24])).
% 5.55/5.51 tff(2567,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2566])).
% 5.55/5.51 tff(2568,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2567, 23])).
% 5.55/5.51 tff(2569,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2568])).
% 5.55/5.51 tff(2570,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2569, 22])).
% 5.55/5.51 tff(2571,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2570])).
% 5.55/5.51 tff(2572,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2571, 21])).
% 5.55/5.51 tff(2573,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2572])).
% 5.55/5.51 tff(2574,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2573, 20])).
% 5.55/5.51 tff(2575,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2574])).
% 5.55/5.51 tff(2576,plain,
% 5.55/5.51 (NPX2!31 = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[395, 2575, 19])).
% 5.55/5.51 tff(2577,plain,
% 5.55/5.51 (succ(NPX2!31) = succ(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2576])).
% 5.55/5.51 tff(2578,plain,
% 5.55/5.51 (succ(NPX2!31) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2577, 53])).
% 5.55/5.51 tff(2579,plain,
% 5.55/5.51 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n8, n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2578, 2548])).
% 5.55/5.51 tff(2580,plain,
% 5.55/5.51 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2579, 64])).
% 5.55/5.51 tff(2581,plain,
% 5.55/5.51 (succ(X2!57) = succ(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2554])).
% 5.55/5.51 tff(2582,plain,
% 5.55/5.51 (succ(X2!57) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2581, 53])).
% 5.55/5.51 tff(2583,plain,
% 5.55/5.51 (succ(succ(X2!57)) = succ(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2582])).
% 5.55/5.51 tff(2584,plain,
% 5.55/5.51 (succ(succ(X2!57)) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2583, 45])).
% 5.55/5.51 tff(2585,plain,
% 5.55/5.51 (succ(succ(succ(X2!57))) = succ(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2584])).
% 5.55/5.51 tff(2586,plain,
% 5.55/5.51 (succ(succ(succ(X2!57))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2585, 28])).
% 5.55/5.51 tff(2587,plain,
% 5.55/5.51 (succ(succ(succ(succ(X2!57)))) = succ(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2586])).
% 5.55/5.51 tff(2588,plain,
% 5.55/5.51 (succ(succ(succ(succ(X2!57)))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2587, 42])).
% 5.55/5.51 tff(2589,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(X2!57))))) = succ(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2588])).
% 5.55/5.51 tff(2590,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(X2!57))))) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2589, 58])).
% 5.55/5.51 tff(2591,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2590])).
% 5.55/5.51 tff(2592,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[2591, 36])).
% 5.55/5.51 tff(2593,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2592])).
% 5.55/5.51 tff(2594,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2593, 48])).
% 5.55/5.51 tff(2595,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2594])).
% 5.55/5.51 tff(2596,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2595, 14])).
% 5.55/5.51 tff(2597,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2596])).
% 5.55/5.51 tff(2598,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2597, 33])).
% 5.55/5.51 tff(2599,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2598])).
% 5.55/5.51 tff(2600,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[2599, 30])).
% 5.55/5.51 tff(2601,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2600])).
% 5.55/5.51 tff(2602,plain,
% 5.55/5.51 (NSX2!29 = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[420, 2601, 39])).
% 5.55/5.51 tff(2603,plain,
% 5.55/5.51 (pred(NSX2!29) = pred(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2602])).
% 5.55/5.51 tff(2604,plain,
% 5.55/5.51 (pred(NSX2!29) = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[2603, 18])).
% 5.55/5.51 tff(2605,plain,
% 5.55/5.51 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n6, n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2604, 2580])).
% 5.55/5.51 tff(2606,plain,
% 5.55/5.51 (Y3!54 = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[425, 2605, 788])).
% 5.55/5.51 tff(2607,plain,
% 5.55/5.51 (pred(Y3!54) = pred(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2606])).
% 5.55/5.51 tff(2608,plain,
% 5.55/5.51 (pred(Y3!54) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2607, 17])).
% 5.55/5.51 tff(2609,plain,
% 5.55/5.51 (pred(pred(Y3!54)) = pred(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2608])).
% 5.55/5.51 tff(2610,plain,
% 5.55/5.51 (pred(pred(Y3!54)) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2609, 16])).
% 5.55/5.51 tff(2611,plain,
% 5.55/5.51 (pred(pred(pred(Y3!54))) = pred(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2610])).
% 5.55/5.51 tff(2612,plain,
% 5.55/5.51 (pred(pred(pred(Y3!54))) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2611, 15])).
% 5.55/5.51 tff(2613,plain,
% 5.55/5.51 (pred(pred(pred(pred(Y3!54)))) = pred(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2612])).
% 5.55/5.51 tff(2614,plain,
% 5.55/5.51 (pred(pred(pred(pred(Y3!54)))) = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[2613, 25])).
% 5.55/5.51 tff(2615,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2614])).
% 5.55/5.51 tff(2616,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(Y3!54))))) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2615, 24])).
% 5.55/5.51 tff(2617,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2616])).
% 5.55/5.51 tff(2618,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2617, 23])).
% 5.55/5.51 tff(2619,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2618])).
% 5.55/5.51 tff(2620,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2619, 22])).
% 5.55/5.51 tff(2621,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2620])).
% 5.55/5.51 tff(2622,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2621, 21])).
% 5.55/5.51 tff(2623,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2622])).
% 5.55/5.51 tff(2624,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2623, 20])).
% 5.55/5.51 tff(2625,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2624])).
% 5.55/5.51 tff(2626,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2625, 19])).
% 5.55/5.51 tff(2627,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2626])).
% 5.55/5.51 tff(2628,plain,
% 5.55/5.51 (NPY3!26 = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[462, 2627, 18])).
% 5.55/5.51 tff(2629,plain,
% 5.55/5.51 (succ(NPY3!26) = succ(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2628])).
% 5.55/5.51 tff(2630,plain,
% 5.55/5.51 (succ(NPY3!26) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2629, 39])).
% 5.55/5.51 tff(2631,plain,
% 5.55/5.51 (succ(Y3!54) = succ(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2606])).
% 5.55/5.51 tff(2632,plain,
% 5.55/5.51 (succ(Y3!54) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2631, 39])).
% 5.55/5.51 tff(2633,plain,
% 5.55/5.51 (succ(succ(Y3!54)) = succ(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2632])).
% 5.55/5.51 tff(2634,plain,
% 5.55/5.51 (succ(succ(Y3!54)) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2633, 53])).
% 5.55/5.51 tff(2635,plain,
% 5.55/5.51 (succ(succ(succ(Y3!54))) = succ(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2634])).
% 5.55/5.51 tff(2636,plain,
% 5.55/5.51 (succ(succ(succ(Y3!54))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2635, 45])).
% 5.55/5.51 tff(2637,plain,
% 5.55/5.51 (succ(succ(succ(succ(Y3!54)))) = succ(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2636])).
% 5.55/5.51 tff(2638,plain,
% 5.55/5.51 (succ(succ(succ(succ(Y3!54)))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2637, 28])).
% 5.55/5.51 tff(2639,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2638])).
% 5.55/5.51 tff(2640,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(Y3!54))))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2639, 42])).
% 5.55/5.51 tff(2641,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2640])).
% 5.55/5.51 tff(2642,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2641, 58])).
% 5.55/5.51 tff(2643,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2642])).
% 5.55/5.51 tff(2644,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[2643, 36])).
% 5.55/5.51 tff(2645,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2644])).
% 5.55/5.51 tff(2646,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2645, 48])).
% 5.55/5.51 tff(2647,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2646])).
% 5.55/5.51 tff(2648,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2647, 14])).
% 5.55/5.51 tff(2649,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2648])).
% 5.55/5.51 tff(2650,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2649, 33])).
% 5.55/5.51 tff(2651,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2650])).
% 5.55/5.51 tff(2652,plain,
% 5.55/5.51 (NSY3!24 = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[485, 2651, 30])).
% 5.55/5.51 tff(2653,plain,
% 5.55/5.51 (pred(NSY3!24) = pred(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2652])).
% 5.55/5.51 tff(2654,plain,
% 5.55/5.51 (pred(NSY3!24) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2653, 17])).
% 5.55/5.51 tff(2655,plain,
% 5.55/5.51 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n5, n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2654, 2630])).
% 5.55/5.51 tff(2656,plain,
% 5.55/5.51 (sum(pred(NSY3!24), succ(NPY3!26)) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2655, 50])).
% 5.55/5.51 tff(2657,plain,
% 5.55/5.51 (sum(pred(Y2!56), succ(X2!57)) = sum(n6, n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2500, 2582])).
% 5.55/5.51 tff(2658,plain,
% 5.55/5.51 (sum(pred(Y2!56), succ(X2!57)) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2657, 52])).
% 5.55/5.51 tff(2659,plain,
% 5.55/5.51 (sum(pred(X2!57), succ(Y2!56)) = sum(n6, n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2556, 2524])).
% 5.55/5.51 tff(2660,plain,
% 5.55/5.51 (sum(pred(X2!57), succ(Y2!56)) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2659, 52])).
% 5.55/5.51 tff(2661,plain,
% 5.55/5.51 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n3, n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2660, 2658])).
% 5.55/5.51 tff(2662,plain,
% 5.55/5.51 (X3!55 = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[323, 2661, 51])).
% 5.55/5.51 tff(2663,plain,
% 5.55/5.51 (pred(X3!55) = pred(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2662])).
% 5.55/5.51 tff(2664,plain,
% 5.55/5.51 (pred(X3!55) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2663, 17])).
% 5.55/5.51 tff(2665,plain,
% 5.55/5.51 (pred(pred(X3!55)) = pred(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2664])).
% 5.55/5.51 tff(2666,plain,
% 5.55/5.51 (pred(pred(X3!55)) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2665, 16])).
% 5.55/5.51 tff(2667,plain,
% 5.55/5.51 (pred(pred(pred(X3!55))) = pred(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2666])).
% 5.55/5.51 tff(2668,plain,
% 5.55/5.51 (pred(pred(pred(X3!55))) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2667, 15])).
% 5.55/5.51 tff(2669,plain,
% 5.55/5.51 (pred(pred(pred(pred(X3!55)))) = pred(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2668])).
% 5.55/5.51 tff(2670,plain,
% 5.55/5.51 (pred(pred(pred(pred(X3!55)))) = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[2669, 25])).
% 5.55/5.51 tff(2671,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(X3!55))))) = pred(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2670])).
% 5.55/5.51 tff(2672,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(X3!55))))) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2671, 24])).
% 5.55/5.51 tff(2673,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2672])).
% 5.55/5.51 tff(2674,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2673, 23])).
% 5.55/5.51 tff(2675,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2674])).
% 5.55/5.51 tff(2676,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2675, 22])).
% 5.55/5.51 tff(2677,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2676])).
% 5.55/5.51 tff(2678,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2677, 21])).
% 5.55/5.51 tff(2679,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2678])).
% 5.55/5.51 tff(2680,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2679, 20])).
% 5.55/5.51 tff(2681,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2680])).
% 5.55/5.51 tff(2682,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2681, 19])).
% 5.55/5.51 tff(2683,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2682])).
% 5.55/5.51 tff(2684,plain,
% 5.55/5.51 (NPX3!27 = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[510, 2683, 18])).
% 5.55/5.51 tff(2685,plain,
% 5.55/5.51 (succ(NPX3!27) = succ(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2684])).
% 5.55/5.51 tff(2686,plain,
% 5.55/5.51 (succ(NPX3!27) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2685, 39])).
% 5.55/5.51 tff(2687,plain,
% 5.55/5.51 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n7, n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2686, 2656])).
% 5.55/5.51 tff(2688,plain,
% 5.55/5.51 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2687, 787])).
% 5.55/5.51 tff(2689,plain,
% 5.55/5.51 (succ(X3!55) = succ(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2662])).
% 5.55/5.51 tff(2690,plain,
% 5.55/5.51 (succ(X3!55) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2689, 39])).
% 5.55/5.51 tff(2691,plain,
% 5.55/5.51 (succ(succ(X3!55)) = succ(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2690])).
% 5.55/5.51 tff(2692,plain,
% 5.55/5.51 (succ(succ(X3!55)) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2691, 53])).
% 5.55/5.51 tff(2693,plain,
% 5.55/5.51 (succ(succ(succ(X3!55))) = succ(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2692])).
% 5.55/5.51 tff(2694,plain,
% 5.55/5.51 (succ(succ(succ(X3!55))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2693, 45])).
% 5.55/5.51 tff(2695,plain,
% 5.55/5.51 (succ(succ(succ(succ(X3!55)))) = succ(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2694])).
% 5.55/5.51 tff(2696,plain,
% 5.55/5.51 (succ(succ(succ(succ(X3!55)))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2695, 28])).
% 5.55/5.51 tff(2697,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(X3!55))))) = succ(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2696])).
% 5.55/5.51 tff(2698,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(X3!55))))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2697, 42])).
% 5.55/5.51 tff(2699,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2698])).
% 5.55/5.51 tff(2700,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2699, 58])).
% 5.55/5.51 tff(2701,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2700])).
% 5.55/5.51 tff(2702,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[2701, 36])).
% 5.55/5.51 tff(2703,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2702])).
% 5.55/5.51 tff(2704,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2703, 48])).
% 5.55/5.51 tff(2705,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2704])).
% 5.55/5.51 tff(2706,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2705, 14])).
% 5.55/5.51 tff(2707,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2706])).
% 5.55/5.51 tff(2708,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2707, 33])).
% 5.55/5.51 tff(2709,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2708])).
% 5.55/5.51 tff(2710,plain,
% 5.55/5.51 (NSX3!25 = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[535, 2709, 30])).
% 5.55/5.51 tff(2711,plain,
% 5.55/5.51 (pred(NSX3!25) = pred(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2710])).
% 5.55/5.51 tff(2712,plain,
% 5.55/5.51 (pred(NSX3!25) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2711, 17])).
% 5.55/5.51 tff(2713,plain,
% 5.55/5.51 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n5, n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2712, 2688])).
% 5.55/5.51 tff(2714,plain,
% 5.55/5.51 (Y4!52 = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[540, 2713, 558])).
% 5.55/5.51 tff(2715,plain,
% 5.55/5.51 (pred(Y4!52) = pred(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2714])).
% 5.55/5.51 tff(2716,plain,
% 5.55/5.51 (pred(Y4!52) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2715, 24])).
% 5.55/5.51 tff(2717,plain,
% 5.55/5.51 (pred(pred(Y4!52)) = pred(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2716])).
% 5.55/5.51 tff(2718,plain,
% 5.55/5.51 (pred(pred(Y4!52)) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2717, 23])).
% 5.55/5.51 tff(2719,plain,
% 5.55/5.51 (pred(pred(pred(Y4!52))) = pred(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2718])).
% 5.55/5.51 tff(2720,plain,
% 5.55/5.51 (pred(pred(pred(Y4!52))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2719, 22])).
% 5.55/5.51 tff(2721,plain,
% 5.55/5.51 (pred(pred(pred(pred(Y4!52)))) = pred(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2720])).
% 5.55/5.51 tff(2722,plain,
% 5.55/5.51 (pred(pred(pred(pred(Y4!52)))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2721, 21])).
% 5.55/5.51 tff(2723,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2722])).
% 5.55/5.51 tff(2724,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(Y4!52))))) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2723, 20])).
% 5.55/5.51 tff(2725,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2724])).
% 5.55/5.51 tff(2726,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2725, 19])).
% 5.55/5.51 tff(2727,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2726])).
% 5.55/5.51 tff(2728,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[2727, 18])).
% 5.55/5.51 tff(2729,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2728])).
% 5.55/5.51 tff(2730,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2729, 17])).
% 5.55/5.51 tff(2731,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2730])).
% 5.55/5.51 tff(2732,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2731, 16])).
% 5.55/5.51 tff(2733,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2732])).
% 5.55/5.51 tff(2734,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2733, 15])).
% 5.55/5.51 tff(2735,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2734])).
% 5.55/5.51 tff(2736,plain,
% 5.55/5.51 (NPY4!22 = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[578, 2735, 25])).
% 5.55/5.51 tff(2737,plain,
% 5.55/5.51 (succ(NPY4!22) = succ(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2736])).
% 5.55/5.51 tff(2738,plain,
% 5.55/5.51 (succ(NPY4!22) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2737, 48])).
% 5.55/5.51 tff(2739,plain,
% 5.55/5.51 (succ(Y4!52) = succ(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2714])).
% 5.55/5.51 tff(2740,plain,
% 5.55/5.51 (succ(Y4!52) = n3),
% 5.55/5.51 inference(transitivity,[status(thm)],[2739, 48])).
% 5.55/5.51 tff(2741,plain,
% 5.55/5.51 (succ(succ(Y4!52)) = succ(n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2740])).
% 5.55/5.51 tff(2742,plain,
% 5.55/5.51 (succ(succ(Y4!52)) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2741, 14])).
% 5.55/5.51 tff(2743,plain,
% 5.55/5.51 (succ(succ(succ(Y4!52))) = succ(n4)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2742])).
% 5.55/5.51 tff(2744,plain,
% 5.55/5.51 (succ(succ(succ(Y4!52))) = n5),
% 5.55/5.51 inference(transitivity,[status(thm)],[2743, 33])).
% 5.55/5.51 tff(2745,plain,
% 5.55/5.51 (succ(succ(succ(succ(Y4!52)))) = succ(n5)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2744])).
% 5.55/5.51 tff(2746,plain,
% 5.55/5.51 (succ(succ(succ(succ(Y4!52)))) = n6),
% 5.55/5.51 inference(transitivity,[status(thm)],[2745, 30])).
% 5.55/5.51 tff(2747,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n6)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2746])).
% 5.55/5.51 tff(2748,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(Y4!52))))) = n7),
% 5.55/5.51 inference(transitivity,[status(thm)],[2747, 39])).
% 5.55/5.51 tff(2749,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2748])).
% 5.55/5.51 tff(2750,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2749, 53])).
% 5.55/5.51 tff(2751,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2750])).
% 5.55/5.51 tff(2752,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2751, 45])).
% 5.55/5.51 tff(2753,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2752])).
% 5.55/5.51 tff(2754,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2753, 28])).
% 5.55/5.51 tff(2755,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2754])).
% 5.55/5.51 tff(2756,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2755, 42])).
% 5.55/5.51 tff(2757,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2756])).
% 5.55/5.51 tff(2758,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2757, 58])).
% 5.55/5.51 tff(2759,plain,
% 5.55/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2758])).
% 5.55/5.51 tff(2760,plain,
% 5.55/5.51 (NSY4!20 = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[601, 2759, 36])).
% 5.55/5.51 tff(2761,plain,
% 5.55/5.51 (pred(NSY4!20) = pred(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2760])).
% 5.55/5.51 tff(2762,plain,
% 5.55/5.51 (pred(NSY4!20) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2761, 24])).
% 5.55/5.51 tff(2763,plain,
% 5.55/5.51 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n1, n3)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2762, 2738])).
% 5.55/5.51 tff(2764,plain,
% 5.55/5.51 (sum(pred(NSY4!20), succ(NPY4!22)) = n4),
% 5.55/5.51 inference(transitivity,[status(thm)],[2763, 47])).
% 5.55/5.51 tff(2765,plain,
% 5.55/5.51 (sum(pred(Y3!54), succ(X3!55)) = sum(n5, n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2608, 2690])).
% 5.55/5.51 tff(2766,plain,
% 5.55/5.51 (sum(pred(Y3!54), succ(X3!55)) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2765, 50])).
% 5.55/5.51 tff(2767,plain,
% 5.55/5.51 (sum(pred(X3!55), succ(Y3!54)) = sum(n5, n7)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2664, 2632])).
% 5.55/5.51 tff(2768,plain,
% 5.55/5.51 (sum(pred(X3!55), succ(Y3!54)) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2767, 50])).
% 5.55/5.51 tff(2769,plain,
% 5.55/5.51 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n1, n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2768, 2766])).
% 5.55/5.51 tff(2770,plain,
% 5.55/5.51 (X4!53 = n2),
% 5.55/5.51 inference(transitivity,[status(thm)],[438, 2769, 49])).
% 5.55/5.51 tff(2771,plain,
% 5.55/5.51 (pred(X4!53) = pred(n2)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2770])).
% 5.55/5.51 tff(2772,plain,
% 5.55/5.51 (pred(X4!53) = n1),
% 5.55/5.51 inference(transitivity,[status(thm)],[2771, 24])).
% 5.55/5.51 tff(2773,plain,
% 5.55/5.51 (pred(pred(X4!53)) = pred(n1)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2772])).
% 5.55/5.51 tff(2774,plain,
% 5.55/5.51 (pred(pred(X4!53)) = n0),
% 5.55/5.51 inference(transitivity,[status(thm)],[2773, 23])).
% 5.55/5.51 tff(2775,plain,
% 5.55/5.51 (pred(pred(pred(X4!53))) = pred(n0)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2774])).
% 5.55/5.51 tff(2776,plain,
% 5.55/5.51 (pred(pred(pred(X4!53))) = n10),
% 5.55/5.51 inference(transitivity,[status(thm)],[2775, 22])).
% 5.55/5.51 tff(2777,plain,
% 5.55/5.51 (pred(pred(pred(pred(X4!53)))) = pred(n10)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2776])).
% 5.55/5.51 tff(2778,plain,
% 5.55/5.51 (pred(pred(pred(pred(X4!53)))) = n9),
% 5.55/5.51 inference(transitivity,[status(thm)],[2777, 21])).
% 5.55/5.51 tff(2779,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(X4!53))))) = pred(n9)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2778])).
% 5.55/5.51 tff(2780,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(X4!53))))) = n8),
% 5.55/5.51 inference(transitivity,[status(thm)],[2779, 20])).
% 5.55/5.51 tff(2781,plain,
% 5.55/5.51 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n8)),
% 5.55/5.51 inference(monotonicity,[status(thm)],[2780])).
% 5.58/5.51 tff(2782,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n7),
% 5.58/5.51 inference(transitivity,[status(thm)],[2781, 19])).
% 5.58/5.51 tff(2783,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n7)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2782])).
% 5.58/5.51 tff(2784,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n6),
% 5.58/5.51 inference(transitivity,[status(thm)],[2783, 18])).
% 5.58/5.51 tff(2785,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n6)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2784])).
% 5.58/5.51 tff(2786,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n5),
% 5.58/5.51 inference(transitivity,[status(thm)],[2785, 17])).
% 5.58/5.51 tff(2787,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n5)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2786])).
% 5.58/5.51 tff(2788,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n4),
% 5.58/5.51 inference(transitivity,[status(thm)],[2787, 16])).
% 5.58/5.51 tff(2789,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n4)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2788])).
% 5.58/5.51 tff(2790,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n3),
% 5.58/5.51 inference(transitivity,[status(thm)],[2789, 15])).
% 5.58/5.51 tff(2791,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n3)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2790])).
% 5.58/5.51 tff(2792,plain,
% 5.58/5.51 (NPX4!23 = n2),
% 5.58/5.51 inference(transitivity,[status(thm)],[626, 2791, 25])).
% 5.58/5.51 tff(2793,plain,
% 5.58/5.51 (succ(NPX4!23) = succ(n2)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2792])).
% 5.58/5.51 tff(2794,plain,
% 5.58/5.51 (succ(NPX4!23) = n3),
% 5.58/5.51 inference(transitivity,[status(thm)],[2793, 48])).
% 5.58/5.51 tff(2795,plain,
% 5.58/5.51 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n3, n4)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2794, 2764])).
% 5.58/5.51 tff(2796,plain,
% 5.58/5.51 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n7),
% 5.58/5.51 inference(transitivity,[status(thm)],[2795, 786])).
% 5.58/5.51 tff(2797,plain,
% 5.58/5.51 (succ(X4!53) = succ(n2)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2770])).
% 5.58/5.51 tff(2798,plain,
% 5.58/5.51 (succ(X4!53) = n3),
% 5.58/5.51 inference(transitivity,[status(thm)],[2797, 48])).
% 5.58/5.51 tff(2799,plain,
% 5.58/5.51 (succ(succ(X4!53)) = succ(n3)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2798])).
% 5.58/5.51 tff(2800,plain,
% 5.58/5.51 (succ(succ(X4!53)) = n4),
% 5.58/5.51 inference(transitivity,[status(thm)],[2799, 14])).
% 5.58/5.51 tff(2801,plain,
% 5.58/5.51 (succ(succ(succ(X4!53))) = succ(n4)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2800])).
% 5.58/5.51 tff(2802,plain,
% 5.58/5.51 (succ(succ(succ(X4!53))) = n5),
% 5.58/5.51 inference(transitivity,[status(thm)],[2801, 33])).
% 5.58/5.51 tff(2803,plain,
% 5.58/5.51 (succ(succ(succ(succ(X4!53)))) = succ(n5)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2802])).
% 5.58/5.51 tff(2804,plain,
% 5.58/5.51 (succ(succ(succ(succ(X4!53)))) = n6),
% 5.58/5.51 inference(transitivity,[status(thm)],[2803, 30])).
% 5.58/5.51 tff(2805,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(X4!53))))) = succ(n6)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2804])).
% 5.58/5.51 tff(2806,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(X4!53))))) = n7),
% 5.58/5.51 inference(transitivity,[status(thm)],[2805, 39])).
% 5.58/5.51 tff(2807,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n7)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2806])).
% 5.58/5.51 tff(2808,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n8),
% 5.58/5.51 inference(transitivity,[status(thm)],[2807, 53])).
% 5.58/5.51 tff(2809,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n8)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2808])).
% 5.58/5.51 tff(2810,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n9),
% 5.58/5.51 inference(transitivity,[status(thm)],[2809, 45])).
% 5.58/5.51 tff(2811,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n9)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2810])).
% 5.58/5.51 tff(2812,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n10),
% 5.58/5.51 inference(transitivity,[status(thm)],[2811, 28])).
% 5.58/5.51 tff(2813,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n10)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2812])).
% 5.58/5.51 tff(2814,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n0),
% 5.58/5.51 inference(transitivity,[status(thm)],[2813, 42])).
% 5.58/5.51 tff(2815,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n0)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2814])).
% 5.58/5.51 tff(2816,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n1),
% 5.58/5.51 inference(transitivity,[status(thm)],[2815, 58])).
% 5.58/5.51 tff(2817,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n1)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2816])).
% 5.58/5.51 tff(2818,plain,
% 5.58/5.51 (NSX4!21 = n2),
% 5.58/5.51 inference(transitivity,[status(thm)],[651, 2817, 36])).
% 5.58/5.51 tff(2819,plain,
% 5.58/5.51 (pred(NSX4!21) = pred(n2)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2818])).
% 5.58/5.51 tff(2820,plain,
% 5.58/5.51 (pred(NSX4!21) = n1),
% 5.58/5.51 inference(transitivity,[status(thm)],[2819, 24])).
% 5.58/5.51 tff(2821,plain,
% 5.58/5.51 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n1, n7)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2820, 2796])).
% 5.58/5.51 tff(2822,plain,
% 5.58/5.51 (Y5!50 = n8),
% 5.58/5.51 inference(transitivity,[status(thm)],[656, 2821, 791])).
% 5.58/5.51 tff(2823,plain,
% 5.58/5.51 (pred(Y5!50) = pred(n8)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2822])).
% 5.58/5.51 tff(2824,plain,
% 5.58/5.51 (pred(Y5!50) = n7),
% 5.58/5.51 inference(transitivity,[status(thm)],[2823, 19])).
% 5.58/5.51 tff(2825,plain,
% 5.58/5.51 (pred(pred(Y5!50)) = pred(n7)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2824])).
% 5.58/5.51 tff(2826,plain,
% 5.58/5.51 (pred(pred(Y5!50)) = n6),
% 5.58/5.51 inference(transitivity,[status(thm)],[2825, 18])).
% 5.58/5.51 tff(2827,plain,
% 5.58/5.51 (pred(pred(pred(Y5!50))) = pred(n6)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2826])).
% 5.58/5.51 tff(2828,plain,
% 5.58/5.51 (pred(pred(pred(Y5!50))) = n5),
% 5.58/5.51 inference(transitivity,[status(thm)],[2827, 17])).
% 5.58/5.51 tff(2829,plain,
% 5.58/5.51 (pred(pred(pred(pred(Y5!50)))) = pred(n5)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2828])).
% 5.58/5.51 tff(2830,plain,
% 5.58/5.51 (pred(pred(pred(pred(Y5!50)))) = n4),
% 5.58/5.51 inference(transitivity,[status(thm)],[2829, 16])).
% 5.58/5.51 tff(2831,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n4)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2830])).
% 5.58/5.51 tff(2832,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(Y5!50))))) = n3),
% 5.58/5.51 inference(transitivity,[status(thm)],[2831, 15])).
% 5.58/5.51 tff(2833,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n3)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2832])).
% 5.58/5.51 tff(2834,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n2),
% 5.58/5.51 inference(transitivity,[status(thm)],[2833, 25])).
% 5.58/5.51 tff(2835,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n2)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2834])).
% 5.58/5.51 tff(2836,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n1),
% 5.58/5.51 inference(transitivity,[status(thm)],[2835, 24])).
% 5.58/5.51 tff(2837,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n1)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2836])).
% 5.58/5.51 tff(2838,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n0),
% 5.58/5.51 inference(transitivity,[status(thm)],[2837, 23])).
% 5.58/5.51 tff(2839,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n0)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2838])).
% 5.58/5.51 tff(2840,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n10),
% 5.58/5.51 inference(transitivity,[status(thm)],[2839, 22])).
% 5.58/5.51 tff(2841,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n10)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2840])).
% 5.58/5.51 tff(2842,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n9),
% 5.58/5.51 inference(transitivity,[status(thm)],[2841, 21])).
% 5.58/5.51 tff(2843,plain,
% 5.58/5.51 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n9)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2842])).
% 5.58/5.51 tff(2844,plain,
% 5.58/5.51 (NPY5!18 = n8),
% 5.58/5.51 inference(transitivity,[status(thm)],[694, 2843, 20])).
% 5.58/5.51 tff(2845,plain,
% 5.58/5.51 (succ(NPY5!18) = succ(n8)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2844])).
% 5.58/5.51 tff(2846,plain,
% 5.58/5.51 (succ(NPY5!18) = n9),
% 5.58/5.51 inference(transitivity,[status(thm)],[2845, 45])).
% 5.58/5.51 tff(2847,plain,
% 5.58/5.51 (succ(Y5!50) = succ(n8)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2822])).
% 5.58/5.51 tff(2848,plain,
% 5.58/5.51 (succ(Y5!50) = n9),
% 5.58/5.51 inference(transitivity,[status(thm)],[2847, 45])).
% 5.58/5.51 tff(2849,plain,
% 5.58/5.51 (succ(succ(Y5!50)) = succ(n9)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2848])).
% 5.58/5.51 tff(2850,plain,
% 5.58/5.51 (succ(succ(Y5!50)) = n10),
% 5.58/5.51 inference(transitivity,[status(thm)],[2849, 28])).
% 5.58/5.51 tff(2851,plain,
% 5.58/5.51 (succ(succ(succ(Y5!50))) = succ(n10)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2850])).
% 5.58/5.51 tff(2852,plain,
% 5.58/5.51 (succ(succ(succ(Y5!50))) = n0),
% 5.58/5.51 inference(transitivity,[status(thm)],[2851, 42])).
% 5.58/5.51 tff(2853,plain,
% 5.58/5.51 (succ(succ(succ(succ(Y5!50)))) = succ(n0)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2852])).
% 5.58/5.51 tff(2854,plain,
% 5.58/5.51 (succ(succ(succ(succ(Y5!50)))) = n1),
% 5.58/5.51 inference(transitivity,[status(thm)],[2853, 58])).
% 5.58/5.51 tff(2855,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n1)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2854])).
% 5.58/5.51 tff(2856,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(Y5!50))))) = n2),
% 5.58/5.51 inference(transitivity,[status(thm)],[2855, 36])).
% 5.58/5.51 tff(2857,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n2)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2856])).
% 5.58/5.51 tff(2858,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n3),
% 5.58/5.51 inference(transitivity,[status(thm)],[2857, 48])).
% 5.58/5.51 tff(2859,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n3)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2858])).
% 5.58/5.51 tff(2860,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n4),
% 5.58/5.51 inference(transitivity,[status(thm)],[2859, 14])).
% 5.58/5.51 tff(2861,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n4)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2860])).
% 5.58/5.51 tff(2862,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n5),
% 5.58/5.51 inference(transitivity,[status(thm)],[2861, 33])).
% 5.58/5.51 tff(2863,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n5)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2862])).
% 5.58/5.51 tff(2864,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n6),
% 5.58/5.51 inference(transitivity,[status(thm)],[2863, 30])).
% 5.58/5.51 tff(2865,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n6)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2864])).
% 5.58/5.51 tff(2866,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n7),
% 5.58/5.51 inference(transitivity,[status(thm)],[2865, 39])).
% 5.58/5.51 tff(2867,plain,
% 5.58/5.51 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n7)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2866])).
% 5.58/5.51 tff(2868,plain,
% 5.58/5.51 (NSY5!16 = n8),
% 5.58/5.51 inference(transitivity,[status(thm)],[717, 2867, 53])).
% 5.58/5.51 tff(2869,plain,
% 5.58/5.51 (pred(NSY5!16) = pred(n8)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2868])).
% 5.58/5.51 tff(2870,plain,
% 5.58/5.51 (pred(NSY5!16) = n7),
% 5.58/5.51 inference(transitivity,[status(thm)],[2869, 19])).
% 5.58/5.51 tff(2871,plain,
% 5.58/5.51 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n7, n9)),
% 5.58/5.51 inference(monotonicity,[status(thm)],[2870, 2846])).
% 5.58/5.51 tff(2872,plain,
% 5.58/5.51 (sum(pred(NSY5!16), succ(NPY5!18)) = n5),
% 5.58/5.51 inference(transitivity,[status(thm)],[2871, 44])).
% 5.58/5.52 tff(2873,plain,
% 5.58/5.52 (sum(pred(Y4!52), succ(X4!53)) = sum(n1, n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2716, 2798])).
% 5.58/5.52 tff(2874,plain,
% 5.58/5.52 (sum(pred(Y4!52), succ(X4!53)) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[2873, 47])).
% 5.58/5.52 tff(2875,plain,
% 5.58/5.52 (sum(pred(X4!53), succ(Y4!52)) = sum(n1, n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2772, 2740])).
% 5.58/5.52 tff(2876,plain,
% 5.58/5.52 (sum(pred(X4!53), succ(Y4!52)) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[2875, 47])).
% 5.58/5.52 tff(2877,plain,
% 5.58/5.52 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n4, n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2876, 2874])).
% 5.58/5.52 tff(2878,plain,
% 5.58/5.52 (X5!51 = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[553, 2877, 46])).
% 5.58/5.52 tff(2879,plain,
% 5.58/5.52 (pred(X5!51) = pred(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2878])).
% 5.58/5.52 tff(2880,plain,
% 5.58/5.52 (pred(X5!51) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[2879, 19])).
% 5.58/5.52 tff(2881,plain,
% 5.58/5.52 (pred(pred(X5!51)) = pred(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2880])).
% 5.58/5.52 tff(2882,plain,
% 5.58/5.52 (pred(pred(X5!51)) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[2881, 18])).
% 5.58/5.52 tff(2883,plain,
% 5.58/5.52 (pred(pred(pred(X5!51))) = pred(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2882])).
% 5.58/5.52 tff(2884,plain,
% 5.58/5.52 (pred(pred(pred(X5!51))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[2883, 17])).
% 5.58/5.52 tff(2885,plain,
% 5.58/5.52 (pred(pred(pred(pred(X5!51)))) = pred(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2884])).
% 5.58/5.52 tff(2886,plain,
% 5.58/5.52 (pred(pred(pred(pred(X5!51)))) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[2885, 16])).
% 5.58/5.52 tff(2887,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(X5!51))))) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2886])).
% 5.58/5.52 tff(2888,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(X5!51))))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[2887, 15])).
% 5.58/5.52 tff(2889,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2888])).
% 5.58/5.52 tff(2890,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[2889, 25])).
% 5.58/5.52 tff(2891,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2890])).
% 5.58/5.52 tff(2892,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[2891, 24])).
% 5.58/5.52 tff(2893,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2892])).
% 5.58/5.52 tff(2894,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[2893, 23])).
% 5.58/5.52 tff(2895,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2894])).
% 5.58/5.52 tff(2896,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[2895, 22])).
% 5.58/5.52 tff(2897,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2896])).
% 5.58/5.52 tff(2898,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2897, 21])).
% 5.58/5.52 tff(2899,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2898])).
% 5.58/5.52 tff(2900,plain,
% 5.58/5.52 (NPX5!19 = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[742, 2899, 20])).
% 5.58/5.52 tff(2901,plain,
% 5.58/5.52 (succ(NPX5!19) = succ(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2900])).
% 5.58/5.52 tff(2902,plain,
% 5.58/5.52 (succ(NPX5!19) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2901, 45])).
% 5.58/5.52 tff(2903,plain,
% 5.58/5.52 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n9, n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2902, 2872])).
% 5.58/5.52 tff(2904,plain,
% 5.58/5.52 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[2903, 790])).
% 5.58/5.52 tff(2905,plain,
% 5.58/5.52 (succ(X5!51) = succ(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2878])).
% 5.58/5.52 tff(2906,plain,
% 5.58/5.52 (succ(X5!51) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2905, 45])).
% 5.58/5.52 tff(2907,plain,
% 5.58/5.52 (succ(succ(X5!51)) = succ(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2906])).
% 5.58/5.52 tff(2908,plain,
% 5.58/5.52 (succ(succ(X5!51)) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[2907, 28])).
% 5.58/5.52 tff(2909,plain,
% 5.58/5.52 (succ(succ(succ(X5!51))) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2908])).
% 5.58/5.52 tff(2910,plain,
% 5.58/5.52 (succ(succ(succ(X5!51))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[2909, 42])).
% 5.58/5.52 tff(2911,plain,
% 5.58/5.52 (succ(succ(succ(succ(X5!51)))) = succ(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2910])).
% 5.58/5.52 tff(2912,plain,
% 5.58/5.52 (succ(succ(succ(succ(X5!51)))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[2911, 58])).
% 5.58/5.52 tff(2913,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(X5!51))))) = succ(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2912])).
% 5.58/5.52 tff(2914,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(X5!51))))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[2913, 36])).
% 5.58/5.52 tff(2915,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2914])).
% 5.58/5.52 tff(2916,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[2915, 48])).
% 5.58/5.52 tff(2917,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2916])).
% 5.58/5.52 tff(2918,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[2917, 14])).
% 5.58/5.52 tff(2919,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2918])).
% 5.58/5.52 tff(2920,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[2919, 33])).
% 5.58/5.52 tff(2921,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2920])).
% 5.58/5.52 tff(2922,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[2921, 30])).
% 5.58/5.52 tff(2923,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2922])).
% 5.58/5.52 tff(2924,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[2923, 39])).
% 5.58/5.52 tff(2925,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2924])).
% 5.58/5.52 tff(2926,plain,
% 5.58/5.52 (NSX5!17 = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[767, 2925, 53])).
% 5.58/5.52 tff(2927,plain,
% 5.58/5.52 (pred(NSX5!17) = pred(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2926])).
% 5.58/5.52 tff(2928,plain,
% 5.58/5.52 (pred(NSX5!17) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[2927, 19])).
% 5.58/5.52 tff(2929,plain,
% 5.58/5.52 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n7, n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2928, 2904])).
% 5.58/5.52 tff(2930,plain,
% 5.58/5.52 (Y6!48 = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[772, 2929, 789])).
% 5.58/5.52 tff(2931,plain,
% 5.58/5.52 (pred(Y6!48) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2930])).
% 5.58/5.52 tff(2932,plain,
% 5.58/5.52 (pred(Y6!48) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2931, 21])).
% 5.58/5.52 tff(2933,plain,
% 5.58/5.52 (pred(pred(Y6!48)) = pred(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2932])).
% 5.58/5.52 tff(2934,plain,
% 5.58/5.52 (pred(pred(Y6!48)) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[2933, 20])).
% 5.58/5.52 tff(2935,plain,
% 5.58/5.52 (pred(pred(pred(Y6!48))) = pred(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2934])).
% 5.58/5.52 tff(2936,plain,
% 5.58/5.52 (pred(pred(pred(Y6!48))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[2935, 19])).
% 5.58/5.52 tff(2937,plain,
% 5.58/5.52 (pred(pred(pred(pred(Y6!48)))) = pred(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2936])).
% 5.58/5.52 tff(2938,plain,
% 5.58/5.52 (pred(pred(pred(pred(Y6!48)))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[2937, 18])).
% 5.58/5.52 tff(2939,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2938])).
% 5.58/5.52 tff(2940,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(Y6!48))))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[2939, 17])).
% 5.58/5.52 tff(2941,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2940])).
% 5.58/5.52 tff(2942,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[2941, 16])).
% 5.58/5.52 tff(2943,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2942])).
% 5.58/5.52 tff(2944,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[2943, 15])).
% 5.58/5.52 tff(2945,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2944])).
% 5.58/5.52 tff(2946,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[2945, 25])).
% 5.58/5.52 tff(2947,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2946])).
% 5.58/5.52 tff(2948,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[2947, 24])).
% 5.58/5.52 tff(2949,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2948])).
% 5.58/5.52 tff(2950,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[2949, 23])).
% 5.58/5.52 tff(2951,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2950])).
% 5.58/5.52 tff(2952,plain,
% 5.58/5.52 (NPY6!14 = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[1465, 2951, 22])).
% 5.58/5.52 tff(2953,plain,
% 5.58/5.52 (succ(NPY6!14) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2952])).
% 5.58/5.52 tff(2954,plain,
% 5.58/5.52 (succ(NPY6!14) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[2953, 42])).
% 5.58/5.52 tff(2955,plain,
% 5.58/5.52 (succ(Y6!48) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2930])).
% 5.58/5.52 tff(2956,plain,
% 5.58/5.52 (succ(Y6!48) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[2955, 42])).
% 5.58/5.52 tff(2957,plain,
% 5.58/5.52 (succ(succ(Y6!48)) = succ(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2956])).
% 5.58/5.52 tff(2958,plain,
% 5.58/5.52 (succ(succ(Y6!48)) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[2957, 58])).
% 5.58/5.52 tff(2959,plain,
% 5.58/5.52 (succ(succ(succ(Y6!48))) = succ(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2958])).
% 5.58/5.52 tff(2960,plain,
% 5.58/5.52 (succ(succ(succ(Y6!48))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[2959, 36])).
% 5.58/5.52 tff(2961,plain,
% 5.58/5.52 (succ(succ(succ(succ(Y6!48)))) = succ(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2960])).
% 5.58/5.52 tff(2962,plain,
% 5.58/5.52 (succ(succ(succ(succ(Y6!48)))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[2961, 48])).
% 5.58/5.52 tff(2963,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2962])).
% 5.58/5.52 tff(2964,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(Y6!48))))) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[2963, 14])).
% 5.58/5.52 tff(2965,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2964])).
% 5.58/5.52 tff(2966,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[2965, 33])).
% 5.58/5.52 tff(2967,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2966])).
% 5.58/5.52 tff(2968,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[2967, 30])).
% 5.58/5.52 tff(2969,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2968])).
% 5.58/5.52 tff(2970,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[2969, 39])).
% 5.58/5.52 tff(2971,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2970])).
% 5.58/5.52 tff(2972,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[2971, 53])).
% 5.58/5.52 tff(2973,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2972])).
% 5.58/5.52 tff(2974,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2973, 45])).
% 5.58/5.52 tff(2975,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2974])).
% 5.58/5.52 tff(2976,plain,
% 5.58/5.52 (NSY6!12 = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[1490, 2975, 28])).
% 5.58/5.52 tff(2977,plain,
% 5.58/5.52 (pred(NSY6!12) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2976])).
% 5.58/5.52 tff(2978,plain,
% 5.58/5.52 (pred(NSY6!12) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2977, 21])).
% 5.58/5.52 tff(2979,plain,
% 5.58/5.52 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n9, n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2978, 2954])).
% 5.58/5.52 tff(2980,plain,
% 5.58/5.52 (sum(pred(NSY6!12), succ(NPY6!14)) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2979, 41])).
% 5.58/5.52 tff(2981,plain,
% 5.58/5.52 (sum(pred(Y5!50), succ(X5!51)) = sum(n7, n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2824, 2906])).
% 5.58/5.52 tff(2982,plain,
% 5.58/5.52 (sum(pred(Y5!50), succ(X5!51)) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[2981, 44])).
% 5.58/5.52 tff(2983,plain,
% 5.58/5.52 (sum(pred(X5!51), succ(Y5!50)) = sum(n7, n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2880, 2848])).
% 5.58/5.52 tff(2984,plain,
% 5.58/5.52 (sum(pred(X5!51), succ(Y5!50)) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[2983, 44])).
% 5.58/5.52 tff(2985,plain,
% 5.58/5.52 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n5, n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2984, 2982])).
% 5.58/5.52 tff(2986,plain,
% 5.58/5.52 (X6!49 = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[669, 2985, 43])).
% 5.58/5.52 tff(2987,plain,
% 5.58/5.52 (pred(X6!49) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2986])).
% 5.58/5.52 tff(2988,plain,
% 5.58/5.52 (pred(X6!49) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[2987, 21])).
% 5.58/5.52 tff(2989,plain,
% 5.58/5.52 (pred(pred(X6!49)) = pred(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2988])).
% 5.58/5.52 tff(2990,plain,
% 5.58/5.52 (pred(pred(X6!49)) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[2989, 20])).
% 5.58/5.52 tff(2991,plain,
% 5.58/5.52 (pred(pred(pred(X6!49))) = pred(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2990])).
% 5.58/5.52 tff(2992,plain,
% 5.58/5.52 (pred(pred(pred(X6!49))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[2991, 19])).
% 5.58/5.52 tff(2993,plain,
% 5.58/5.52 (pred(pred(pred(pred(X6!49)))) = pred(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2992])).
% 5.58/5.52 tff(2994,plain,
% 5.58/5.52 (pred(pred(pred(pred(X6!49)))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[2993, 18])).
% 5.58/5.52 tff(2995,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(X6!49))))) = pred(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2994])).
% 5.58/5.52 tff(2996,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(X6!49))))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[2995, 17])).
% 5.58/5.52 tff(2997,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2996])).
% 5.58/5.52 tff(2998,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[2997, 16])).
% 5.58/5.52 tff(2999,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2998])).
% 5.58/5.52 tff(3000,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[2999, 15])).
% 5.58/5.52 tff(3001,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3000])).
% 5.58/5.52 tff(3002,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3001, 25])).
% 5.58/5.52 tff(3003,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3002])).
% 5.58/5.52 tff(3004,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3003, 24])).
% 5.58/5.52 tff(3005,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3004])).
% 5.58/5.52 tff(3006,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3005, 23])).
% 5.58/5.52 tff(3007,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3006])).
% 5.58/5.52 tff(3008,plain,
% 5.58/5.52 (NPX6!15 = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[1523, 3007, 22])).
% 5.58/5.52 tff(3009,plain,
% 5.58/5.52 (succ(NPX6!15) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3008])).
% 5.58/5.52 tff(3010,plain,
% 5.58/5.52 (succ(NPX6!15) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3009, 42])).
% 5.58/5.52 tff(3011,plain,
% 5.58/5.52 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n0, n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3010, 2980])).
% 5.58/5.52 tff(3012,plain,
% 5.58/5.52 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3011, 40])).
% 5.58/5.52 tff(3013,plain,
% 5.58/5.52 (succ(X6!49) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2986])).
% 5.58/5.52 tff(3014,plain,
% 5.58/5.52 (succ(X6!49) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3013, 42])).
% 5.58/5.52 tff(3015,plain,
% 5.58/5.52 (succ(succ(X6!49)) = succ(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3014])).
% 5.58/5.52 tff(3016,plain,
% 5.58/5.52 (succ(succ(X6!49)) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3015, 58])).
% 5.58/5.52 tff(3017,plain,
% 5.58/5.52 (succ(succ(succ(X6!49))) = succ(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3016])).
% 5.58/5.52 tff(3018,plain,
% 5.58/5.52 (succ(succ(succ(X6!49))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3017, 36])).
% 5.58/5.52 tff(3019,plain,
% 5.58/5.52 (succ(succ(succ(succ(X6!49)))) = succ(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3018])).
% 5.58/5.52 tff(3020,plain,
% 5.58/5.52 (succ(succ(succ(succ(X6!49)))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3019, 48])).
% 5.58/5.52 tff(3021,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(X6!49))))) = succ(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3020])).
% 5.58/5.52 tff(3022,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(X6!49))))) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[3021, 14])).
% 5.58/5.52 tff(3023,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3022])).
% 5.58/5.52 tff(3024,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[3023, 33])).
% 5.58/5.52 tff(3025,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3024])).
% 5.58/5.52 tff(3026,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3025, 30])).
% 5.58/5.52 tff(3027,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3026])).
% 5.58/5.52 tff(3028,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[3027, 39])).
% 5.58/5.52 tff(3029,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3028])).
% 5.58/5.52 tff(3030,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3029, 53])).
% 5.58/5.52 tff(3031,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3030])).
% 5.58/5.52 tff(3032,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3031, 45])).
% 5.58/5.52 tff(3033,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3032])).
% 5.58/5.52 tff(3034,plain,
% 5.58/5.52 (NSX6!13 = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[1550, 3033, 28])).
% 5.58/5.52 tff(3035,plain,
% 5.58/5.52 (pred(NSX6!13) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3034])).
% 5.58/5.52 tff(3036,plain,
% 5.58/5.52 (pred(NSX6!13) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3035, 21])).
% 5.58/5.52 tff(3037,plain,
% 5.58/5.52 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n9, n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3036, 3012])).
% 5.58/5.52 tff(3038,plain,
% 5.58/5.52 (sum(n9, n9) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.58/5.52 inference(symmetry,[status(thm)],[3037])).
% 5.58/5.52 tff(3039,plain,
% 5.58/5.52 (sum(pred(Y6!48), succ(X6!49)) = sum(n9, n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2932, 3014])).
% 5.58/5.52 tff(3040,plain,
% 5.58/5.52 (sum(pred(Y6!48), succ(X6!49)) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3039, 41])).
% 5.58/5.52 tff(3041,plain,
% 5.58/5.52 (sum(pred(X6!49), succ(Y6!48)) = sum(n9, n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2988, 2956])).
% 5.58/5.52 tff(3042,plain,
% 5.58/5.52 (sum(pred(X6!49), succ(Y6!48)) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3041, 41])).
% 5.58/5.52 tff(3043,plain,
% 5.58/5.52 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n9, n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3042, 3040])).
% 5.58/5.52 tff(3044,plain,
% 5.58/5.52 (X7!47 = sum(n9, n9)),
% 5.58/5.52 inference(transitivity,[status(thm)],[785, 3043])).
% 5.58/5.52 tff(3045,plain,
% 5.58/5.52 ((X7!47 = Y7!46) <=> (sum(n9, n9) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))))),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3044, 793])).
% 5.58/5.52 tff(3046,plain,
% 5.58/5.52 ((~(X7!47 = Y7!46)) <=> (~(sum(n9, n9) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))))),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3045])).
% 5.58/5.52 tff(3047,plain,
% 5.58/5.52 (~(sum(n9, n9) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))))),
% 5.58/5.52 inference(modus_ponens,[status(thm)],[792, 3046])).
% 5.58/5.52 tff(3048,plain,
% 5.58/5.52 ($false),
% 5.58/5.52 inference(unit_resolution,[status(thm)],[3047, 3038])).
% 5.58/5.52 tff(3049,plain,((~(X0!61 = n9)) | (~(Y0!60 = n7)) | (X7!47 = Y7!46)), inference(lemma,lemma(discharge,[]))).
% 5.58/5.52 tff(3050,plain,
% 5.58/5.52 (~(X0!61 = n9)),
% 5.58/5.52 inference(unit_resolution,[status(thm)],[3049, 2285, 792])).
% 5.58/5.52 tff(3051,plain,
% 5.58/5.52 (sum(n5, n10) = n4),
% 5.58/5.52 inference(and_elim,[status(thm)],[9])).
% 5.58/5.52 tff(3052,plain,
% 5.58/5.52 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n7, n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[874, 2335])).
% 5.58/5.52 tff(3053,plain,
% 5.58/5.52 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[3052, 789])).
% 5.58/5.52 tff(3054,plain,
% 5.58/5.52 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n5, n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[900, 3053])).
% 5.58/5.52 tff(3055,plain,
% 5.58/5.52 (Y1!58 = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[196, 3054, 3051])).
% 5.58/5.52 tff(3056,plain,
% 5.58/5.52 (pred(Y1!58) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3055])).
% 5.58/5.52 tff(3057,plain,
% 5.58/5.52 (pred(Y1!58) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3056, 15])).
% 5.58/5.52 tff(3058,plain,
% 5.58/5.52 (pred(pred(Y1!58)) = pred(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3057])).
% 5.58/5.52 tff(3059,plain,
% 5.58/5.52 (pred(pred(Y1!58)) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3058, 25])).
% 5.58/5.52 tff(3060,plain,
% 5.58/5.52 (pred(pred(pred(Y1!58))) = pred(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3059])).
% 5.58/5.52 tff(3061,plain,
% 5.58/5.52 (pred(pred(pred(Y1!58))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3060, 24])).
% 5.58/5.52 tff(3062,plain,
% 5.58/5.52 (pred(pred(pred(pred(Y1!58)))) = pred(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3061])).
% 5.58/5.52 tff(3063,plain,
% 5.58/5.52 (pred(pred(pred(pred(Y1!58)))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3062, 23])).
% 5.58/5.52 tff(3064,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3063])).
% 5.58/5.52 tff(3065,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(Y1!58))))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[3064, 22])).
% 5.58/5.52 tff(3066,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3065])).
% 5.58/5.52 tff(3067,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3066, 21])).
% 5.58/5.52 tff(3068,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3067])).
% 5.58/5.52 tff(3069,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3068, 20])).
% 5.58/5.52 tff(3070,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3069])).
% 5.58/5.52 tff(3071,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[3070, 19])).
% 5.58/5.52 tff(3072,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3071])).
% 5.58/5.52 tff(3073,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3072, 18])).
% 5.58/5.52 tff(3074,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3073])).
% 5.58/5.52 tff(3075,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[3074, 17])).
% 5.58/5.52 tff(3076,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3075])).
% 5.58/5.52 tff(3077,plain,
% 5.58/5.52 (NPY1!34 = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[232, 3076, 16])).
% 5.58/5.52 tff(3078,plain,
% 5.58/5.52 (succ(NPY1!34) = succ(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3077])).
% 5.58/5.52 tff(3079,plain,
% 5.58/5.52 (succ(NPY1!34) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[3078, 33])).
% 5.58/5.52 tff(3080,plain,
% 5.58/5.52 (succ(Y1!58) = succ(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3055])).
% 5.58/5.52 tff(3081,plain,
% 5.58/5.52 (succ(Y1!58) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[3080, 33])).
% 5.58/5.52 tff(3082,plain,
% 5.58/5.52 (succ(succ(Y1!58)) = succ(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3081])).
% 5.58/5.52 tff(3083,plain,
% 5.58/5.52 (succ(succ(Y1!58)) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3082, 30])).
% 5.58/5.52 tff(3084,plain,
% 5.58/5.52 (succ(succ(succ(Y1!58))) = succ(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3083])).
% 5.58/5.52 tff(3085,plain,
% 5.58/5.52 (succ(succ(succ(Y1!58))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[3084, 39])).
% 5.58/5.52 tff(3086,plain,
% 5.58/5.52 (succ(succ(succ(succ(Y1!58)))) = succ(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3085])).
% 5.58/5.52 tff(3087,plain,
% 5.58/5.52 (succ(succ(succ(succ(Y1!58)))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3086, 53])).
% 5.58/5.52 tff(3088,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3087])).
% 5.58/5.52 tff(3089,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(Y1!58))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3088, 45])).
% 5.58/5.52 tff(3090,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3089])).
% 5.58/5.52 tff(3091,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[3090, 28])).
% 5.58/5.52 tff(3092,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3091])).
% 5.58/5.52 tff(3093,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3092, 42])).
% 5.58/5.52 tff(3094,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3093])).
% 5.58/5.52 tff(3095,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3094, 58])).
% 5.58/5.52 tff(3096,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3095])).
% 5.58/5.52 tff(3097,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3096, 36])).
% 5.58/5.52 tff(3098,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3097])).
% 5.58/5.52 tff(3099,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3098, 48])).
% 5.58/5.52 tff(3100,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3099])).
% 5.58/5.52 tff(3101,plain,
% 5.58/5.52 (NSY1!32 = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[255, 3100, 14])).
% 5.58/5.52 tff(3102,plain,
% 5.58/5.52 (pred(NSY1!32) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3101])).
% 5.58/5.52 tff(3103,plain,
% 5.58/5.52 (pred(NSY1!32) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3102, 15])).
% 5.58/5.52 tff(3104,plain,
% 5.58/5.52 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n3, n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3103, 3079])).
% 5.58/5.52 tff(3105,plain,
% 5.58/5.52 (sum(pred(NSY1!32), succ(NPY1!34)) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3104, 32])).
% 5.58/5.52 tff(3106,plain,
% 5.58/5.52 (sum(pred(Y0!60), succ(X0!61)) = sum(n6, n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[2287, 878])).
% 5.58/5.52 tff(3107,plain,
% 5.58/5.52 (sum(pred(Y0!60), succ(X0!61)) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3106, 38])).
% 5.58/5.52 tff(3108,plain,
% 5.58/5.52 (sum(pred(X0!61), succ(Y0!60)) = sum(n5, n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[852, 2311])).
% 5.58/5.52 tff(3109,plain,
% 5.58/5.52 (sum(pred(X0!61), succ(Y0!60)) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3108, 558])).
% 5.58/5.52 tff(3110,plain,
% 5.58/5.52 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n2, n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3109, 3107])).
% 5.58/5.52 tff(3111,plain,
% 5.58/5.52 (X1!59 = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[93, 3110, 34])).
% 5.58/5.52 tff(3112,plain,
% 5.58/5.52 (pred(X1!59) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3111])).
% 5.58/5.52 tff(3113,plain,
% 5.58/5.52 (pred(X1!59) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3112, 15])).
% 5.58/5.52 tff(3114,plain,
% 5.58/5.52 (pred(pred(X1!59)) = pred(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3113])).
% 5.58/5.52 tff(3115,plain,
% 5.58/5.52 (pred(pred(X1!59)) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3114, 25])).
% 5.58/5.52 tff(3116,plain,
% 5.58/5.52 (pred(pred(pred(X1!59))) = pred(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3115])).
% 5.58/5.52 tff(3117,plain,
% 5.58/5.52 (pred(pred(pred(X1!59))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3116, 24])).
% 5.58/5.52 tff(3118,plain,
% 5.58/5.52 (pred(pred(pred(pred(X1!59)))) = pred(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3117])).
% 5.58/5.52 tff(3119,plain,
% 5.58/5.52 (pred(pred(pred(pred(X1!59)))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3118, 23])).
% 5.58/5.52 tff(3120,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(X1!59))))) = pred(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3119])).
% 5.58/5.52 tff(3121,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(X1!59))))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[3120, 22])).
% 5.58/5.52 tff(3122,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3121])).
% 5.58/5.52 tff(3123,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3122, 21])).
% 5.58/5.52 tff(3124,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3123])).
% 5.58/5.52 tff(3125,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3124, 20])).
% 5.58/5.52 tff(3126,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3125])).
% 5.58/5.52 tff(3127,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[3126, 19])).
% 5.58/5.52 tff(3128,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3127])).
% 5.58/5.52 tff(3129,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3128, 18])).
% 5.58/5.52 tff(3130,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3129])).
% 5.58/5.52 tff(3131,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[3130, 17])).
% 5.58/5.52 tff(3132,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3131])).
% 5.58/5.52 tff(3133,plain,
% 5.58/5.52 (NPX1!35 = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[280, 3132, 16])).
% 5.58/5.52 tff(3134,plain,
% 5.58/5.52 (succ(NPX1!35) = succ(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3133])).
% 5.58/5.52 tff(3135,plain,
% 5.58/5.52 (succ(NPX1!35) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[3134, 33])).
% 5.58/5.52 tff(3136,plain,
% 5.58/5.52 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n5, n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3135, 3105])).
% 5.58/5.52 tff(3137,plain,
% 5.58/5.52 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3136, 558])).
% 5.58/5.52 tff(3138,plain,
% 5.58/5.52 (succ(X1!59) = succ(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3111])).
% 5.58/5.52 tff(3139,plain,
% 5.58/5.52 (succ(X1!59) = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[3138, 33])).
% 5.58/5.52 tff(3140,plain,
% 5.58/5.52 (succ(succ(X1!59)) = succ(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3139])).
% 5.58/5.52 tff(3141,plain,
% 5.58/5.52 (succ(succ(X1!59)) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3140, 30])).
% 5.58/5.52 tff(3142,plain,
% 5.58/5.52 (succ(succ(succ(X1!59))) = succ(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3141])).
% 5.58/5.52 tff(3143,plain,
% 5.58/5.52 (succ(succ(succ(X1!59))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[3142, 39])).
% 5.58/5.52 tff(3144,plain,
% 5.58/5.52 (succ(succ(succ(succ(X1!59)))) = succ(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3143])).
% 5.58/5.52 tff(3145,plain,
% 5.58/5.52 (succ(succ(succ(succ(X1!59)))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3144, 53])).
% 5.58/5.52 tff(3146,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(X1!59))))) = succ(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3145])).
% 5.58/5.52 tff(3147,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(X1!59))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3146, 45])).
% 5.58/5.52 tff(3148,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3147])).
% 5.58/5.52 tff(3149,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[3148, 28])).
% 5.58/5.52 tff(3150,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3149])).
% 5.58/5.52 tff(3151,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3150, 42])).
% 5.58/5.52 tff(3152,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3151])).
% 5.58/5.52 tff(3153,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3152, 58])).
% 5.58/5.52 tff(3154,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3153])).
% 5.58/5.52 tff(3155,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3154, 36])).
% 5.58/5.52 tff(3156,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3155])).
% 5.58/5.52 tff(3157,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3156, 48])).
% 5.58/5.52 tff(3158,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3157])).
% 5.58/5.52 tff(3159,plain,
% 5.58/5.52 (NSX1!33 = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[305, 3158, 14])).
% 5.58/5.52 tff(3160,plain,
% 5.58/5.52 (pred(NSX1!33) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3159])).
% 5.58/5.52 tff(3161,plain,
% 5.58/5.52 (pred(NSX1!33) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3160, 15])).
% 5.58/5.52 tff(3162,plain,
% 5.58/5.52 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n3, n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3161, 3137])).
% 5.58/5.52 tff(3163,plain,
% 5.58/5.52 (Y2!56 = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[310, 3162, 557])).
% 5.58/5.52 tff(3164,plain,
% 5.58/5.52 (pred(Y2!56) = pred(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3163])).
% 5.58/5.52 tff(3165,plain,
% 5.58/5.52 (pred(Y2!56) = n4),
% 5.58/5.52 inference(transitivity,[status(thm)],[3164, 16])).
% 5.58/5.52 tff(3166,plain,
% 5.58/5.52 (pred(pred(Y2!56)) = pred(n4)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3165])).
% 5.58/5.52 tff(3167,plain,
% 5.58/5.52 (pred(pred(Y2!56)) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3166, 15])).
% 5.58/5.52 tff(3168,plain,
% 5.58/5.52 (pred(pred(pred(Y2!56))) = pred(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3167])).
% 5.58/5.52 tff(3169,plain,
% 5.58/5.52 (pred(pred(pred(Y2!56))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3168, 25])).
% 5.58/5.52 tff(3170,plain,
% 5.58/5.52 (pred(pred(pred(pred(Y2!56)))) = pred(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3169])).
% 5.58/5.52 tff(3171,plain,
% 5.58/5.52 (pred(pred(pred(pred(Y2!56)))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3170, 24])).
% 5.58/5.52 tff(3172,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3171])).
% 5.58/5.52 tff(3173,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(Y2!56))))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3172, 23])).
% 5.58/5.52 tff(3174,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3173])).
% 5.58/5.52 tff(3175,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[3174, 22])).
% 5.58/5.52 tff(3176,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3175])).
% 5.58/5.52 tff(3177,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3176, 21])).
% 5.58/5.52 tff(3178,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3177])).
% 5.58/5.52 tff(3179,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3178, 20])).
% 5.58/5.52 tff(3180,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3179])).
% 5.58/5.52 tff(3181,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[3180, 19])).
% 5.58/5.52 tff(3182,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3181])).
% 5.58/5.52 tff(3183,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3182, 18])).
% 5.58/5.52 tff(3184,plain,
% 5.58/5.52 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3183])).
% 5.58/5.52 tff(3185,plain,
% 5.58/5.52 (NPY2!30 = n5),
% 5.58/5.52 inference(transitivity,[status(thm)],[347, 3184, 17])).
% 5.58/5.52 tff(3186,plain,
% 5.58/5.52 (succ(NPY2!30) = succ(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3185])).
% 5.58/5.52 tff(3187,plain,
% 5.58/5.52 (succ(NPY2!30) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3186, 30])).
% 5.58/5.52 tff(3188,plain,
% 5.58/5.52 (succ(Y2!56) = succ(n5)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3163])).
% 5.58/5.52 tff(3189,plain,
% 5.58/5.52 (succ(Y2!56) = n6),
% 5.58/5.52 inference(transitivity,[status(thm)],[3188, 30])).
% 5.58/5.52 tff(3190,plain,
% 5.58/5.52 (succ(succ(Y2!56)) = succ(n6)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3189])).
% 5.58/5.52 tff(3191,plain,
% 5.58/5.52 (succ(succ(Y2!56)) = n7),
% 5.58/5.52 inference(transitivity,[status(thm)],[3190, 39])).
% 5.58/5.52 tff(3192,plain,
% 5.58/5.52 (succ(succ(succ(Y2!56))) = succ(n7)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3191])).
% 5.58/5.52 tff(3193,plain,
% 5.58/5.52 (succ(succ(succ(Y2!56))) = n8),
% 5.58/5.52 inference(transitivity,[status(thm)],[3192, 53])).
% 5.58/5.52 tff(3194,plain,
% 5.58/5.52 (succ(succ(succ(succ(Y2!56)))) = succ(n8)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3193])).
% 5.58/5.52 tff(3195,plain,
% 5.58/5.52 (succ(succ(succ(succ(Y2!56)))) = n9),
% 5.58/5.52 inference(transitivity,[status(thm)],[3194, 45])).
% 5.58/5.52 tff(3196,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n9)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3195])).
% 5.58/5.52 tff(3197,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(Y2!56))))) = n10),
% 5.58/5.52 inference(transitivity,[status(thm)],[3196, 28])).
% 5.58/5.52 tff(3198,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n10)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3197])).
% 5.58/5.52 tff(3199,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n0),
% 5.58/5.52 inference(transitivity,[status(thm)],[3198, 42])).
% 5.58/5.52 tff(3200,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n0)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3199])).
% 5.58/5.52 tff(3201,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n1),
% 5.58/5.52 inference(transitivity,[status(thm)],[3200, 58])).
% 5.58/5.52 tff(3202,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n1)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3201])).
% 5.58/5.52 tff(3203,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n2),
% 5.58/5.52 inference(transitivity,[status(thm)],[3202, 36])).
% 5.58/5.52 tff(3204,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n2)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3203])).
% 5.58/5.52 tff(3205,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n3),
% 5.58/5.52 inference(transitivity,[status(thm)],[3204, 48])).
% 5.58/5.52 tff(3206,plain,
% 5.58/5.52 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n3)),
% 5.58/5.52 inference(monotonicity,[status(thm)],[3205])).
% 5.58/5.52 tff(3207,plain,
% 5.58/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n4),
% 5.58/5.53 inference(transitivity,[status(thm)],[3206, 14])).
% 5.58/5.53 tff(3208,plain,
% 5.58/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n4)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3207])).
% 5.58/5.53 tff(3209,plain,
% 5.58/5.53 (NSY2!28 = n5),
% 5.58/5.53 inference(transitivity,[status(thm)],[370, 3208, 33])).
% 5.58/5.53 tff(3210,plain,
% 5.58/5.53 (pred(NSY2!28) = pred(n5)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3209])).
% 5.58/5.53 tff(3211,plain,
% 5.58/5.53 (pred(NSY2!28) = n4),
% 5.58/5.53 inference(transitivity,[status(thm)],[3210, 16])).
% 5.58/5.53 tff(3212,plain,
% 5.58/5.53 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n4, n6)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3211, 3187])).
% 5.58/5.53 tff(3213,plain,
% 5.58/5.53 (sum(pred(NSY2!28), succ(NPY2!30)) = n10),
% 5.58/5.53 inference(transitivity,[status(thm)],[3212, 12])).
% 5.58/5.53 tff(3214,plain,
% 5.58/5.53 (sum(pred(Y1!58), succ(X1!59)) = sum(n3, n5)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3057, 3139])).
% 5.58/5.53 tff(3215,plain,
% 5.58/5.53 (sum(pred(Y1!58), succ(X1!59)) = n8),
% 5.58/5.53 inference(transitivity,[status(thm)],[3214, 32])).
% 5.58/5.53 tff(3216,plain,
% 5.58/5.53 (sum(pred(X1!59), succ(Y1!58)) = sum(n3, n5)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3113, 3081])).
% 5.58/5.53 tff(3217,plain,
% 5.58/5.53 (sum(pred(X1!59), succ(Y1!58)) = n8),
% 5.58/5.53 inference(transitivity,[status(thm)],[3216, 32])).
% 5.58/5.53 tff(3218,plain,
% 5.58/5.53 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n8, n8)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3217, 3215])).
% 5.58/5.53 tff(3219,plain,
% 5.58/5.53 (X2!57 = n5),
% 5.58/5.53 inference(transitivity,[status(thm)],[209, 3218, 31])).
% 5.58/5.53 tff(3220,plain,
% 5.58/5.53 (pred(X2!57) = pred(n5)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3219])).
% 5.58/5.53 tff(3221,plain,
% 5.58/5.53 (pred(X2!57) = n4),
% 5.58/5.53 inference(transitivity,[status(thm)],[3220, 16])).
% 5.58/5.53 tff(3222,plain,
% 5.58/5.53 (pred(pred(X2!57)) = pred(n4)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3221])).
% 5.58/5.53 tff(3223,plain,
% 5.58/5.53 (pred(pred(X2!57)) = n3),
% 5.58/5.53 inference(transitivity,[status(thm)],[3222, 15])).
% 5.58/5.53 tff(3224,plain,
% 5.58/5.53 (pred(pred(pred(X2!57))) = pred(n3)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3223])).
% 5.58/5.53 tff(3225,plain,
% 5.58/5.53 (pred(pred(pred(X2!57))) = n2),
% 5.58/5.53 inference(transitivity,[status(thm)],[3224, 25])).
% 5.58/5.53 tff(3226,plain,
% 5.58/5.53 (pred(pred(pred(pred(X2!57)))) = pred(n2)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3225])).
% 5.58/5.53 tff(3227,plain,
% 5.58/5.53 (pred(pred(pred(pred(X2!57)))) = n1),
% 5.58/5.53 inference(transitivity,[status(thm)],[3226, 24])).
% 5.58/5.53 tff(3228,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(X2!57))))) = pred(n1)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3227])).
% 5.58/5.53 tff(3229,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(X2!57))))) = n0),
% 5.58/5.53 inference(transitivity,[status(thm)],[3228, 23])).
% 5.58/5.53 tff(3230,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n0)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3229])).
% 5.58/5.53 tff(3231,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n10),
% 5.58/5.53 inference(transitivity,[status(thm)],[3230, 22])).
% 5.58/5.53 tff(3232,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n10)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3231])).
% 5.58/5.53 tff(3233,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n9),
% 5.58/5.53 inference(transitivity,[status(thm)],[3232, 21])).
% 5.58/5.53 tff(3234,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n9)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3233])).
% 5.58/5.53 tff(3235,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n8),
% 5.58/5.53 inference(transitivity,[status(thm)],[3234, 20])).
% 5.58/5.53 tff(3236,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n8)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3235])).
% 5.58/5.53 tff(3237,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n7),
% 5.58/5.53 inference(transitivity,[status(thm)],[3236, 19])).
% 5.58/5.53 tff(3238,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n7)),
% 5.58/5.53 inference(monotonicity,[status(thm)],[3237])).
% 5.58/5.53 tff(3239,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n6),
% 5.58/5.53 inference(transitivity,[status(thm)],[3238, 18])).
% 5.58/5.53 tff(3240,plain,
% 5.58/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3239])).
% 5.59/5.53 tff(3241,plain,
% 5.59/5.53 (NPX2!31 = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[395, 3240, 17])).
% 5.59/5.53 tff(3242,plain,
% 5.59/5.53 (succ(NPX2!31) = succ(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3241])).
% 5.59/5.53 tff(3243,plain,
% 5.59/5.53 (succ(NPX2!31) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3242, 30])).
% 5.59/5.53 tff(3244,plain,
% 5.59/5.53 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n6, n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3243, 3213])).
% 5.59/5.53 tff(3245,plain,
% 5.59/5.53 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3244, 674])).
% 5.59/5.53 tff(3246,plain,
% 5.59/5.53 (succ(X2!57) = succ(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3219])).
% 5.59/5.53 tff(3247,plain,
% 5.59/5.53 (succ(X2!57) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3246, 30])).
% 5.59/5.53 tff(3248,plain,
% 5.59/5.53 (succ(succ(X2!57)) = succ(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3247])).
% 5.59/5.53 tff(3249,plain,
% 5.59/5.53 (succ(succ(X2!57)) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3248, 39])).
% 5.59/5.53 tff(3250,plain,
% 5.59/5.53 (succ(succ(succ(X2!57))) = succ(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3249])).
% 5.59/5.53 tff(3251,plain,
% 5.59/5.53 (succ(succ(succ(X2!57))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3250, 53])).
% 5.59/5.53 tff(3252,plain,
% 5.59/5.53 (succ(succ(succ(succ(X2!57)))) = succ(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3251])).
% 5.59/5.53 tff(3253,plain,
% 5.59/5.53 (succ(succ(succ(succ(X2!57)))) = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[3252, 45])).
% 5.59/5.53 tff(3254,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(X2!57))))) = succ(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3253])).
% 5.59/5.53 tff(3255,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(X2!57))))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3254, 28])).
% 5.59/5.53 tff(3256,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3255])).
% 5.59/5.53 tff(3257,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3256, 42])).
% 5.59/5.53 tff(3258,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3257])).
% 5.59/5.53 tff(3259,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3258, 58])).
% 5.59/5.53 tff(3260,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3259])).
% 5.59/5.53 tff(3261,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3260, 36])).
% 5.59/5.53 tff(3262,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3261])).
% 5.59/5.53 tff(3263,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[3262, 48])).
% 5.59/5.53 tff(3264,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3263])).
% 5.59/5.53 tff(3265,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3264, 14])).
% 5.59/5.53 tff(3266,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3265])).
% 5.59/5.53 tff(3267,plain,
% 5.59/5.53 (NSX2!29 = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[420, 3266, 33])).
% 5.59/5.53 tff(3268,plain,
% 5.59/5.53 (pred(NSX2!29) = pred(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3267])).
% 5.59/5.53 tff(3269,plain,
% 5.59/5.53 (pred(NSX2!29) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3268, 16])).
% 5.59/5.53 tff(3270,plain,
% 5.59/5.53 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n4, n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3269, 3245])).
% 5.59/5.53 tff(3271,plain,
% 5.59/5.53 (Y3!54 = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[425, 3270, 673])).
% 5.59/5.53 tff(3272,plain,
% 5.59/5.53 (pred(Y3!54) = pred(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3271])).
% 5.59/5.53 tff(3273,plain,
% 5.59/5.53 (pred(Y3!54) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3272, 20])).
% 5.59/5.53 tff(3274,plain,
% 5.59/5.53 (pred(pred(Y3!54)) = pred(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3273])).
% 5.59/5.53 tff(3275,plain,
% 5.59/5.53 (pred(pred(Y3!54)) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3274, 19])).
% 5.59/5.53 tff(3276,plain,
% 5.59/5.53 (pred(pred(pred(Y3!54))) = pred(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3275])).
% 5.59/5.53 tff(3277,plain,
% 5.59/5.53 (pred(pred(pred(Y3!54))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3276, 18])).
% 5.59/5.53 tff(3278,plain,
% 5.59/5.53 (pred(pred(pred(pred(Y3!54)))) = pred(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3277])).
% 5.59/5.53 tff(3279,plain,
% 5.59/5.53 (pred(pred(pred(pred(Y3!54)))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3278, 17])).
% 5.59/5.53 tff(3280,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3279])).
% 5.59/5.53 tff(3281,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(Y3!54))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3280, 16])).
% 5.59/5.53 tff(3282,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3281])).
% 5.59/5.53 tff(3283,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[3282, 15])).
% 5.59/5.53 tff(3284,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3283])).
% 5.59/5.53 tff(3285,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3284, 25])).
% 5.59/5.53 tff(3286,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3285])).
% 5.59/5.53 tff(3287,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3286, 24])).
% 5.59/5.53 tff(3288,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3287])).
% 5.59/5.53 tff(3289,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3288, 23])).
% 5.59/5.53 tff(3290,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3289])).
% 5.59/5.53 tff(3291,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3290, 22])).
% 5.59/5.53 tff(3292,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3291])).
% 5.59/5.53 tff(3293,plain,
% 5.59/5.53 (NPY3!26 = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[462, 3292, 21])).
% 5.59/5.53 tff(3294,plain,
% 5.59/5.53 (succ(NPY3!26) = succ(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3293])).
% 5.59/5.53 tff(3295,plain,
% 5.59/5.53 (succ(NPY3!26) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3294, 28])).
% 5.59/5.53 tff(3296,plain,
% 5.59/5.53 (succ(Y3!54) = succ(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3271])).
% 5.59/5.53 tff(3297,plain,
% 5.59/5.53 (succ(Y3!54) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3296, 28])).
% 5.59/5.53 tff(3298,plain,
% 5.59/5.53 (succ(succ(Y3!54)) = succ(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3297])).
% 5.59/5.53 tff(3299,plain,
% 5.59/5.53 (succ(succ(Y3!54)) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3298, 42])).
% 5.59/5.53 tff(3300,plain,
% 5.59/5.53 (succ(succ(succ(Y3!54))) = succ(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3299])).
% 5.59/5.53 tff(3301,plain,
% 5.59/5.53 (succ(succ(succ(Y3!54))) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3300, 58])).
% 5.59/5.53 tff(3302,plain,
% 5.59/5.53 (succ(succ(succ(succ(Y3!54)))) = succ(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3301])).
% 5.59/5.53 tff(3303,plain,
% 5.59/5.53 (succ(succ(succ(succ(Y3!54)))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3302, 36])).
% 5.59/5.53 tff(3304,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3303])).
% 5.59/5.53 tff(3305,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(Y3!54))))) = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[3304, 48])).
% 5.59/5.53 tff(3306,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3305])).
% 5.59/5.53 tff(3307,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3306, 14])).
% 5.59/5.53 tff(3308,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3307])).
% 5.59/5.53 tff(3309,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3308, 33])).
% 5.59/5.53 tff(3310,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3309])).
% 5.59/5.53 tff(3311,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3310, 30])).
% 5.59/5.53 tff(3312,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3311])).
% 5.59/5.53 tff(3313,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3312, 39])).
% 5.59/5.53 tff(3314,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3313])).
% 5.59/5.53 tff(3315,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3314, 53])).
% 5.59/5.53 tff(3316,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3315])).
% 5.59/5.53 tff(3317,plain,
% 5.59/5.53 (NSY3!24 = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[485, 3316, 45])).
% 5.59/5.53 tff(3318,plain,
% 5.59/5.53 (pred(NSY3!24) = pred(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3317])).
% 5.59/5.53 tff(3319,plain,
% 5.59/5.53 (pred(NSY3!24) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3318, 20])).
% 5.59/5.53 tff(3320,plain,
% 5.59/5.53 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n8, n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3319, 3295])).
% 5.59/5.53 tff(3321,plain,
% 5.59/5.53 (sum(pred(NSY3!24), succ(NPY3!26)) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3320, 27])).
% 5.59/5.53 tff(3322,plain,
% 5.59/5.53 (sum(pred(Y2!56), succ(X2!57)) = sum(n4, n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3165, 3247])).
% 5.59/5.53 tff(3323,plain,
% 5.59/5.53 (sum(pred(Y2!56), succ(X2!57)) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3322, 12])).
% 5.59/5.53 tff(3324,plain,
% 5.59/5.53 (sum(pred(X2!57), succ(Y2!56)) = sum(n4, n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3221, 3189])).
% 5.59/5.53 tff(3325,plain,
% 5.59/5.53 (sum(pred(X2!57), succ(Y2!56)) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3324, 12])).
% 5.59/5.53 tff(3326,plain,
% 5.59/5.53 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n10, n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3325, 3323])).
% 5.59/5.53 tff(3327,plain,
% 5.59/5.53 (X3!55 = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[323, 3326, 29])).
% 5.59/5.53 tff(3328,plain,
% 5.59/5.53 (pred(X3!55) = pred(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3327])).
% 5.59/5.53 tff(3329,plain,
% 5.59/5.53 (pred(X3!55) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3328, 20])).
% 5.59/5.53 tff(3330,plain,
% 5.59/5.53 (pred(pred(X3!55)) = pred(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3329])).
% 5.59/5.53 tff(3331,plain,
% 5.59/5.53 (pred(pred(X3!55)) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3330, 19])).
% 5.59/5.53 tff(3332,plain,
% 5.59/5.53 (pred(pred(pred(X3!55))) = pred(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3331])).
% 5.59/5.53 tff(3333,plain,
% 5.59/5.53 (pred(pred(pred(X3!55))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3332, 18])).
% 5.59/5.53 tff(3334,plain,
% 5.59/5.53 (pred(pred(pred(pred(X3!55)))) = pred(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3333])).
% 5.59/5.53 tff(3335,plain,
% 5.59/5.53 (pred(pred(pred(pred(X3!55)))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3334, 17])).
% 5.59/5.53 tff(3336,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(X3!55))))) = pred(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3335])).
% 5.59/5.53 tff(3337,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(X3!55))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3336, 16])).
% 5.59/5.53 tff(3338,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3337])).
% 5.59/5.53 tff(3339,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[3338, 15])).
% 5.59/5.53 tff(3340,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3339])).
% 5.59/5.53 tff(3341,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3340, 25])).
% 5.59/5.53 tff(3342,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3341])).
% 5.59/5.53 tff(3343,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3342, 24])).
% 5.59/5.53 tff(3344,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3343])).
% 5.59/5.53 tff(3345,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3344, 23])).
% 5.59/5.53 tff(3346,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3345])).
% 5.59/5.53 tff(3347,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3346, 22])).
% 5.59/5.53 tff(3348,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3347])).
% 5.59/5.53 tff(3349,plain,
% 5.59/5.53 (NPX3!27 = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[510, 3348, 21])).
% 5.59/5.53 tff(3350,plain,
% 5.59/5.53 (succ(NPX3!27) = succ(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3349])).
% 5.59/5.53 tff(3351,plain,
% 5.59/5.53 (succ(NPX3!27) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3350, 28])).
% 5.59/5.53 tff(3352,plain,
% 5.59/5.53 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n10, n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3351, 3321])).
% 5.59/5.53 tff(3353,plain,
% 5.59/5.53 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3352, 69])).
% 5.59/5.53 tff(3354,plain,
% 5.59/5.53 (succ(X3!55) = succ(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3327])).
% 5.59/5.53 tff(3355,plain,
% 5.59/5.53 (succ(X3!55) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3354, 28])).
% 5.59/5.53 tff(3356,plain,
% 5.59/5.53 (succ(succ(X3!55)) = succ(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3355])).
% 5.59/5.53 tff(3357,plain,
% 5.59/5.53 (succ(succ(X3!55)) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3356, 42])).
% 5.59/5.53 tff(3358,plain,
% 5.59/5.53 (succ(succ(succ(X3!55))) = succ(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3357])).
% 5.59/5.53 tff(3359,plain,
% 5.59/5.53 (succ(succ(succ(X3!55))) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3358, 58])).
% 5.59/5.53 tff(3360,plain,
% 5.59/5.53 (succ(succ(succ(succ(X3!55)))) = succ(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3359])).
% 5.59/5.53 tff(3361,plain,
% 5.59/5.53 (succ(succ(succ(succ(X3!55)))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3360, 36])).
% 5.59/5.53 tff(3362,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(X3!55))))) = succ(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3361])).
% 5.59/5.53 tff(3363,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(X3!55))))) = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[3362, 48])).
% 5.59/5.53 tff(3364,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3363])).
% 5.59/5.53 tff(3365,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3364, 14])).
% 5.59/5.53 tff(3366,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3365])).
% 5.59/5.53 tff(3367,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3366, 33])).
% 5.59/5.53 tff(3368,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3367])).
% 5.59/5.53 tff(3369,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3368, 30])).
% 5.59/5.53 tff(3370,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3369])).
% 5.59/5.53 tff(3371,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3370, 39])).
% 5.59/5.53 tff(3372,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3371])).
% 5.59/5.53 tff(3373,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3372, 53])).
% 5.59/5.53 tff(3374,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3373])).
% 5.59/5.53 tff(3375,plain,
% 5.59/5.53 (NSX3!25 = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[535, 3374, 45])).
% 5.59/5.53 tff(3376,plain,
% 5.59/5.53 (pred(NSX3!25) = pred(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3375])).
% 5.59/5.53 tff(3377,plain,
% 5.59/5.53 (pred(NSX3!25) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3376, 20])).
% 5.59/5.53 tff(3378,plain,
% 5.59/5.53 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n8, n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3377, 3353])).
% 5.59/5.53 tff(3379,plain,
% 5.59/5.53 (Y4!52 = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[540, 3378, 98])).
% 5.59/5.53 tff(3380,plain,
% 5.59/5.53 (pred(Y4!52) = pred(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3379])).
% 5.59/5.53 tff(3381,plain,
% 5.59/5.53 (pred(Y4!52) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3380, 25])).
% 5.59/5.53 tff(3382,plain,
% 5.59/5.53 (pred(pred(Y4!52)) = pred(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3381])).
% 5.59/5.53 tff(3383,plain,
% 5.59/5.53 (pred(pred(Y4!52)) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3382, 24])).
% 5.59/5.53 tff(3384,plain,
% 5.59/5.53 (pred(pred(pred(Y4!52))) = pred(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3383])).
% 5.59/5.53 tff(3385,plain,
% 5.59/5.53 (pred(pred(pred(Y4!52))) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3384, 23])).
% 5.59/5.53 tff(3386,plain,
% 5.59/5.53 (pred(pred(pred(pred(Y4!52)))) = pred(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3385])).
% 5.59/5.53 tff(3387,plain,
% 5.59/5.53 (pred(pred(pred(pred(Y4!52)))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3386, 22])).
% 5.59/5.53 tff(3388,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3387])).
% 5.59/5.53 tff(3389,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(Y4!52))))) = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[3388, 21])).
% 5.59/5.53 tff(3390,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3389])).
% 5.59/5.53 tff(3391,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3390, 20])).
% 5.59/5.53 tff(3392,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3391])).
% 5.59/5.53 tff(3393,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3392, 19])).
% 5.59/5.53 tff(3394,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3393])).
% 5.59/5.53 tff(3395,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3394, 18])).
% 5.59/5.53 tff(3396,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3395])).
% 5.59/5.53 tff(3397,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3396, 17])).
% 5.59/5.53 tff(3398,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3397])).
% 5.59/5.53 tff(3399,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3398, 16])).
% 5.59/5.53 tff(3400,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3399])).
% 5.59/5.53 tff(3401,plain,
% 5.59/5.53 (NPY4!22 = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[578, 3400, 15])).
% 5.59/5.53 tff(3402,plain,
% 5.59/5.53 (succ(NPY4!22) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3401])).
% 5.59/5.53 tff(3403,plain,
% 5.59/5.53 (succ(NPY4!22) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3402, 14])).
% 5.59/5.53 tff(3404,plain,
% 5.59/5.53 (succ(Y4!52) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3379])).
% 5.59/5.53 tff(3405,plain,
% 5.59/5.53 (succ(Y4!52) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3404, 14])).
% 5.59/5.53 tff(3406,plain,
% 5.59/5.53 (succ(succ(Y4!52)) = succ(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3405])).
% 5.59/5.53 tff(3407,plain,
% 5.59/5.53 (succ(succ(Y4!52)) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3406, 33])).
% 5.59/5.53 tff(3408,plain,
% 5.59/5.53 (succ(succ(succ(Y4!52))) = succ(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3407])).
% 5.59/5.53 tff(3409,plain,
% 5.59/5.53 (succ(succ(succ(Y4!52))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3408, 30])).
% 5.59/5.53 tff(3410,plain,
% 5.59/5.53 (succ(succ(succ(succ(Y4!52)))) = succ(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3409])).
% 5.59/5.53 tff(3411,plain,
% 5.59/5.53 (succ(succ(succ(succ(Y4!52)))) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3410, 39])).
% 5.59/5.53 tff(3412,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3411])).
% 5.59/5.53 tff(3413,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(Y4!52))))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3412, 53])).
% 5.59/5.53 tff(3414,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3413])).
% 5.59/5.53 tff(3415,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[3414, 45])).
% 5.59/5.53 tff(3416,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3415])).
% 5.59/5.53 tff(3417,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3416, 28])).
% 5.59/5.53 tff(3418,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3417])).
% 5.59/5.53 tff(3419,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3418, 42])).
% 5.59/5.53 tff(3420,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3419])).
% 5.59/5.53 tff(3421,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3420, 58])).
% 5.59/5.53 tff(3422,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3421])).
% 5.59/5.53 tff(3423,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3422, 36])).
% 5.59/5.53 tff(3424,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3423])).
% 5.59/5.53 tff(3425,plain,
% 5.59/5.53 (NSY4!20 = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[601, 3424, 48])).
% 5.59/5.53 tff(3426,plain,
% 5.59/5.53 (pred(NSY4!20) = pred(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3425])).
% 5.59/5.53 tff(3427,plain,
% 5.59/5.53 (pred(NSY4!20) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3426, 25])).
% 5.59/5.53 tff(3428,plain,
% 5.59/5.53 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n2, n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3427, 3403])).
% 5.59/5.53 tff(3429,plain,
% 5.59/5.53 (sum(pred(NSY4!20), succ(NPY4!22)) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3428, 13])).
% 5.59/5.53 tff(3430,plain,
% 5.59/5.53 (sum(pred(Y3!54), succ(X3!55)) = sum(n8, n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3273, 3355])).
% 5.59/5.53 tff(3431,plain,
% 5.59/5.53 (sum(pred(Y3!54), succ(X3!55)) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3430, 27])).
% 5.59/5.53 tff(3432,plain,
% 5.59/5.53 (sum(pred(X3!55), succ(Y3!54)) = sum(n8, n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3329, 3297])).
% 5.59/5.53 tff(3433,plain,
% 5.59/5.53 (sum(pred(X3!55), succ(Y3!54)) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3432, 27])).
% 5.59/5.53 tff(3434,plain,
% 5.59/5.53 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n7, n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3433, 3431])).
% 5.59/5.53 tff(3435,plain,
% 5.59/5.53 (X4!53 = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[438, 3434, 26])).
% 5.59/5.53 tff(3436,plain,
% 5.59/5.53 (pred(X4!53) = pred(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3435])).
% 5.59/5.53 tff(3437,plain,
% 5.59/5.53 (pred(X4!53) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3436, 25])).
% 5.59/5.53 tff(3438,plain,
% 5.59/5.53 (pred(pred(X4!53)) = pred(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3437])).
% 5.59/5.53 tff(3439,plain,
% 5.59/5.53 (pred(pred(X4!53)) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3438, 24])).
% 5.59/5.53 tff(3440,plain,
% 5.59/5.53 (pred(pred(pred(X4!53))) = pred(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3439])).
% 5.59/5.53 tff(3441,plain,
% 5.59/5.53 (pred(pred(pred(X4!53))) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3440, 23])).
% 5.59/5.53 tff(3442,plain,
% 5.59/5.53 (pred(pred(pred(pred(X4!53)))) = pred(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3441])).
% 5.59/5.53 tff(3443,plain,
% 5.59/5.53 (pred(pred(pred(pred(X4!53)))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3442, 22])).
% 5.59/5.53 tff(3444,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(X4!53))))) = pred(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3443])).
% 5.59/5.53 tff(3445,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(X4!53))))) = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[3444, 21])).
% 5.59/5.53 tff(3446,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3445])).
% 5.59/5.53 tff(3447,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3446, 20])).
% 5.59/5.53 tff(3448,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3447])).
% 5.59/5.53 tff(3449,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3448, 19])).
% 5.59/5.53 tff(3450,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3449])).
% 5.59/5.53 tff(3451,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3450, 18])).
% 5.59/5.53 tff(3452,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3451])).
% 5.59/5.53 tff(3453,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3452, 17])).
% 5.59/5.53 tff(3454,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3453])).
% 5.59/5.53 tff(3455,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3454, 16])).
% 5.59/5.53 tff(3456,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3455])).
% 5.59/5.53 tff(3457,plain,
% 5.59/5.53 (NPX4!23 = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[626, 3456, 15])).
% 5.59/5.53 tff(3458,plain,
% 5.59/5.53 (succ(NPX4!23) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3457])).
% 5.59/5.53 tff(3459,plain,
% 5.59/5.53 (succ(NPX4!23) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3458, 14])).
% 5.59/5.53 tff(3460,plain,
% 5.59/5.53 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n4, n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3459, 3429])).
% 5.59/5.53 tff(3461,plain,
% 5.59/5.53 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3460, 12])).
% 5.59/5.53 tff(3462,plain,
% 5.59/5.53 (succ(X4!53) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3435])).
% 5.59/5.53 tff(3463,plain,
% 5.59/5.53 (succ(X4!53) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3462, 14])).
% 5.59/5.53 tff(3464,plain,
% 5.59/5.53 (succ(succ(X4!53)) = succ(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3463])).
% 5.59/5.53 tff(3465,plain,
% 5.59/5.53 (succ(succ(X4!53)) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3464, 33])).
% 5.59/5.53 tff(3466,plain,
% 5.59/5.53 (succ(succ(succ(X4!53))) = succ(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3465])).
% 5.59/5.53 tff(3467,plain,
% 5.59/5.53 (succ(succ(succ(X4!53))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3466, 30])).
% 5.59/5.53 tff(3468,plain,
% 5.59/5.53 (succ(succ(succ(succ(X4!53)))) = succ(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3467])).
% 5.59/5.53 tff(3469,plain,
% 5.59/5.53 (succ(succ(succ(succ(X4!53)))) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3468, 39])).
% 5.59/5.53 tff(3470,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(X4!53))))) = succ(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3469])).
% 5.59/5.53 tff(3471,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(X4!53))))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3470, 53])).
% 5.59/5.53 tff(3472,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3471])).
% 5.59/5.53 tff(3473,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[3472, 45])).
% 5.59/5.53 tff(3474,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3473])).
% 5.59/5.53 tff(3475,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3474, 28])).
% 5.59/5.53 tff(3476,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3475])).
% 5.59/5.53 tff(3477,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3476, 42])).
% 5.59/5.53 tff(3478,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3477])).
% 5.59/5.53 tff(3479,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[3478, 58])).
% 5.59/5.53 tff(3480,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3479])).
% 5.59/5.53 tff(3481,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3480, 36])).
% 5.59/5.53 tff(3482,plain,
% 5.59/5.53 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3481])).
% 5.59/5.53 tff(3483,plain,
% 5.59/5.53 (NSX4!21 = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[651, 3482, 48])).
% 5.59/5.53 tff(3484,plain,
% 5.59/5.53 (pred(NSX4!21) = pred(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3483])).
% 5.59/5.53 tff(3485,plain,
% 5.59/5.53 (pred(NSX4!21) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3484, 25])).
% 5.59/5.53 tff(3486,plain,
% 5.59/5.53 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n2, n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3485, 3461])).
% 5.59/5.53 tff(3487,plain,
% 5.59/5.53 (Y5!50 = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[656, 3486, 327])).
% 5.59/5.53 tff(3488,plain,
% 5.59/5.53 (pred(Y5!50) = pred(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3487])).
% 5.59/5.53 tff(3489,plain,
% 5.59/5.53 (pred(Y5!50) = n0),
% 5.59/5.53 inference(transitivity,[status(thm)],[3488, 23])).
% 5.59/5.53 tff(3490,plain,
% 5.59/5.53 (pred(pred(Y5!50)) = pred(n0)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3489])).
% 5.59/5.53 tff(3491,plain,
% 5.59/5.53 (pred(pred(Y5!50)) = n10),
% 5.59/5.53 inference(transitivity,[status(thm)],[3490, 22])).
% 5.59/5.53 tff(3492,plain,
% 5.59/5.53 (pred(pred(pred(Y5!50))) = pred(n10)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3491])).
% 5.59/5.53 tff(3493,plain,
% 5.59/5.53 (pred(pred(pred(Y5!50))) = n9),
% 5.59/5.53 inference(transitivity,[status(thm)],[3492, 21])).
% 5.59/5.53 tff(3494,plain,
% 5.59/5.53 (pred(pred(pred(pred(Y5!50)))) = pred(n9)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3493])).
% 5.59/5.53 tff(3495,plain,
% 5.59/5.53 (pred(pred(pred(pred(Y5!50)))) = n8),
% 5.59/5.53 inference(transitivity,[status(thm)],[3494, 20])).
% 5.59/5.53 tff(3496,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n8)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3495])).
% 5.59/5.53 tff(3497,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(Y5!50))))) = n7),
% 5.59/5.53 inference(transitivity,[status(thm)],[3496, 19])).
% 5.59/5.53 tff(3498,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n7)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3497])).
% 5.59/5.53 tff(3499,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n6),
% 5.59/5.53 inference(transitivity,[status(thm)],[3498, 18])).
% 5.59/5.53 tff(3500,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n6)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3499])).
% 5.59/5.53 tff(3501,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n5),
% 5.59/5.53 inference(transitivity,[status(thm)],[3500, 17])).
% 5.59/5.53 tff(3502,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n5)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3501])).
% 5.59/5.53 tff(3503,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3502, 16])).
% 5.59/5.53 tff(3504,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3503])).
% 5.59/5.53 tff(3505,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[3504, 15])).
% 5.59/5.53 tff(3506,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3505])).
% 5.59/5.53 tff(3507,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3506, 25])).
% 5.59/5.53 tff(3508,plain,
% 5.59/5.53 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3507])).
% 5.59/5.53 tff(3509,plain,
% 5.59/5.53 (NPY5!18 = n1),
% 5.59/5.53 inference(transitivity,[status(thm)],[694, 3508, 24])).
% 5.59/5.53 tff(3510,plain,
% 5.59/5.53 (succ(NPY5!18) = succ(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3509])).
% 5.59/5.53 tff(3511,plain,
% 5.59/5.53 (succ(NPY5!18) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3510, 36])).
% 5.59/5.53 tff(3512,plain,
% 5.59/5.53 (succ(Y5!50) = succ(n1)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3487])).
% 5.59/5.53 tff(3513,plain,
% 5.59/5.53 (succ(Y5!50) = n2),
% 5.59/5.53 inference(transitivity,[status(thm)],[3512, 36])).
% 5.59/5.53 tff(3514,plain,
% 5.59/5.53 (succ(succ(Y5!50)) = succ(n2)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3513])).
% 5.59/5.53 tff(3515,plain,
% 5.59/5.53 (succ(succ(Y5!50)) = n3),
% 5.59/5.53 inference(transitivity,[status(thm)],[3514, 48])).
% 5.59/5.53 tff(3516,plain,
% 5.59/5.53 (succ(succ(succ(Y5!50))) = succ(n3)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3515])).
% 5.59/5.53 tff(3517,plain,
% 5.59/5.53 (succ(succ(succ(Y5!50))) = n4),
% 5.59/5.53 inference(transitivity,[status(thm)],[3516, 14])).
% 5.59/5.53 tff(3518,plain,
% 5.59/5.53 (succ(succ(succ(succ(Y5!50)))) = succ(n4)),
% 5.59/5.53 inference(monotonicity,[status(thm)],[3517])).
% 5.59/5.54 tff(3519,plain,
% 5.59/5.54 (succ(succ(succ(succ(Y5!50)))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3518, 33])).
% 5.59/5.54 tff(3520,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3519])).
% 5.59/5.54 tff(3521,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(Y5!50))))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3520, 30])).
% 5.59/5.54 tff(3522,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3521])).
% 5.59/5.54 tff(3523,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3522, 39])).
% 5.59/5.54 tff(3524,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3523])).
% 5.59/5.54 tff(3525,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3524, 53])).
% 5.59/5.54 tff(3526,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3525])).
% 5.59/5.54 tff(3527,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3526, 45])).
% 5.59/5.54 tff(3528,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3527])).
% 5.59/5.54 tff(3529,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3528, 28])).
% 5.59/5.54 tff(3530,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3529])).
% 5.59/5.54 tff(3531,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3530, 42])).
% 5.59/5.54 tff(3532,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3531])).
% 5.59/5.54 tff(3533,plain,
% 5.59/5.54 (NSY5!16 = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[717, 3532, 58])).
% 5.59/5.54 tff(3534,plain,
% 5.59/5.54 (pred(NSY5!16) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3533])).
% 5.59/5.54 tff(3535,plain,
% 5.59/5.54 (pred(NSY5!16) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3534, 23])).
% 5.59/5.54 tff(3536,plain,
% 5.59/5.54 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n0, n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3535, 3511])).
% 5.59/5.54 tff(3537,plain,
% 5.59/5.54 (sum(pred(NSY5!16), succ(NPY5!18)) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3536, 35])).
% 5.59/5.54 tff(3538,plain,
% 5.59/5.54 (sum(pred(Y4!52), succ(X4!53)) = sum(n2, n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3381, 3463])).
% 5.59/5.54 tff(3539,plain,
% 5.59/5.54 (sum(pred(Y4!52), succ(X4!53)) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3538, 13])).
% 5.59/5.54 tff(3540,plain,
% 5.59/5.54 (sum(pred(X4!53), succ(Y4!52)) = sum(n2, n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3437, 3405])).
% 5.59/5.54 tff(3541,plain,
% 5.59/5.54 (sum(pred(X4!53), succ(Y4!52)) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3540, 13])).
% 5.59/5.54 tff(3542,plain,
% 5.59/5.54 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n6, n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3541, 3539])).
% 5.59/5.54 tff(3543,plain,
% 5.59/5.54 (X5!51 = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[553, 3542, 37])).
% 5.59/5.54 tff(3544,plain,
% 5.59/5.54 (pred(X5!51) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3543])).
% 5.59/5.54 tff(3545,plain,
% 5.59/5.54 (pred(X5!51) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3544, 23])).
% 5.59/5.54 tff(3546,plain,
% 5.59/5.54 (pred(pred(X5!51)) = pred(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3545])).
% 5.59/5.54 tff(3547,plain,
% 5.59/5.54 (pred(pred(X5!51)) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3546, 22])).
% 5.59/5.54 tff(3548,plain,
% 5.59/5.54 (pred(pred(pred(X5!51))) = pred(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3547])).
% 5.59/5.54 tff(3549,plain,
% 5.59/5.54 (pred(pred(pred(X5!51))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3548, 21])).
% 5.59/5.54 tff(3550,plain,
% 5.59/5.54 (pred(pred(pred(pred(X5!51)))) = pred(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3549])).
% 5.59/5.54 tff(3551,plain,
% 5.59/5.54 (pred(pred(pred(pred(X5!51)))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3550, 20])).
% 5.59/5.54 tff(3552,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(X5!51))))) = pred(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3551])).
% 5.59/5.54 tff(3553,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(X5!51))))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3552, 19])).
% 5.59/5.54 tff(3554,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3553])).
% 5.59/5.54 tff(3555,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3554, 18])).
% 5.59/5.54 tff(3556,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3555])).
% 5.59/5.54 tff(3557,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3556, 17])).
% 5.59/5.54 tff(3558,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3557])).
% 5.59/5.54 tff(3559,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3558, 16])).
% 5.59/5.54 tff(3560,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3559])).
% 5.59/5.54 tff(3561,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3560, 15])).
% 5.59/5.54 tff(3562,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3561])).
% 5.59/5.54 tff(3563,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3562, 25])).
% 5.59/5.54 tff(3564,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3563])).
% 5.59/5.54 tff(3565,plain,
% 5.59/5.54 (NPX5!19 = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[742, 3564, 24])).
% 5.59/5.54 tff(3566,plain,
% 5.59/5.54 (succ(NPX5!19) = succ(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3565])).
% 5.59/5.54 tff(3567,plain,
% 5.59/5.54 (succ(NPX5!19) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3566, 36])).
% 5.59/5.54 tff(3568,plain,
% 5.59/5.54 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n2, n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3567, 3537])).
% 5.59/5.54 tff(3569,plain,
% 5.59/5.54 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3568, 34])).
% 5.59/5.54 tff(3570,plain,
% 5.59/5.54 (succ(X5!51) = succ(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3543])).
% 5.59/5.54 tff(3571,plain,
% 5.59/5.54 (succ(X5!51) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3570, 36])).
% 5.59/5.54 tff(3572,plain,
% 5.59/5.54 (succ(succ(X5!51)) = succ(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3571])).
% 5.59/5.54 tff(3573,plain,
% 5.59/5.54 (succ(succ(X5!51)) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3572, 48])).
% 5.59/5.54 tff(3574,plain,
% 5.59/5.54 (succ(succ(succ(X5!51))) = succ(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3573])).
% 5.59/5.54 tff(3575,plain,
% 5.59/5.54 (succ(succ(succ(X5!51))) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3574, 14])).
% 5.59/5.54 tff(3576,plain,
% 5.59/5.54 (succ(succ(succ(succ(X5!51)))) = succ(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3575])).
% 5.59/5.54 tff(3577,plain,
% 5.59/5.54 (succ(succ(succ(succ(X5!51)))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3576, 33])).
% 5.59/5.54 tff(3578,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(X5!51))))) = succ(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3577])).
% 5.59/5.54 tff(3579,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(X5!51))))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3578, 30])).
% 5.59/5.54 tff(3580,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3579])).
% 5.59/5.54 tff(3581,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3580, 39])).
% 5.59/5.54 tff(3582,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3581])).
% 5.59/5.54 tff(3583,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3582, 53])).
% 5.59/5.54 tff(3584,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3583])).
% 5.59/5.54 tff(3585,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3584, 45])).
% 5.59/5.54 tff(3586,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3585])).
% 5.59/5.54 tff(3587,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3586, 28])).
% 5.59/5.54 tff(3588,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3587])).
% 5.59/5.54 tff(3589,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3588, 42])).
% 5.59/5.54 tff(3590,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3589])).
% 5.59/5.54 tff(3591,plain,
% 5.59/5.54 (NSX5!17 = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[767, 3590, 58])).
% 5.59/5.54 tff(3592,plain,
% 5.59/5.54 (pred(NSX5!17) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3591])).
% 5.59/5.54 tff(3593,plain,
% 5.59/5.54 (pred(NSX5!17) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3592, 23])).
% 5.59/5.54 tff(3594,plain,
% 5.59/5.54 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n0, n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3593, 3569])).
% 5.59/5.54 tff(3595,plain,
% 5.59/5.54 (Y6!48 = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[772, 3594, 442])).
% 5.59/5.54 tff(3596,plain,
% 5.59/5.54 (pred(Y6!48) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3595])).
% 5.59/5.54 tff(3597,plain,
% 5.59/5.54 (pred(Y6!48) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3596, 15])).
% 5.59/5.54 tff(3598,plain,
% 5.59/5.54 (pred(pred(Y6!48)) = pred(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3597])).
% 5.59/5.54 tff(3599,plain,
% 5.59/5.54 (pred(pred(Y6!48)) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3598, 25])).
% 5.59/5.54 tff(3600,plain,
% 5.59/5.54 (pred(pred(pred(Y6!48))) = pred(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3599])).
% 5.59/5.54 tff(3601,plain,
% 5.59/5.54 (pred(pred(pred(Y6!48))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3600, 24])).
% 5.59/5.54 tff(3602,plain,
% 5.59/5.54 (pred(pred(pred(pred(Y6!48)))) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3601])).
% 5.59/5.54 tff(3603,plain,
% 5.59/5.54 (pred(pred(pred(pred(Y6!48)))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3602, 23])).
% 5.59/5.54 tff(3604,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3603])).
% 5.59/5.54 tff(3605,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(Y6!48))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3604, 22])).
% 5.59/5.54 tff(3606,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3605])).
% 5.59/5.54 tff(3607,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3606, 21])).
% 5.59/5.54 tff(3608,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3607])).
% 5.59/5.54 tff(3609,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3608, 20])).
% 5.59/5.54 tff(3610,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3609])).
% 5.59/5.54 tff(3611,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3610, 19])).
% 5.59/5.54 tff(3612,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3611])).
% 5.59/5.54 tff(3613,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3612, 18])).
% 5.59/5.54 tff(3614,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3613])).
% 5.59/5.54 tff(3615,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3614, 17])).
% 5.59/5.54 tff(3616,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3615])).
% 5.59/5.54 tff(3617,plain,
% 5.59/5.54 (NPY6!14 = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[1465, 3616, 16])).
% 5.59/5.54 tff(3618,plain,
% 5.59/5.54 (succ(NPY6!14) = succ(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3617])).
% 5.59/5.54 tff(3619,plain,
% 5.59/5.54 (succ(NPY6!14) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3618, 33])).
% 5.59/5.54 tff(3620,plain,
% 5.59/5.54 (succ(Y6!48) = succ(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3595])).
% 5.59/5.54 tff(3621,plain,
% 5.59/5.54 (succ(Y6!48) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3620, 33])).
% 5.59/5.54 tff(3622,plain,
% 5.59/5.54 (succ(succ(Y6!48)) = succ(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3621])).
% 5.59/5.54 tff(3623,plain,
% 5.59/5.54 (succ(succ(Y6!48)) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3622, 30])).
% 5.59/5.54 tff(3624,plain,
% 5.59/5.54 (succ(succ(succ(Y6!48))) = succ(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3623])).
% 5.59/5.54 tff(3625,plain,
% 5.59/5.54 (succ(succ(succ(Y6!48))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3624, 39])).
% 5.59/5.54 tff(3626,plain,
% 5.59/5.54 (succ(succ(succ(succ(Y6!48)))) = succ(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3625])).
% 5.59/5.54 tff(3627,plain,
% 5.59/5.54 (succ(succ(succ(succ(Y6!48)))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3626, 53])).
% 5.59/5.54 tff(3628,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3627])).
% 5.59/5.54 tff(3629,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(Y6!48))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3628, 45])).
% 5.59/5.54 tff(3630,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3629])).
% 5.59/5.54 tff(3631,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3630, 28])).
% 5.59/5.54 tff(3632,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3631])).
% 5.59/5.54 tff(3633,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3632, 42])).
% 5.59/5.54 tff(3634,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3633])).
% 5.59/5.54 tff(3635,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3634, 58])).
% 5.59/5.54 tff(3636,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3635])).
% 5.59/5.54 tff(3637,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3636, 36])).
% 5.59/5.54 tff(3638,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3637])).
% 5.59/5.54 tff(3639,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3638, 48])).
% 5.59/5.54 tff(3640,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3639])).
% 5.59/5.54 tff(3641,plain,
% 5.59/5.54 (NSY6!12 = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[1490, 3640, 14])).
% 5.59/5.54 tff(3642,plain,
% 5.59/5.54 (pred(NSY6!12) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3641])).
% 5.59/5.54 tff(3643,plain,
% 5.59/5.54 (pred(NSY6!12) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3642, 15])).
% 5.59/5.54 tff(3644,plain,
% 5.59/5.54 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n3, n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3643, 3619])).
% 5.59/5.54 tff(3645,plain,
% 5.59/5.54 (sum(pred(NSY6!12), succ(NPY6!14)) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3644, 32])).
% 5.59/5.54 tff(3646,plain,
% 5.59/5.54 (sum(pred(Y5!50), succ(X5!51)) = sum(n0, n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3489, 3571])).
% 5.59/5.54 tff(3647,plain,
% 5.59/5.54 (sum(pred(Y5!50), succ(X5!51)) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3646, 35])).
% 5.59/5.54 tff(3648,plain,
% 5.59/5.54 (sum(pred(X5!51), succ(Y5!50)) = sum(n0, n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3545, 3513])).
% 5.59/5.54 tff(3649,plain,
% 5.59/5.54 (sum(pred(X5!51), succ(Y5!50)) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3648, 35])).
% 5.59/5.54 tff(3650,plain,
% 5.59/5.54 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n2, n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3649, 3647])).
% 5.59/5.54 tff(3651,plain,
% 5.59/5.54 (X6!49 = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[669, 3650, 34])).
% 5.59/5.54 tff(3652,plain,
% 5.59/5.54 (pred(X6!49) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3651])).
% 5.59/5.54 tff(3653,plain,
% 5.59/5.54 (pred(X6!49) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3652, 15])).
% 5.59/5.54 tff(3654,plain,
% 5.59/5.54 (pred(pred(X6!49)) = pred(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3653])).
% 5.59/5.54 tff(3655,plain,
% 5.59/5.54 (pred(pred(X6!49)) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3654, 25])).
% 5.59/5.54 tff(3656,plain,
% 5.59/5.54 (pred(pred(pred(X6!49))) = pred(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3655])).
% 5.59/5.54 tff(3657,plain,
% 5.59/5.54 (pred(pred(pred(X6!49))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3656, 24])).
% 5.59/5.54 tff(3658,plain,
% 5.59/5.54 (pred(pred(pred(pred(X6!49)))) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3657])).
% 5.59/5.54 tff(3659,plain,
% 5.59/5.54 (pred(pred(pred(pred(X6!49)))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3658, 23])).
% 5.59/5.54 tff(3660,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(X6!49))))) = pred(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3659])).
% 5.59/5.54 tff(3661,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(X6!49))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3660, 22])).
% 5.59/5.54 tff(3662,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3661])).
% 5.59/5.54 tff(3663,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3662, 21])).
% 5.59/5.54 tff(3664,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3663])).
% 5.59/5.54 tff(3665,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3664, 20])).
% 5.59/5.54 tff(3666,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3665])).
% 5.59/5.54 tff(3667,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3666, 19])).
% 5.59/5.54 tff(3668,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3667])).
% 5.59/5.54 tff(3669,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3668, 18])).
% 5.59/5.54 tff(3670,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3669])).
% 5.59/5.54 tff(3671,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3670, 17])).
% 5.59/5.54 tff(3672,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3671])).
% 5.59/5.54 tff(3673,plain,
% 5.59/5.54 (NPX6!15 = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[1523, 3672, 16])).
% 5.59/5.54 tff(3674,plain,
% 5.59/5.54 (succ(NPX6!15) = succ(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3673])).
% 5.59/5.54 tff(3675,plain,
% 5.59/5.54 (succ(NPX6!15) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3674, 33])).
% 5.59/5.54 tff(3676,plain,
% 5.59/5.54 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n5, n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3675, 3645])).
% 5.59/5.54 tff(3677,plain,
% 5.59/5.54 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3676, 558])).
% 5.59/5.54 tff(3678,plain,
% 5.59/5.54 (succ(X6!49) = succ(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3651])).
% 5.59/5.54 tff(3679,plain,
% 5.59/5.54 (succ(X6!49) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3678, 33])).
% 5.59/5.54 tff(3680,plain,
% 5.59/5.54 (succ(succ(X6!49)) = succ(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3679])).
% 5.59/5.54 tff(3681,plain,
% 5.59/5.54 (succ(succ(X6!49)) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3680, 30])).
% 5.59/5.54 tff(3682,plain,
% 5.59/5.54 (succ(succ(succ(X6!49))) = succ(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3681])).
% 5.59/5.54 tff(3683,plain,
% 5.59/5.54 (succ(succ(succ(X6!49))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3682, 39])).
% 5.59/5.54 tff(3684,plain,
% 5.59/5.54 (succ(succ(succ(succ(X6!49)))) = succ(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3683])).
% 5.59/5.54 tff(3685,plain,
% 5.59/5.54 (succ(succ(succ(succ(X6!49)))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3684, 53])).
% 5.59/5.54 tff(3686,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(X6!49))))) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3685])).
% 5.59/5.54 tff(3687,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(X6!49))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3686, 45])).
% 5.59/5.54 tff(3688,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3687])).
% 5.59/5.54 tff(3689,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3688, 28])).
% 5.59/5.54 tff(3690,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3689])).
% 5.59/5.54 tff(3691,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3690, 42])).
% 5.59/5.54 tff(3692,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3691])).
% 5.59/5.54 tff(3693,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3692, 58])).
% 5.59/5.54 tff(3694,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3693])).
% 5.59/5.54 tff(3695,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3694, 36])).
% 5.59/5.54 tff(3696,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3695])).
% 5.59/5.54 tff(3697,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3696, 48])).
% 5.59/5.54 tff(3698,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3697])).
% 5.59/5.54 tff(3699,plain,
% 5.59/5.54 (NSX6!13 = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[1550, 3698, 14])).
% 5.59/5.54 tff(3700,plain,
% 5.59/5.54 (pred(NSX6!13) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3699])).
% 5.59/5.54 tff(3701,plain,
% 5.59/5.54 (pred(NSX6!13) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3700, 15])).
% 5.59/5.54 tff(3702,plain,
% 5.59/5.54 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n3, n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3701, 3677])).
% 5.59/5.54 tff(3703,plain,
% 5.59/5.54 (sum(n3, n2) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.59/5.54 inference(symmetry,[status(thm)],[3702])).
% 5.59/5.54 tff(3704,plain,
% 5.59/5.54 (sum(pred(Y6!48), succ(X6!49)) = sum(n3, n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3597, 3679])).
% 5.59/5.54 tff(3705,plain,
% 5.59/5.54 (sum(pred(Y6!48), succ(X6!49)) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3704, 32])).
% 5.59/5.54 tff(3706,plain,
% 5.59/5.54 (sum(pred(X6!49), succ(Y6!48)) = sum(n3, n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3653, 3621])).
% 5.59/5.54 tff(3707,plain,
% 5.59/5.54 (sum(pred(X6!49), succ(Y6!48)) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3706, 32])).
% 5.59/5.54 tff(3708,plain,
% 5.59/5.54 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n8, n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3707, 3705])).
% 5.59/5.54 tff(3709,plain,
% 5.59/5.54 (X7!47 = Y7!46),
% 5.59/5.54 inference(transitivity,[status(thm)],[785, 3708, 31, 2275, 3703, 794])).
% 5.59/5.54 tff(3710,plain,
% 5.59/5.54 ($false),
% 5.59/5.54 inference(unit_resolution,[status(thm)],[792, 3709])).
% 5.59/5.54 tff(3711,plain,((~(Y0!60 = n7)) | (X7!47 = Y7!46) | (~(X0!61 = n6))), inference(lemma,lemma(discharge,[]))).
% 5.59/5.54 tff(3712,plain,
% 5.59/5.54 (~(X0!61 = n6)),
% 5.59/5.54 inference(unit_resolution,[status(thm)],[3711, 2285, 792])).
% 5.59/5.54 tff(3713,plain,
% 5.59/5.54 (sum(n9, n3) = n1),
% 5.59/5.54 inference(and_elim,[status(thm)],[9])).
% 5.59/5.54 tff(3714,plain,
% 5.59/5.54 (sum(n0, n3) = n3),
% 5.59/5.54 inference(and_elim,[status(thm)],[9])).
% 5.59/5.54 tff(3715,assumption,(X0!61 = n10), introduced(assumption)).
% 5.59/5.54 tff(3716,plain,
% 5.59/5.54 (sum(n9, n10) = n8),
% 5.59/5.54 inference(and_elim,[status(thm)],[9])).
% 5.59/5.54 tff(3717,plain,
% 5.59/5.54 (sum(n0, n10) = n10),
% 5.59/5.54 inference(and_elim,[status(thm)],[9])).
% 5.59/5.54 tff(3718,assumption,(Y0!60 = n5), introduced(assumption)).
% 5.59/5.54 tff(3719,plain,
% 5.59/5.54 (pred(Y0!60) = pred(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3718])).
% 5.59/5.54 tff(3720,plain,
% 5.59/5.54 (pred(Y0!60) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3719, 16])).
% 5.59/5.54 tff(3721,plain,
% 5.59/5.54 (pred(pred(Y0!60)) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3720])).
% 5.59/5.54 tff(3722,plain,
% 5.59/5.54 (pred(pred(Y0!60)) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3721, 15])).
% 5.59/5.54 tff(3723,plain,
% 5.59/5.54 (pred(pred(pred(Y0!60))) = pred(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3722])).
% 5.59/5.54 tff(3724,plain,
% 5.59/5.54 (pred(pred(pred(Y0!60))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3723, 25])).
% 5.59/5.54 tff(3725,plain,
% 5.59/5.54 (pred(pred(pred(pred(Y0!60)))) = pred(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3724])).
% 5.59/5.54 tff(3726,plain,
% 5.59/5.54 (pred(pred(pred(pred(Y0!60)))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3725, 24])).
% 5.59/5.54 tff(3727,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3726])).
% 5.59/5.54 tff(3728,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(Y0!60))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3727, 23])).
% 5.59/5.54 tff(3729,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3728])).
% 5.59/5.54 tff(3730,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3729, 22])).
% 5.59/5.54 tff(3731,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3730])).
% 5.59/5.54 tff(3732,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3731, 21])).
% 5.59/5.54 tff(3733,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3732])).
% 5.59/5.54 tff(3734,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3733, 20])).
% 5.59/5.54 tff(3735,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3734])).
% 5.59/5.54 tff(3736,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3735, 19])).
% 5.59/5.54 tff(3737,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3736])).
% 5.59/5.54 tff(3738,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3737, 18])).
% 5.59/5.54 tff(3739,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3738])).
% 5.59/5.54 tff(3740,plain,
% 5.59/5.54 (NPY0!38 = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[118, 3739, 17])).
% 5.59/5.54 tff(3741,plain,
% 5.59/5.54 (succ(NPY0!38) = succ(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3740])).
% 5.59/5.54 tff(3742,plain,
% 5.59/5.54 (succ(NPY0!38) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3741, 30])).
% 5.59/5.54 tff(3743,plain,
% 5.59/5.54 (succ(Y0!60) = succ(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3718])).
% 5.59/5.54 tff(3744,plain,
% 5.59/5.54 (succ(Y0!60) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3743, 30])).
% 5.59/5.54 tff(3745,plain,
% 5.59/5.54 (succ(succ(Y0!60)) = succ(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3744])).
% 5.59/5.54 tff(3746,plain,
% 5.59/5.54 (succ(succ(Y0!60)) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3745, 39])).
% 5.59/5.54 tff(3747,plain,
% 5.59/5.54 (succ(succ(succ(Y0!60))) = succ(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3746])).
% 5.59/5.54 tff(3748,plain,
% 5.59/5.54 (succ(succ(succ(Y0!60))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3747, 53])).
% 5.59/5.54 tff(3749,plain,
% 5.59/5.54 (succ(succ(succ(succ(Y0!60)))) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3748])).
% 5.59/5.54 tff(3750,plain,
% 5.59/5.54 (succ(succ(succ(succ(Y0!60)))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3749, 45])).
% 5.59/5.54 tff(3751,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3750])).
% 5.59/5.54 tff(3752,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(Y0!60))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3751, 28])).
% 5.59/5.54 tff(3753,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3752])).
% 5.59/5.54 tff(3754,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3753, 42])).
% 5.59/5.54 tff(3755,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3754])).
% 5.59/5.54 tff(3756,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3755, 58])).
% 5.59/5.54 tff(3757,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3756])).
% 5.59/5.54 tff(3758,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3757, 36])).
% 5.59/5.54 tff(3759,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3758])).
% 5.59/5.54 tff(3760,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3759, 48])).
% 5.59/5.54 tff(3761,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3760])).
% 5.59/5.54 tff(3762,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3761, 14])).
% 5.59/5.54 tff(3763,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3762])).
% 5.59/5.54 tff(3764,plain,
% 5.59/5.54 (NSY0!36 = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[141, 3763, 33])).
% 5.59/5.54 tff(3765,plain,
% 5.59/5.54 (pred(NSY0!36) = pred(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3764])).
% 5.59/5.54 tff(3766,plain,
% 5.59/5.54 (pred(NSY0!36) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3765, 16])).
% 5.59/5.54 tff(3767,plain,
% 5.59/5.54 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n4, n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3766, 3742])).
% 5.59/5.54 tff(3768,plain,
% 5.59/5.54 (sum(pred(NSY0!36), succ(NPY0!38)) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3767, 12])).
% 5.59/5.54 tff(3769,plain,
% 5.59/5.54 (pred(X0!61) = pred(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3715])).
% 5.59/5.54 tff(3770,plain,
% 5.59/5.54 (pred(X0!61) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3769, 21])).
% 5.59/5.54 tff(3771,plain,
% 5.59/5.54 (pred(pred(X0!61)) = pred(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3770])).
% 5.59/5.54 tff(3772,plain,
% 5.59/5.54 (pred(pred(X0!61)) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3771, 20])).
% 5.59/5.54 tff(3773,plain,
% 5.59/5.54 (pred(pred(pred(X0!61))) = pred(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3772])).
% 5.59/5.54 tff(3774,plain,
% 5.59/5.54 (pred(pred(pred(X0!61))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3773, 19])).
% 5.59/5.54 tff(3775,plain,
% 5.59/5.54 (pred(pred(pred(pred(X0!61)))) = pred(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3774])).
% 5.59/5.54 tff(3776,plain,
% 5.59/5.54 (pred(pred(pred(pred(X0!61)))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3775, 18])).
% 5.59/5.54 tff(3777,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(X0!61))))) = pred(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3776])).
% 5.59/5.54 tff(3778,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(X0!61))))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3777, 17])).
% 5.59/5.54 tff(3779,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3778])).
% 5.59/5.54 tff(3780,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3779, 16])).
% 5.59/5.54 tff(3781,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3780])).
% 5.59/5.54 tff(3782,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3781, 15])).
% 5.59/5.54 tff(3783,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3782])).
% 5.59/5.54 tff(3784,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3783, 25])).
% 5.59/5.54 tff(3785,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3784])).
% 5.59/5.54 tff(3786,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3785, 24])).
% 5.59/5.54 tff(3787,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3786])).
% 5.59/5.54 tff(3788,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3787, 23])).
% 5.59/5.54 tff(3789,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3788])).
% 5.59/5.54 tff(3790,plain,
% 5.59/5.54 (NPX0!39 = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[166, 3789, 22])).
% 5.59/5.54 tff(3791,plain,
% 5.59/5.54 (succ(NPX0!39) = succ(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3790])).
% 5.59/5.54 tff(3792,plain,
% 5.59/5.54 (succ(NPX0!39) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3791, 42])).
% 5.59/5.54 tff(3793,plain,
% 5.59/5.54 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n0, n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3792, 3768])).
% 5.59/5.54 tff(3794,plain,
% 5.59/5.54 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3793, 3717])).
% 5.59/5.54 tff(3795,plain,
% 5.59/5.54 (succ(X0!61) = succ(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3715])).
% 5.59/5.54 tff(3796,plain,
% 5.59/5.54 (succ(X0!61) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3795, 42])).
% 5.59/5.54 tff(3797,plain,
% 5.59/5.54 (succ(succ(X0!61)) = succ(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3796])).
% 5.59/5.54 tff(3798,plain,
% 5.59/5.54 (succ(succ(X0!61)) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3797, 58])).
% 5.59/5.54 tff(3799,plain,
% 5.59/5.54 (succ(succ(succ(X0!61))) = succ(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3798])).
% 5.59/5.54 tff(3800,plain,
% 5.59/5.54 (succ(succ(succ(X0!61))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3799, 36])).
% 5.59/5.54 tff(3801,plain,
% 5.59/5.54 (succ(succ(succ(succ(X0!61)))) = succ(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3800])).
% 5.59/5.54 tff(3802,plain,
% 5.59/5.54 (succ(succ(succ(succ(X0!61)))) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3801, 48])).
% 5.59/5.54 tff(3803,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(X0!61))))) = succ(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3802])).
% 5.59/5.54 tff(3804,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(X0!61))))) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3803, 14])).
% 5.59/5.54 tff(3805,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3804])).
% 5.59/5.54 tff(3806,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3805, 33])).
% 5.59/5.54 tff(3807,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3806])).
% 5.59/5.54 tff(3808,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3807, 30])).
% 5.59/5.54 tff(3809,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3808])).
% 5.59/5.54 tff(3810,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3809, 39])).
% 5.59/5.54 tff(3811,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3810])).
% 5.59/5.54 tff(3812,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[3811, 53])).
% 5.59/5.54 tff(3813,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3812])).
% 5.59/5.54 tff(3814,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3813, 45])).
% 5.59/5.54 tff(3815,plain,
% 5.59/5.54 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3814])).
% 5.59/5.54 tff(3816,plain,
% 5.59/5.54 (NSX0!37 = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[191, 3815, 28])).
% 5.59/5.54 tff(3817,plain,
% 5.59/5.54 (pred(NSX0!37) = pred(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3816])).
% 5.59/5.54 tff(3818,plain,
% 5.59/5.54 (pred(NSX0!37) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3817, 21])).
% 5.59/5.54 tff(3819,plain,
% 5.59/5.54 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n9, n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3818, 3794])).
% 5.59/5.54 tff(3820,plain,
% 5.59/5.54 (Y1!58 = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[196, 3819, 3716])).
% 5.59/5.54 tff(3821,plain,
% 5.59/5.54 (pred(Y1!58) = pred(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3820])).
% 5.59/5.54 tff(3822,plain,
% 5.59/5.54 (pred(Y1!58) = n7),
% 5.59/5.54 inference(transitivity,[status(thm)],[3821, 19])).
% 5.59/5.54 tff(3823,plain,
% 5.59/5.54 (pred(pred(Y1!58)) = pred(n7)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3822])).
% 5.59/5.54 tff(3824,plain,
% 5.59/5.54 (pred(pred(Y1!58)) = n6),
% 5.59/5.54 inference(transitivity,[status(thm)],[3823, 18])).
% 5.59/5.54 tff(3825,plain,
% 5.59/5.54 (pred(pred(pred(Y1!58))) = pred(n6)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3824])).
% 5.59/5.54 tff(3826,plain,
% 5.59/5.54 (pred(pred(pred(Y1!58))) = n5),
% 5.59/5.54 inference(transitivity,[status(thm)],[3825, 17])).
% 5.59/5.54 tff(3827,plain,
% 5.59/5.54 (pred(pred(pred(pred(Y1!58)))) = pred(n5)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3826])).
% 5.59/5.54 tff(3828,plain,
% 5.59/5.54 (pred(pred(pred(pred(Y1!58)))) = n4),
% 5.59/5.54 inference(transitivity,[status(thm)],[3827, 16])).
% 5.59/5.54 tff(3829,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n4)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3828])).
% 5.59/5.54 tff(3830,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(Y1!58))))) = n3),
% 5.59/5.54 inference(transitivity,[status(thm)],[3829, 15])).
% 5.59/5.54 tff(3831,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n3)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3830])).
% 5.59/5.54 tff(3832,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n2),
% 5.59/5.54 inference(transitivity,[status(thm)],[3831, 25])).
% 5.59/5.54 tff(3833,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n2)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3832])).
% 5.59/5.54 tff(3834,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n1),
% 5.59/5.54 inference(transitivity,[status(thm)],[3833, 24])).
% 5.59/5.54 tff(3835,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n1)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3834])).
% 5.59/5.54 tff(3836,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n0),
% 5.59/5.54 inference(transitivity,[status(thm)],[3835, 23])).
% 5.59/5.54 tff(3837,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n0)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3836])).
% 5.59/5.54 tff(3838,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n10),
% 5.59/5.54 inference(transitivity,[status(thm)],[3837, 22])).
% 5.59/5.54 tff(3839,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n10)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3838])).
% 5.59/5.54 tff(3840,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3839, 21])).
% 5.59/5.54 tff(3841,plain,
% 5.59/5.54 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3840])).
% 5.59/5.54 tff(3842,plain,
% 5.59/5.54 (NPY1!34 = n8),
% 5.59/5.54 inference(transitivity,[status(thm)],[232, 3841, 20])).
% 5.59/5.54 tff(3843,plain,
% 5.59/5.54 (succ(NPY1!34) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3842])).
% 5.59/5.54 tff(3844,plain,
% 5.59/5.54 (succ(NPY1!34) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3843, 45])).
% 5.59/5.54 tff(3845,plain,
% 5.59/5.54 (succ(Y1!58) = succ(n8)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3820])).
% 5.59/5.54 tff(3846,plain,
% 5.59/5.54 (succ(Y1!58) = n9),
% 5.59/5.54 inference(transitivity,[status(thm)],[3845, 45])).
% 5.59/5.54 tff(3847,plain,
% 5.59/5.54 (succ(succ(Y1!58)) = succ(n9)),
% 5.59/5.54 inference(monotonicity,[status(thm)],[3846])).
% 5.59/5.55 tff(3848,plain,
% 5.59/5.55 (succ(succ(Y1!58)) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[3847, 28])).
% 5.59/5.55 tff(3849,plain,
% 5.59/5.55 (succ(succ(succ(Y1!58))) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3848])).
% 5.59/5.55 tff(3850,plain,
% 5.59/5.55 (succ(succ(succ(Y1!58))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[3849, 42])).
% 5.59/5.55 tff(3851,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y1!58)))) = succ(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3850])).
% 5.59/5.55 tff(3852,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y1!58)))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[3851, 58])).
% 5.59/5.55 tff(3853,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3852])).
% 5.59/5.55 tff(3854,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y1!58))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[3853, 36])).
% 5.59/5.55 tff(3855,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3854])).
% 5.59/5.55 tff(3856,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[3855, 48])).
% 5.59/5.55 tff(3857,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3856])).
% 5.59/5.55 tff(3858,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3857, 14])).
% 5.59/5.55 tff(3859,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3858])).
% 5.59/5.55 tff(3860,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3859, 33])).
% 5.59/5.55 tff(3861,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3860])).
% 5.59/5.55 tff(3862,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[3861, 30])).
% 5.59/5.55 tff(3863,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3862])).
% 5.59/5.55 tff(3864,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3863, 39])).
% 5.59/5.55 tff(3865,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3864])).
% 5.59/5.55 tff(3866,plain,
% 5.59/5.55 (NSY1!32 = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[255, 3865, 53])).
% 5.59/5.55 tff(3867,plain,
% 5.59/5.55 (pred(NSY1!32) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3866])).
% 5.59/5.55 tff(3868,plain,
% 5.59/5.55 (pred(NSY1!32) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3867, 19])).
% 5.59/5.55 tff(3869,plain,
% 5.59/5.55 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n7, n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3868, 3844])).
% 5.59/5.55 tff(3870,plain,
% 5.59/5.55 (sum(pred(NSY1!32), succ(NPY1!34)) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3869, 44])).
% 5.59/5.55 tff(3871,plain,
% 5.59/5.55 (sum(n4, n0) = n4),
% 5.59/5.55 inference(and_elim,[status(thm)],[9])).
% 5.59/5.55 tff(3872,plain,
% 5.59/5.55 (sum(pred(Y0!60), succ(X0!61)) = sum(n4, n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3720, 3796])).
% 5.59/5.55 tff(3873,plain,
% 5.59/5.55 (sum(pred(Y0!60), succ(X0!61)) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3872, 3871])).
% 5.59/5.55 tff(3874,plain,
% 5.59/5.55 (sum(n9, n6) = n4),
% 5.59/5.55 inference(and_elim,[status(thm)],[9])).
% 5.59/5.55 tff(3875,plain,
% 5.59/5.55 (sum(pred(X0!61), succ(Y0!60)) = sum(n9, n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3770, 3744])).
% 5.59/5.55 tff(3876,plain,
% 5.59/5.55 (sum(pred(X0!61), succ(Y0!60)) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3875, 3874])).
% 5.59/5.55 tff(3877,plain,
% 5.59/5.55 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n4, n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3876, 3873])).
% 5.59/5.55 tff(3878,plain,
% 5.59/5.55 (X1!59 = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[93, 3877, 46])).
% 5.59/5.55 tff(3879,plain,
% 5.59/5.55 (pred(X1!59) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3878])).
% 5.59/5.55 tff(3880,plain,
% 5.59/5.55 (pred(X1!59) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3879, 19])).
% 5.59/5.55 tff(3881,plain,
% 5.59/5.55 (pred(pred(X1!59)) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3880])).
% 5.59/5.55 tff(3882,plain,
% 5.59/5.55 (pred(pred(X1!59)) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[3881, 18])).
% 5.59/5.55 tff(3883,plain,
% 5.59/5.55 (pred(pred(pred(X1!59))) = pred(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3882])).
% 5.59/5.55 tff(3884,plain,
% 5.59/5.55 (pred(pred(pred(X1!59))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3883, 17])).
% 5.59/5.55 tff(3885,plain,
% 5.59/5.55 (pred(pred(pred(pred(X1!59)))) = pred(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3884])).
% 5.59/5.55 tff(3886,plain,
% 5.59/5.55 (pred(pred(pred(pred(X1!59)))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3885, 16])).
% 5.59/5.55 tff(3887,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(X1!59))))) = pred(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3886])).
% 5.59/5.55 tff(3888,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(X1!59))))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[3887, 15])).
% 5.59/5.55 tff(3889,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3888])).
% 5.59/5.55 tff(3890,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[3889, 25])).
% 5.59/5.55 tff(3891,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3890])).
% 5.59/5.55 tff(3892,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[3891, 24])).
% 5.59/5.55 tff(3893,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3892])).
% 5.59/5.55 tff(3894,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[3893, 23])).
% 5.59/5.55 tff(3895,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3894])).
% 5.59/5.55 tff(3896,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[3895, 22])).
% 5.59/5.55 tff(3897,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3896])).
% 5.59/5.55 tff(3898,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3897, 21])).
% 5.59/5.55 tff(3899,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3898])).
% 5.59/5.55 tff(3900,plain,
% 5.59/5.55 (NPX1!35 = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[280, 3899, 20])).
% 5.59/5.55 tff(3901,plain,
% 5.59/5.55 (succ(NPX1!35) = succ(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3900])).
% 5.59/5.55 tff(3902,plain,
% 5.59/5.55 (succ(NPX1!35) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3901, 45])).
% 5.59/5.55 tff(3903,plain,
% 5.59/5.55 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n9, n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3902, 3870])).
% 5.59/5.55 tff(3904,plain,
% 5.59/5.55 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[3903, 790])).
% 5.59/5.55 tff(3905,plain,
% 5.59/5.55 (succ(X1!59) = succ(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3878])).
% 5.59/5.55 tff(3906,plain,
% 5.59/5.55 (succ(X1!59) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3905, 45])).
% 5.59/5.55 tff(3907,plain,
% 5.59/5.55 (succ(succ(X1!59)) = succ(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3906])).
% 5.59/5.55 tff(3908,plain,
% 5.59/5.55 (succ(succ(X1!59)) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[3907, 28])).
% 5.59/5.55 tff(3909,plain,
% 5.59/5.55 (succ(succ(succ(X1!59))) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3908])).
% 5.59/5.55 tff(3910,plain,
% 5.59/5.55 (succ(succ(succ(X1!59))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[3909, 42])).
% 5.59/5.55 tff(3911,plain,
% 5.59/5.55 (succ(succ(succ(succ(X1!59)))) = succ(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3910])).
% 5.59/5.55 tff(3912,plain,
% 5.59/5.55 (succ(succ(succ(succ(X1!59)))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[3911, 58])).
% 5.59/5.55 tff(3913,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(X1!59))))) = succ(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3912])).
% 5.59/5.55 tff(3914,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(X1!59))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[3913, 36])).
% 5.59/5.55 tff(3915,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3914])).
% 5.59/5.55 tff(3916,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[3915, 48])).
% 5.59/5.55 tff(3917,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3916])).
% 5.59/5.55 tff(3918,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3917, 14])).
% 5.59/5.55 tff(3919,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3918])).
% 5.59/5.55 tff(3920,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3919, 33])).
% 5.59/5.55 tff(3921,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3920])).
% 5.59/5.55 tff(3922,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[3921, 30])).
% 5.59/5.55 tff(3923,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3922])).
% 5.59/5.55 tff(3924,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3923, 39])).
% 5.59/5.55 tff(3925,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3924])).
% 5.59/5.55 tff(3926,plain,
% 5.59/5.55 (NSX1!33 = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[305, 3925, 53])).
% 5.59/5.55 tff(3927,plain,
% 5.59/5.55 (pred(NSX1!33) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3926])).
% 5.59/5.55 tff(3928,plain,
% 5.59/5.55 (pred(NSX1!33) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3927, 19])).
% 5.59/5.55 tff(3929,plain,
% 5.59/5.55 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n7, n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3928, 3904])).
% 5.59/5.55 tff(3930,plain,
% 5.59/5.55 (Y2!56 = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[310, 3929, 789])).
% 5.59/5.55 tff(3931,plain,
% 5.59/5.55 (pred(Y2!56) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3930])).
% 5.59/5.55 tff(3932,plain,
% 5.59/5.55 (pred(Y2!56) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3931, 21])).
% 5.59/5.55 tff(3933,plain,
% 5.59/5.55 (pred(pred(Y2!56)) = pred(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3932])).
% 5.59/5.55 tff(3934,plain,
% 5.59/5.55 (pred(pred(Y2!56)) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[3933, 20])).
% 5.59/5.55 tff(3935,plain,
% 5.59/5.55 (pred(pred(pred(Y2!56))) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3934])).
% 5.59/5.55 tff(3936,plain,
% 5.59/5.55 (pred(pred(pred(Y2!56))) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3935, 19])).
% 5.59/5.55 tff(3937,plain,
% 5.59/5.55 (pred(pred(pred(pred(Y2!56)))) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3936])).
% 5.59/5.55 tff(3938,plain,
% 5.59/5.55 (pred(pred(pred(pred(Y2!56)))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[3937, 18])).
% 5.59/5.55 tff(3939,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3938])).
% 5.59/5.55 tff(3940,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(Y2!56))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3939, 17])).
% 5.59/5.55 tff(3941,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3940])).
% 5.59/5.55 tff(3942,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3941, 16])).
% 5.59/5.55 tff(3943,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3942])).
% 5.59/5.55 tff(3944,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[3943, 15])).
% 5.59/5.55 tff(3945,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3944])).
% 5.59/5.55 tff(3946,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[3945, 25])).
% 5.59/5.55 tff(3947,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3946])).
% 5.59/5.55 tff(3948,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[3947, 24])).
% 5.59/5.55 tff(3949,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3948])).
% 5.59/5.55 tff(3950,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[3949, 23])).
% 5.59/5.55 tff(3951,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3950])).
% 5.59/5.55 tff(3952,plain,
% 5.59/5.55 (NPY2!30 = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[347, 3951, 22])).
% 5.59/5.55 tff(3953,plain,
% 5.59/5.55 (succ(NPY2!30) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3952])).
% 5.59/5.55 tff(3954,plain,
% 5.59/5.55 (succ(NPY2!30) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[3953, 42])).
% 5.59/5.55 tff(3955,plain,
% 5.59/5.55 (succ(Y2!56) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3930])).
% 5.59/5.55 tff(3956,plain,
% 5.59/5.55 (succ(Y2!56) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[3955, 42])).
% 5.59/5.55 tff(3957,plain,
% 5.59/5.55 (succ(succ(Y2!56)) = succ(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3956])).
% 5.59/5.55 tff(3958,plain,
% 5.59/5.55 (succ(succ(Y2!56)) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[3957, 58])).
% 5.59/5.55 tff(3959,plain,
% 5.59/5.55 (succ(succ(succ(Y2!56))) = succ(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3958])).
% 5.59/5.55 tff(3960,plain,
% 5.59/5.55 (succ(succ(succ(Y2!56))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[3959, 36])).
% 5.59/5.55 tff(3961,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y2!56)))) = succ(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3960])).
% 5.59/5.55 tff(3962,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y2!56)))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[3961, 48])).
% 5.59/5.55 tff(3963,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3962])).
% 5.59/5.55 tff(3964,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y2!56))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3963, 14])).
% 5.59/5.55 tff(3965,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3964])).
% 5.59/5.55 tff(3966,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3965, 33])).
% 5.59/5.55 tff(3967,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3966])).
% 5.59/5.55 tff(3968,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[3967, 30])).
% 5.59/5.55 tff(3969,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3968])).
% 5.59/5.55 tff(3970,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3969, 39])).
% 5.59/5.55 tff(3971,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3970])).
% 5.59/5.55 tff(3972,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[3971, 53])).
% 5.59/5.55 tff(3973,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3972])).
% 5.59/5.55 tff(3974,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3973, 45])).
% 5.59/5.55 tff(3975,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3974])).
% 5.59/5.55 tff(3976,plain,
% 5.59/5.55 (NSY2!28 = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[370, 3975, 28])).
% 5.59/5.55 tff(3977,plain,
% 5.59/5.55 (pred(NSY2!28) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3976])).
% 5.59/5.55 tff(3978,plain,
% 5.59/5.55 (pred(NSY2!28) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3977, 21])).
% 5.59/5.55 tff(3979,plain,
% 5.59/5.55 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n9, n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3978, 3954])).
% 5.59/5.55 tff(3980,plain,
% 5.59/5.55 (sum(pred(NSY2!28), succ(NPY2!30)) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3979, 41])).
% 5.59/5.55 tff(3981,plain,
% 5.59/5.55 (sum(pred(Y1!58), succ(X1!59)) = sum(n7, n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3822, 3906])).
% 5.59/5.55 tff(3982,plain,
% 5.59/5.55 (sum(pred(Y1!58), succ(X1!59)) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3981, 44])).
% 5.59/5.55 tff(3983,plain,
% 5.59/5.55 (sum(pred(X1!59), succ(Y1!58)) = sum(n7, n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3880, 3846])).
% 5.59/5.55 tff(3984,plain,
% 5.59/5.55 (sum(pred(X1!59), succ(Y1!58)) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3983, 44])).
% 5.59/5.55 tff(3985,plain,
% 5.59/5.55 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n5, n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3984, 3982])).
% 5.59/5.55 tff(3986,plain,
% 5.59/5.55 (X2!57 = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[209, 3985, 43])).
% 5.59/5.55 tff(3987,plain,
% 5.59/5.55 (pred(X2!57) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3986])).
% 5.59/5.55 tff(3988,plain,
% 5.59/5.55 (pred(X2!57) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[3987, 21])).
% 5.59/5.55 tff(3989,plain,
% 5.59/5.55 (pred(pred(X2!57)) = pred(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3988])).
% 5.59/5.55 tff(3990,plain,
% 5.59/5.55 (pred(pred(X2!57)) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[3989, 20])).
% 5.59/5.55 tff(3991,plain,
% 5.59/5.55 (pred(pred(pred(X2!57))) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3990])).
% 5.59/5.55 tff(3992,plain,
% 5.59/5.55 (pred(pred(pred(X2!57))) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[3991, 19])).
% 5.59/5.55 tff(3993,plain,
% 5.59/5.55 (pred(pred(pred(pred(X2!57)))) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3992])).
% 5.59/5.55 tff(3994,plain,
% 5.59/5.55 (pred(pred(pred(pred(X2!57)))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[3993, 18])).
% 5.59/5.55 tff(3995,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(X2!57))))) = pred(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3994])).
% 5.59/5.55 tff(3996,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(X2!57))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[3995, 17])).
% 5.59/5.55 tff(3997,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3996])).
% 5.59/5.55 tff(3998,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[3997, 16])).
% 5.59/5.55 tff(3999,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3998])).
% 5.59/5.55 tff(4000,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[3999, 15])).
% 5.59/5.55 tff(4001,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4000])).
% 5.59/5.55 tff(4002,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4001, 25])).
% 5.59/5.55 tff(4003,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4002])).
% 5.59/5.55 tff(4004,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4003, 24])).
% 5.59/5.55 tff(4005,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4004])).
% 5.59/5.55 tff(4006,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4005, 23])).
% 5.59/5.55 tff(4007,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4006])).
% 5.59/5.55 tff(4008,plain,
% 5.59/5.55 (NPX2!31 = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[395, 4007, 22])).
% 5.59/5.55 tff(4009,plain,
% 5.59/5.55 (succ(NPX2!31) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4008])).
% 5.59/5.55 tff(4010,plain,
% 5.59/5.55 (succ(NPX2!31) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4009, 42])).
% 5.59/5.55 tff(4011,plain,
% 5.59/5.55 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n0, n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4010, 3980])).
% 5.59/5.55 tff(4012,plain,
% 5.59/5.55 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4011, 40])).
% 5.59/5.55 tff(4013,plain,
% 5.59/5.55 (succ(X2!57) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3986])).
% 5.59/5.55 tff(4014,plain,
% 5.59/5.55 (succ(X2!57) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4013, 42])).
% 5.59/5.55 tff(4015,plain,
% 5.59/5.55 (succ(succ(X2!57)) = succ(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4014])).
% 5.59/5.55 tff(4016,plain,
% 5.59/5.55 (succ(succ(X2!57)) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4015, 58])).
% 5.59/5.55 tff(4017,plain,
% 5.59/5.55 (succ(succ(succ(X2!57))) = succ(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4016])).
% 5.59/5.55 tff(4018,plain,
% 5.59/5.55 (succ(succ(succ(X2!57))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4017, 36])).
% 5.59/5.55 tff(4019,plain,
% 5.59/5.55 (succ(succ(succ(succ(X2!57)))) = succ(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4018])).
% 5.59/5.55 tff(4020,plain,
% 5.59/5.55 (succ(succ(succ(succ(X2!57)))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[4019, 48])).
% 5.59/5.55 tff(4021,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(X2!57))))) = succ(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4020])).
% 5.59/5.55 tff(4022,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(X2!57))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[4021, 14])).
% 5.59/5.55 tff(4023,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4022])).
% 5.59/5.55 tff(4024,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[4023, 33])).
% 5.59/5.55 tff(4025,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4024])).
% 5.59/5.55 tff(4026,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[4025, 30])).
% 5.59/5.55 tff(4027,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4026])).
% 5.59/5.55 tff(4028,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[4027, 39])).
% 5.59/5.55 tff(4029,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4028])).
% 5.59/5.55 tff(4030,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4029, 53])).
% 5.59/5.55 tff(4031,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4030])).
% 5.59/5.55 tff(4032,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4031, 45])).
% 5.59/5.55 tff(4033,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4032])).
% 5.59/5.55 tff(4034,plain,
% 5.59/5.55 (NSX2!29 = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[420, 4033, 28])).
% 5.59/5.55 tff(4035,plain,
% 5.59/5.55 (pred(NSX2!29) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4034])).
% 5.59/5.55 tff(4036,plain,
% 5.59/5.55 (pred(NSX2!29) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4035, 21])).
% 5.59/5.55 tff(4037,plain,
% 5.59/5.55 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n9, n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4036, 4012])).
% 5.59/5.55 tff(4038,plain,
% 5.59/5.55 (Y3!54 = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[425, 4037, 54])).
% 5.59/5.55 tff(4039,plain,
% 5.59/5.55 (pred(Y3!54) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4038])).
% 5.59/5.55 tff(4040,plain,
% 5.59/5.55 (pred(Y3!54) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[4039, 18])).
% 5.59/5.55 tff(4041,plain,
% 5.59/5.55 (pred(pred(Y3!54)) = pred(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4040])).
% 5.59/5.55 tff(4042,plain,
% 5.59/5.55 (pred(pred(Y3!54)) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[4041, 17])).
% 5.59/5.55 tff(4043,plain,
% 5.59/5.55 (pred(pred(pred(Y3!54))) = pred(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4042])).
% 5.59/5.55 tff(4044,plain,
% 5.59/5.55 (pred(pred(pred(Y3!54))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[4043, 16])).
% 5.59/5.55 tff(4045,plain,
% 5.59/5.55 (pred(pred(pred(pred(Y3!54)))) = pred(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4044])).
% 5.59/5.55 tff(4046,plain,
% 5.59/5.55 (pred(pred(pred(pred(Y3!54)))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[4045, 15])).
% 5.59/5.55 tff(4047,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4046])).
% 5.59/5.55 tff(4048,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(Y3!54))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4047, 25])).
% 5.59/5.55 tff(4049,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4048])).
% 5.59/5.55 tff(4050,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4049, 24])).
% 5.59/5.55 tff(4051,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4050])).
% 5.59/5.55 tff(4052,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4051, 23])).
% 5.59/5.55 tff(4053,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4052])).
% 5.59/5.55 tff(4054,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[4053, 22])).
% 5.59/5.55 tff(4055,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4054])).
% 5.59/5.55 tff(4056,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4055, 21])).
% 5.59/5.55 tff(4057,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4056])).
% 5.59/5.55 tff(4058,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4057, 20])).
% 5.59/5.55 tff(4059,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4058])).
% 5.59/5.55 tff(4060,plain,
% 5.59/5.55 (NPY3!26 = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[462, 4059, 19])).
% 5.59/5.55 tff(4061,plain,
% 5.59/5.55 (succ(NPY3!26) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4060])).
% 5.59/5.55 tff(4062,plain,
% 5.59/5.55 (succ(NPY3!26) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4061, 53])).
% 5.59/5.55 tff(4063,plain,
% 5.59/5.55 (succ(Y3!54) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4038])).
% 5.59/5.55 tff(4064,plain,
% 5.59/5.55 (succ(Y3!54) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4063, 53])).
% 5.59/5.55 tff(4065,plain,
% 5.59/5.55 (succ(succ(Y3!54)) = succ(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4064])).
% 5.59/5.55 tff(4066,plain,
% 5.59/5.55 (succ(succ(Y3!54)) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4065, 45])).
% 5.59/5.55 tff(4067,plain,
% 5.59/5.55 (succ(succ(succ(Y3!54))) = succ(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4066])).
% 5.59/5.55 tff(4068,plain,
% 5.59/5.55 (succ(succ(succ(Y3!54))) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[4067, 28])).
% 5.59/5.55 tff(4069,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y3!54)))) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4068])).
% 5.59/5.55 tff(4070,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y3!54)))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4069, 42])).
% 5.59/5.55 tff(4071,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4070])).
% 5.59/5.55 tff(4072,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y3!54))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4071, 58])).
% 5.59/5.55 tff(4073,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4072])).
% 5.59/5.55 tff(4074,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4073, 36])).
% 5.59/5.55 tff(4075,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4074])).
% 5.59/5.55 tff(4076,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[4075, 48])).
% 5.59/5.55 tff(4077,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4076])).
% 5.59/5.55 tff(4078,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[4077, 14])).
% 5.59/5.55 tff(4079,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4078])).
% 5.59/5.55 tff(4080,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[4079, 33])).
% 5.59/5.55 tff(4081,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4080])).
% 5.59/5.55 tff(4082,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[4081, 30])).
% 5.59/5.55 tff(4083,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4082])).
% 5.59/5.55 tff(4084,plain,
% 5.59/5.55 (NSY3!24 = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[485, 4083, 39])).
% 5.59/5.55 tff(4085,plain,
% 5.59/5.55 (pred(NSY3!24) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4084])).
% 5.59/5.55 tff(4086,plain,
% 5.59/5.55 (pred(NSY3!24) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[4085, 18])).
% 5.59/5.55 tff(4087,plain,
% 5.59/5.55 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n6, n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4086, 4062])).
% 5.59/5.55 tff(4088,plain,
% 5.59/5.55 (sum(pred(NSY3!24), succ(NPY3!26)) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[4087, 52])).
% 5.59/5.55 tff(4089,plain,
% 5.59/5.55 (sum(pred(Y2!56), succ(X2!57)) = sum(n9, n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3932, 4014])).
% 5.59/5.55 tff(4090,plain,
% 5.59/5.55 (sum(pred(Y2!56), succ(X2!57)) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4089, 41])).
% 5.59/5.55 tff(4091,plain,
% 5.59/5.55 (sum(pred(X2!57), succ(Y2!56)) = sum(n9, n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[3988, 3956])).
% 5.59/5.55 tff(4092,plain,
% 5.59/5.55 (sum(pred(X2!57), succ(Y2!56)) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4091, 41])).
% 5.59/5.55 tff(4093,plain,
% 5.59/5.55 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n9, n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4092, 4090])).
% 5.59/5.55 tff(4094,plain,
% 5.59/5.55 (X3!55 = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[323, 4093, 54])).
% 5.59/5.55 tff(4095,plain,
% 5.59/5.55 (pred(X3!55) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4094])).
% 5.59/5.55 tff(4096,plain,
% 5.59/5.55 (pred(X3!55) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[4095, 18])).
% 5.59/5.55 tff(4097,plain,
% 5.59/5.55 (pred(pred(X3!55)) = pred(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4096])).
% 5.59/5.55 tff(4098,plain,
% 5.59/5.55 (pred(pred(X3!55)) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[4097, 17])).
% 5.59/5.55 tff(4099,plain,
% 5.59/5.55 (pred(pred(pred(X3!55))) = pred(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4098])).
% 5.59/5.55 tff(4100,plain,
% 5.59/5.55 (pred(pred(pred(X3!55))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[4099, 16])).
% 5.59/5.55 tff(4101,plain,
% 5.59/5.55 (pred(pred(pred(pred(X3!55)))) = pred(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4100])).
% 5.59/5.55 tff(4102,plain,
% 5.59/5.55 (pred(pred(pred(pred(X3!55)))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[4101, 15])).
% 5.59/5.55 tff(4103,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(X3!55))))) = pred(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4102])).
% 5.59/5.55 tff(4104,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(X3!55))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4103, 25])).
% 5.59/5.55 tff(4105,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4104])).
% 5.59/5.55 tff(4106,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4105, 24])).
% 5.59/5.55 tff(4107,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4106])).
% 5.59/5.55 tff(4108,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4107, 23])).
% 5.59/5.55 tff(4109,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4108])).
% 5.59/5.55 tff(4110,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[4109, 22])).
% 5.59/5.55 tff(4111,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4110])).
% 5.59/5.55 tff(4112,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4111, 21])).
% 5.59/5.55 tff(4113,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4112])).
% 5.59/5.55 tff(4114,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4113, 20])).
% 5.59/5.55 tff(4115,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4114])).
% 5.59/5.55 tff(4116,plain,
% 5.59/5.55 (NPX3!27 = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[510, 4115, 19])).
% 5.59/5.55 tff(4117,plain,
% 5.59/5.55 (succ(NPX3!27) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4116])).
% 5.59/5.55 tff(4118,plain,
% 5.59/5.55 (succ(NPX3!27) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4117, 53])).
% 5.59/5.55 tff(4119,plain,
% 5.59/5.55 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n8, n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4118, 4088])).
% 5.59/5.55 tff(4120,plain,
% 5.59/5.55 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4119, 64])).
% 5.59/5.55 tff(4121,plain,
% 5.59/5.55 (succ(X3!55) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4094])).
% 5.59/5.55 tff(4122,plain,
% 5.59/5.55 (succ(X3!55) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4121, 53])).
% 5.59/5.55 tff(4123,plain,
% 5.59/5.55 (succ(succ(X3!55)) = succ(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4122])).
% 5.59/5.55 tff(4124,plain,
% 5.59/5.55 (succ(succ(X3!55)) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4123, 45])).
% 5.59/5.55 tff(4125,plain,
% 5.59/5.55 (succ(succ(succ(X3!55))) = succ(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4124])).
% 5.59/5.55 tff(4126,plain,
% 5.59/5.55 (succ(succ(succ(X3!55))) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[4125, 28])).
% 5.59/5.55 tff(4127,plain,
% 5.59/5.55 (succ(succ(succ(succ(X3!55)))) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4126])).
% 5.59/5.55 tff(4128,plain,
% 5.59/5.55 (succ(succ(succ(succ(X3!55)))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4127, 42])).
% 5.59/5.55 tff(4129,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(X3!55))))) = succ(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4128])).
% 5.59/5.55 tff(4130,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(X3!55))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4129, 58])).
% 5.59/5.55 tff(4131,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4130])).
% 5.59/5.55 tff(4132,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4131, 36])).
% 5.59/5.55 tff(4133,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4132])).
% 5.59/5.55 tff(4134,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[4133, 48])).
% 5.59/5.55 tff(4135,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4134])).
% 5.59/5.55 tff(4136,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[4135, 14])).
% 5.59/5.55 tff(4137,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4136])).
% 5.59/5.55 tff(4138,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[4137, 33])).
% 5.59/5.55 tff(4139,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4138])).
% 5.59/5.55 tff(4140,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[4139, 30])).
% 5.59/5.55 tff(4141,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4140])).
% 5.59/5.55 tff(4142,plain,
% 5.59/5.55 (NSX3!25 = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[535, 4141, 39])).
% 5.59/5.55 tff(4143,plain,
% 5.59/5.55 (pred(NSX3!25) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4142])).
% 5.59/5.55 tff(4144,plain,
% 5.59/5.55 (pred(NSX3!25) = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[4143, 18])).
% 5.59/5.55 tff(4145,plain,
% 5.59/5.55 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n6, n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4144, 4120])).
% 5.59/5.55 tff(4146,plain,
% 5.59/5.55 (Y4!52 = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[540, 4145, 788])).
% 5.59/5.55 tff(4147,plain,
% 5.59/5.55 (pred(Y4!52) = pred(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4146])).
% 5.59/5.55 tff(4148,plain,
% 5.59/5.55 (pred(Y4!52) = n5),
% 5.59/5.55 inference(transitivity,[status(thm)],[4147, 17])).
% 5.59/5.55 tff(4149,plain,
% 5.59/5.55 (pred(pred(Y4!52)) = pred(n5)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4148])).
% 5.59/5.55 tff(4150,plain,
% 5.59/5.55 (pred(pred(Y4!52)) = n4),
% 5.59/5.55 inference(transitivity,[status(thm)],[4149, 16])).
% 5.59/5.55 tff(4151,plain,
% 5.59/5.55 (pred(pred(pred(Y4!52))) = pred(n4)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4150])).
% 5.59/5.55 tff(4152,plain,
% 5.59/5.55 (pred(pred(pred(Y4!52))) = n3),
% 5.59/5.55 inference(transitivity,[status(thm)],[4151, 15])).
% 5.59/5.55 tff(4153,plain,
% 5.59/5.55 (pred(pred(pred(pred(Y4!52)))) = pred(n3)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4152])).
% 5.59/5.55 tff(4154,plain,
% 5.59/5.55 (pred(pred(pred(pred(Y4!52)))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4153, 25])).
% 5.59/5.55 tff(4155,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n2)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4154])).
% 5.59/5.55 tff(4156,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(Y4!52))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4155, 24])).
% 5.59/5.55 tff(4157,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4156])).
% 5.59/5.55 tff(4158,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4157, 23])).
% 5.59/5.55 tff(4159,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4158])).
% 5.59/5.55 tff(4160,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[4159, 22])).
% 5.59/5.55 tff(4161,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4160])).
% 5.59/5.55 tff(4162,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4161, 21])).
% 5.59/5.55 tff(4163,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4162])).
% 5.59/5.55 tff(4164,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4163, 20])).
% 5.59/5.55 tff(4165,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4164])).
% 5.59/5.55 tff(4166,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[4165, 19])).
% 5.59/5.55 tff(4167,plain,
% 5.59/5.55 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4166])).
% 5.59/5.55 tff(4168,plain,
% 5.59/5.55 (NPY4!22 = n6),
% 5.59/5.55 inference(transitivity,[status(thm)],[578, 4167, 18])).
% 5.59/5.55 tff(4169,plain,
% 5.59/5.55 (succ(NPY4!22) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4168])).
% 5.59/5.55 tff(4170,plain,
% 5.59/5.55 (succ(NPY4!22) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[4169, 39])).
% 5.59/5.55 tff(4171,plain,
% 5.59/5.55 (succ(Y4!52) = succ(n6)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4146])).
% 5.59/5.55 tff(4172,plain,
% 5.59/5.55 (succ(Y4!52) = n7),
% 5.59/5.55 inference(transitivity,[status(thm)],[4171, 39])).
% 5.59/5.55 tff(4173,plain,
% 5.59/5.55 (succ(succ(Y4!52)) = succ(n7)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4172])).
% 5.59/5.55 tff(4174,plain,
% 5.59/5.55 (succ(succ(Y4!52)) = n8),
% 5.59/5.55 inference(transitivity,[status(thm)],[4173, 53])).
% 5.59/5.55 tff(4175,plain,
% 5.59/5.55 (succ(succ(succ(Y4!52))) = succ(n8)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4174])).
% 5.59/5.55 tff(4176,plain,
% 5.59/5.55 (succ(succ(succ(Y4!52))) = n9),
% 5.59/5.55 inference(transitivity,[status(thm)],[4175, 45])).
% 5.59/5.55 tff(4177,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y4!52)))) = succ(n9)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4176])).
% 5.59/5.55 tff(4178,plain,
% 5.59/5.55 (succ(succ(succ(succ(Y4!52)))) = n10),
% 5.59/5.55 inference(transitivity,[status(thm)],[4177, 28])).
% 5.59/5.55 tff(4179,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n10)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4178])).
% 5.59/5.55 tff(4180,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(Y4!52))))) = n0),
% 5.59/5.55 inference(transitivity,[status(thm)],[4179, 42])).
% 5.59/5.55 tff(4181,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n0)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4180])).
% 5.59/5.55 tff(4182,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n1),
% 5.59/5.55 inference(transitivity,[status(thm)],[4181, 58])).
% 5.59/5.55 tff(4183,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n1)),
% 5.59/5.55 inference(monotonicity,[status(thm)],[4182])).
% 5.59/5.55 tff(4184,plain,
% 5.59/5.55 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n2),
% 5.59/5.55 inference(transitivity,[status(thm)],[4183, 36])).
% 5.59/5.56 tff(4185,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4184])).
% 5.59/5.56 tff(4186,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4185, 48])).
% 5.59/5.56 tff(4187,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4186])).
% 5.59/5.56 tff(4188,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4187, 14])).
% 5.59/5.56 tff(4189,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4188])).
% 5.59/5.56 tff(4190,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4189, 33])).
% 5.59/5.56 tff(4191,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4190])).
% 5.59/5.56 tff(4192,plain,
% 5.59/5.56 (NSY4!20 = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[601, 4191, 30])).
% 5.59/5.56 tff(4193,plain,
% 5.59/5.56 (pred(NSY4!20) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4192])).
% 5.59/5.56 tff(4194,plain,
% 5.59/5.56 (pred(NSY4!20) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4193, 17])).
% 5.59/5.56 tff(4195,plain,
% 5.59/5.56 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n5, n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4194, 4170])).
% 5.59/5.56 tff(4196,plain,
% 5.59/5.56 (sum(pred(NSY4!20), succ(NPY4!22)) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4195, 50])).
% 5.59/5.56 tff(4197,plain,
% 5.59/5.56 (sum(pred(Y3!54), succ(X3!55)) = sum(n6, n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4040, 4122])).
% 5.59/5.56 tff(4198,plain,
% 5.59/5.56 (sum(pred(Y3!54), succ(X3!55)) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4197, 52])).
% 5.59/5.56 tff(4199,plain,
% 5.59/5.56 (sum(pred(X3!55), succ(Y3!54)) = sum(n6, n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4096, 4064])).
% 5.59/5.56 tff(4200,plain,
% 5.59/5.56 (sum(pred(X3!55), succ(Y3!54)) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4199, 52])).
% 5.59/5.56 tff(4201,plain,
% 5.59/5.56 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n3, n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4200, 4198])).
% 5.59/5.56 tff(4202,plain,
% 5.59/5.56 (X4!53 = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[438, 4201, 51])).
% 5.59/5.56 tff(4203,plain,
% 5.59/5.56 (pred(X4!53) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4202])).
% 5.59/5.56 tff(4204,plain,
% 5.59/5.56 (pred(X4!53) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4203, 17])).
% 5.59/5.56 tff(4205,plain,
% 5.59/5.56 (pred(pred(X4!53)) = pred(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4204])).
% 5.59/5.56 tff(4206,plain,
% 5.59/5.56 (pred(pred(X4!53)) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4205, 16])).
% 5.59/5.56 tff(4207,plain,
% 5.59/5.56 (pred(pred(pred(X4!53))) = pred(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4206])).
% 5.59/5.56 tff(4208,plain,
% 5.59/5.56 (pred(pred(pred(X4!53))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4207, 15])).
% 5.59/5.56 tff(4209,plain,
% 5.59/5.56 (pred(pred(pred(pred(X4!53)))) = pred(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4208])).
% 5.59/5.56 tff(4210,plain,
% 5.59/5.56 (pred(pred(pred(pred(X4!53)))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4209, 25])).
% 5.59/5.56 tff(4211,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(X4!53))))) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4210])).
% 5.59/5.56 tff(4212,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(X4!53))))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4211, 24])).
% 5.59/5.56 tff(4213,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4212])).
% 5.59/5.56 tff(4214,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4213, 23])).
% 5.59/5.56 tff(4215,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4214])).
% 5.59/5.56 tff(4216,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4215, 22])).
% 5.59/5.56 tff(4217,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4216])).
% 5.59/5.56 tff(4218,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4217, 21])).
% 5.59/5.56 tff(4219,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4218])).
% 5.59/5.56 tff(4220,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4219, 20])).
% 5.59/5.56 tff(4221,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4220])).
% 5.59/5.56 tff(4222,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4221, 19])).
% 5.59/5.56 tff(4223,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4222])).
% 5.59/5.56 tff(4224,plain,
% 5.59/5.56 (NPX4!23 = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[626, 4223, 18])).
% 5.59/5.56 tff(4225,plain,
% 5.59/5.56 (succ(NPX4!23) = succ(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4224])).
% 5.59/5.56 tff(4226,plain,
% 5.59/5.56 (succ(NPX4!23) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4225, 39])).
% 5.59/5.56 tff(4227,plain,
% 5.59/5.56 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n7, n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4226, 4196])).
% 5.59/5.56 tff(4228,plain,
% 5.59/5.56 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4227, 787])).
% 5.59/5.56 tff(4229,plain,
% 5.59/5.56 (succ(X4!53) = succ(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4202])).
% 5.59/5.56 tff(4230,plain,
% 5.59/5.56 (succ(X4!53) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4229, 39])).
% 5.59/5.56 tff(4231,plain,
% 5.59/5.56 (succ(succ(X4!53)) = succ(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4230])).
% 5.59/5.56 tff(4232,plain,
% 5.59/5.56 (succ(succ(X4!53)) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4231, 53])).
% 5.59/5.56 tff(4233,plain,
% 5.59/5.56 (succ(succ(succ(X4!53))) = succ(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4232])).
% 5.59/5.56 tff(4234,plain,
% 5.59/5.56 (succ(succ(succ(X4!53))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4233, 45])).
% 5.59/5.56 tff(4235,plain,
% 5.59/5.56 (succ(succ(succ(succ(X4!53)))) = succ(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4234])).
% 5.59/5.56 tff(4236,plain,
% 5.59/5.56 (succ(succ(succ(succ(X4!53)))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4235, 28])).
% 5.59/5.56 tff(4237,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(X4!53))))) = succ(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4236])).
% 5.59/5.56 tff(4238,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(X4!53))))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4237, 42])).
% 5.59/5.56 tff(4239,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4238])).
% 5.59/5.56 tff(4240,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4239, 58])).
% 5.59/5.56 tff(4241,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4240])).
% 5.59/5.56 tff(4242,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4241, 36])).
% 5.59/5.56 tff(4243,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4242])).
% 5.59/5.56 tff(4244,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4243, 48])).
% 5.59/5.56 tff(4245,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4244])).
% 5.59/5.56 tff(4246,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4245, 14])).
% 5.59/5.56 tff(4247,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4246])).
% 5.59/5.56 tff(4248,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4247, 33])).
% 5.59/5.56 tff(4249,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4248])).
% 5.59/5.56 tff(4250,plain,
% 5.59/5.56 (NSX4!21 = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[651, 4249, 30])).
% 5.59/5.56 tff(4251,plain,
% 5.59/5.56 (pred(NSX4!21) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4250])).
% 5.59/5.56 tff(4252,plain,
% 5.59/5.56 (pred(NSX4!21) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4251, 17])).
% 5.59/5.56 tff(4253,plain,
% 5.59/5.56 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n5, n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4252, 4228])).
% 5.59/5.56 tff(4254,plain,
% 5.59/5.56 (Y5!50 = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[656, 4253, 558])).
% 5.59/5.56 tff(4255,plain,
% 5.59/5.56 (pred(Y5!50) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4254])).
% 5.59/5.56 tff(4256,plain,
% 5.59/5.56 (pred(Y5!50) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4255, 24])).
% 5.59/5.56 tff(4257,plain,
% 5.59/5.56 (pred(pred(Y5!50)) = pred(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4256])).
% 5.59/5.56 tff(4258,plain,
% 5.59/5.56 (pred(pred(Y5!50)) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4257, 23])).
% 5.59/5.56 tff(4259,plain,
% 5.59/5.56 (pred(pred(pred(Y5!50))) = pred(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4258])).
% 5.59/5.56 tff(4260,plain,
% 5.59/5.56 (pred(pred(pred(Y5!50))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4259, 22])).
% 5.59/5.56 tff(4261,plain,
% 5.59/5.56 (pred(pred(pred(pred(Y5!50)))) = pred(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4260])).
% 5.59/5.56 tff(4262,plain,
% 5.59/5.56 (pred(pred(pred(pred(Y5!50)))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4261, 21])).
% 5.59/5.56 tff(4263,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4262])).
% 5.59/5.56 tff(4264,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(Y5!50))))) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4263, 20])).
% 5.59/5.56 tff(4265,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4264])).
% 5.59/5.56 tff(4266,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4265, 19])).
% 5.59/5.56 tff(4267,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4266])).
% 5.59/5.56 tff(4268,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4267, 18])).
% 5.59/5.56 tff(4269,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4268])).
% 5.59/5.56 tff(4270,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4269, 17])).
% 5.59/5.56 tff(4271,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4270])).
% 5.59/5.56 tff(4272,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4271, 16])).
% 5.59/5.56 tff(4273,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4272])).
% 5.59/5.56 tff(4274,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4273, 15])).
% 5.59/5.56 tff(4275,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4274])).
% 5.59/5.56 tff(4276,plain,
% 5.59/5.56 (NPY5!18 = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[694, 4275, 25])).
% 5.59/5.56 tff(4277,plain,
% 5.59/5.56 (succ(NPY5!18) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4276])).
% 5.59/5.56 tff(4278,plain,
% 5.59/5.56 (succ(NPY5!18) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4277, 48])).
% 5.59/5.56 tff(4279,plain,
% 5.59/5.56 (succ(Y5!50) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4254])).
% 5.59/5.56 tff(4280,plain,
% 5.59/5.56 (succ(Y5!50) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4279, 48])).
% 5.59/5.56 tff(4281,plain,
% 5.59/5.56 (succ(succ(Y5!50)) = succ(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4280])).
% 5.59/5.56 tff(4282,plain,
% 5.59/5.56 (succ(succ(Y5!50)) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4281, 14])).
% 5.59/5.56 tff(4283,plain,
% 5.59/5.56 (succ(succ(succ(Y5!50))) = succ(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4282])).
% 5.59/5.56 tff(4284,plain,
% 5.59/5.56 (succ(succ(succ(Y5!50))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4283, 33])).
% 5.59/5.56 tff(4285,plain,
% 5.59/5.56 (succ(succ(succ(succ(Y5!50)))) = succ(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4284])).
% 5.59/5.56 tff(4286,plain,
% 5.59/5.56 (succ(succ(succ(succ(Y5!50)))) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4285, 30])).
% 5.59/5.56 tff(4287,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4286])).
% 5.59/5.56 tff(4288,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(Y5!50))))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4287, 39])).
% 5.59/5.56 tff(4289,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4288])).
% 5.59/5.56 tff(4290,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4289, 53])).
% 5.59/5.56 tff(4291,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4290])).
% 5.59/5.56 tff(4292,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4291, 45])).
% 5.59/5.56 tff(4293,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4292])).
% 5.59/5.56 tff(4294,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4293, 28])).
% 5.59/5.56 tff(4295,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4294])).
% 5.59/5.56 tff(4296,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4295, 42])).
% 5.59/5.56 tff(4297,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4296])).
% 5.59/5.56 tff(4298,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4297, 58])).
% 5.59/5.56 tff(4299,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4298])).
% 5.59/5.56 tff(4300,plain,
% 5.59/5.56 (NSY5!16 = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[717, 4299, 36])).
% 5.59/5.56 tff(4301,plain,
% 5.59/5.56 (pred(NSY5!16) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4300])).
% 5.59/5.56 tff(4302,plain,
% 5.59/5.56 (pred(NSY5!16) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4301, 24])).
% 5.59/5.56 tff(4303,plain,
% 5.59/5.56 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n1, n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4302, 4278])).
% 5.59/5.56 tff(4304,plain,
% 5.59/5.56 (sum(pred(NSY5!16), succ(NPY5!18)) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4303, 47])).
% 5.59/5.56 tff(4305,plain,
% 5.59/5.56 (sum(pred(Y4!52), succ(X4!53)) = sum(n5, n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4148, 4230])).
% 5.59/5.56 tff(4306,plain,
% 5.59/5.56 (sum(pred(Y4!52), succ(X4!53)) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4305, 50])).
% 5.59/5.56 tff(4307,plain,
% 5.59/5.56 (sum(pred(X4!53), succ(Y4!52)) = sum(n5, n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4204, 4172])).
% 5.59/5.56 tff(4308,plain,
% 5.59/5.56 (sum(pred(X4!53), succ(Y4!52)) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4307, 50])).
% 5.59/5.56 tff(4309,plain,
% 5.59/5.56 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n1, n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4308, 4306])).
% 5.59/5.56 tff(4310,plain,
% 5.59/5.56 (X5!51 = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[553, 4309, 49])).
% 5.59/5.56 tff(4311,plain,
% 5.59/5.56 (pred(X5!51) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4310])).
% 5.59/5.56 tff(4312,plain,
% 5.59/5.56 (pred(X5!51) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4311, 24])).
% 5.59/5.56 tff(4313,plain,
% 5.59/5.56 (pred(pred(X5!51)) = pred(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4312])).
% 5.59/5.56 tff(4314,plain,
% 5.59/5.56 (pred(pred(X5!51)) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4313, 23])).
% 5.59/5.56 tff(4315,plain,
% 5.59/5.56 (pred(pred(pred(X5!51))) = pred(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4314])).
% 5.59/5.56 tff(4316,plain,
% 5.59/5.56 (pred(pred(pred(X5!51))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4315, 22])).
% 5.59/5.56 tff(4317,plain,
% 5.59/5.56 (pred(pred(pred(pred(X5!51)))) = pred(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4316])).
% 5.59/5.56 tff(4318,plain,
% 5.59/5.56 (pred(pred(pred(pred(X5!51)))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4317, 21])).
% 5.59/5.56 tff(4319,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(X5!51))))) = pred(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4318])).
% 5.59/5.56 tff(4320,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(X5!51))))) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4319, 20])).
% 5.59/5.56 tff(4321,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4320])).
% 5.59/5.56 tff(4322,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4321, 19])).
% 5.59/5.56 tff(4323,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4322])).
% 5.59/5.56 tff(4324,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4323, 18])).
% 5.59/5.56 tff(4325,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4324])).
% 5.59/5.56 tff(4326,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4325, 17])).
% 5.59/5.56 tff(4327,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4326])).
% 5.59/5.56 tff(4328,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4327, 16])).
% 5.59/5.56 tff(4329,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4328])).
% 5.59/5.56 tff(4330,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4329, 15])).
% 5.59/5.56 tff(4331,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4330])).
% 5.59/5.56 tff(4332,plain,
% 5.59/5.56 (NPX5!19 = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[742, 4331, 25])).
% 5.59/5.56 tff(4333,plain,
% 5.59/5.56 (succ(NPX5!19) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4332])).
% 5.59/5.56 tff(4334,plain,
% 5.59/5.56 (succ(NPX5!19) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4333, 48])).
% 5.59/5.56 tff(4335,plain,
% 5.59/5.56 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n3, n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4334, 4304])).
% 5.59/5.56 tff(4336,plain,
% 5.59/5.56 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4335, 786])).
% 5.59/5.56 tff(4337,plain,
% 5.59/5.56 (succ(X5!51) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4310])).
% 5.59/5.56 tff(4338,plain,
% 5.59/5.56 (succ(X5!51) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4337, 48])).
% 5.59/5.56 tff(4339,plain,
% 5.59/5.56 (succ(succ(X5!51)) = succ(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4338])).
% 5.59/5.56 tff(4340,plain,
% 5.59/5.56 (succ(succ(X5!51)) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4339, 14])).
% 5.59/5.56 tff(4341,plain,
% 5.59/5.56 (succ(succ(succ(X5!51))) = succ(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4340])).
% 5.59/5.56 tff(4342,plain,
% 5.59/5.56 (succ(succ(succ(X5!51))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4341, 33])).
% 5.59/5.56 tff(4343,plain,
% 5.59/5.56 (succ(succ(succ(succ(X5!51)))) = succ(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4342])).
% 5.59/5.56 tff(4344,plain,
% 5.59/5.56 (succ(succ(succ(succ(X5!51)))) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4343, 30])).
% 5.59/5.56 tff(4345,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(X5!51))))) = succ(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4344])).
% 5.59/5.56 tff(4346,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(X5!51))))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4345, 39])).
% 5.59/5.56 tff(4347,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4346])).
% 5.59/5.56 tff(4348,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4347, 53])).
% 5.59/5.56 tff(4349,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4348])).
% 5.59/5.56 tff(4350,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4349, 45])).
% 5.59/5.56 tff(4351,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4350])).
% 5.59/5.56 tff(4352,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4351, 28])).
% 5.59/5.56 tff(4353,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4352])).
% 5.59/5.56 tff(4354,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4353, 42])).
% 5.59/5.56 tff(4355,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4354])).
% 5.59/5.56 tff(4356,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4355, 58])).
% 5.59/5.56 tff(4357,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4356])).
% 5.59/5.56 tff(4358,plain,
% 5.59/5.56 (NSX5!17 = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[767, 4357, 36])).
% 5.59/5.56 tff(4359,plain,
% 5.59/5.56 (pred(NSX5!17) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4358])).
% 5.59/5.56 tff(4360,plain,
% 5.59/5.56 (pred(NSX5!17) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4359, 24])).
% 5.59/5.56 tff(4361,plain,
% 5.59/5.56 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n1, n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4360, 4336])).
% 5.59/5.56 tff(4362,plain,
% 5.59/5.56 (Y6!48 = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[772, 4361, 791])).
% 5.59/5.56 tff(4363,plain,
% 5.59/5.56 (pred(Y6!48) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4362])).
% 5.59/5.56 tff(4364,plain,
% 5.59/5.56 (pred(Y6!48) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4363, 19])).
% 5.59/5.56 tff(4365,plain,
% 5.59/5.56 (pred(pred(Y6!48)) = pred(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4364])).
% 5.59/5.56 tff(4366,plain,
% 5.59/5.56 (pred(pred(Y6!48)) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4365, 18])).
% 5.59/5.56 tff(4367,plain,
% 5.59/5.56 (pred(pred(pred(Y6!48))) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4366])).
% 5.59/5.56 tff(4368,plain,
% 5.59/5.56 (pred(pred(pred(Y6!48))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4367, 17])).
% 5.59/5.56 tff(4369,plain,
% 5.59/5.56 (pred(pred(pred(pred(Y6!48)))) = pred(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4368])).
% 5.59/5.56 tff(4370,plain,
% 5.59/5.56 (pred(pred(pred(pred(Y6!48)))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4369, 16])).
% 5.59/5.56 tff(4371,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4370])).
% 5.59/5.56 tff(4372,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(Y6!48))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4371, 15])).
% 5.59/5.56 tff(4373,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4372])).
% 5.59/5.56 tff(4374,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4373, 25])).
% 5.59/5.56 tff(4375,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4374])).
% 5.59/5.56 tff(4376,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4375, 24])).
% 5.59/5.56 tff(4377,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4376])).
% 5.59/5.56 tff(4378,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4377, 23])).
% 5.59/5.56 tff(4379,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4378])).
% 5.59/5.56 tff(4380,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4379, 22])).
% 5.59/5.56 tff(4381,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4380])).
% 5.59/5.56 tff(4382,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4381, 21])).
% 5.59/5.56 tff(4383,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4382])).
% 5.59/5.56 tff(4384,plain,
% 5.59/5.56 (NPY6!14 = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[1465, 4383, 20])).
% 5.59/5.56 tff(4385,plain,
% 5.59/5.56 (succ(NPY6!14) = succ(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4384])).
% 5.59/5.56 tff(4386,plain,
% 5.59/5.56 (succ(NPY6!14) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4385, 45])).
% 5.59/5.56 tff(4387,plain,
% 5.59/5.56 (succ(Y6!48) = succ(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4362])).
% 5.59/5.56 tff(4388,plain,
% 5.59/5.56 (succ(Y6!48) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4387, 45])).
% 5.59/5.56 tff(4389,plain,
% 5.59/5.56 (succ(succ(Y6!48)) = succ(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4388])).
% 5.59/5.56 tff(4390,plain,
% 5.59/5.56 (succ(succ(Y6!48)) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4389, 28])).
% 5.59/5.56 tff(4391,plain,
% 5.59/5.56 (succ(succ(succ(Y6!48))) = succ(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4390])).
% 5.59/5.56 tff(4392,plain,
% 5.59/5.56 (succ(succ(succ(Y6!48))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4391, 42])).
% 5.59/5.56 tff(4393,plain,
% 5.59/5.56 (succ(succ(succ(succ(Y6!48)))) = succ(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4392])).
% 5.59/5.56 tff(4394,plain,
% 5.59/5.56 (succ(succ(succ(succ(Y6!48)))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4393, 58])).
% 5.59/5.56 tff(4395,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4394])).
% 5.59/5.56 tff(4396,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(Y6!48))))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4395, 36])).
% 5.59/5.56 tff(4397,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4396])).
% 5.59/5.56 tff(4398,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4397, 48])).
% 5.59/5.56 tff(4399,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4398])).
% 5.59/5.56 tff(4400,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4399, 14])).
% 5.59/5.56 tff(4401,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4400])).
% 5.59/5.56 tff(4402,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4401, 33])).
% 5.59/5.56 tff(4403,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4402])).
% 5.59/5.56 tff(4404,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4403, 30])).
% 5.59/5.56 tff(4405,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4404])).
% 5.59/5.56 tff(4406,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4405, 39])).
% 5.59/5.56 tff(4407,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4406])).
% 5.59/5.56 tff(4408,plain,
% 5.59/5.56 (NSY6!12 = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[1490, 4407, 53])).
% 5.59/5.56 tff(4409,plain,
% 5.59/5.56 (pred(NSY6!12) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4408])).
% 5.59/5.56 tff(4410,plain,
% 5.59/5.56 (pred(NSY6!12) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4409, 19])).
% 5.59/5.56 tff(4411,plain,
% 5.59/5.56 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n7, n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4410, 4386])).
% 5.59/5.56 tff(4412,plain,
% 5.59/5.56 (sum(pred(NSY6!12), succ(NPY6!14)) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4411, 44])).
% 5.59/5.56 tff(4413,plain,
% 5.59/5.56 (sum(pred(Y5!50), succ(X5!51)) = sum(n1, n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4256, 4338])).
% 5.59/5.56 tff(4414,plain,
% 5.59/5.56 (sum(pred(Y5!50), succ(X5!51)) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4413, 47])).
% 5.59/5.56 tff(4415,plain,
% 5.59/5.56 (sum(pred(X5!51), succ(Y5!50)) = sum(n1, n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4312, 4280])).
% 5.59/5.56 tff(4416,plain,
% 5.59/5.56 (sum(pred(X5!51), succ(Y5!50)) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4415, 47])).
% 5.59/5.56 tff(4417,plain,
% 5.59/5.56 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n4, n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4416, 4414])).
% 5.59/5.56 tff(4418,plain,
% 5.59/5.56 (X6!49 = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[669, 4417, 46])).
% 5.59/5.56 tff(4419,plain,
% 5.59/5.56 (pred(X6!49) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4418])).
% 5.59/5.56 tff(4420,plain,
% 5.59/5.56 (pred(X6!49) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4419, 19])).
% 5.59/5.56 tff(4421,plain,
% 5.59/5.56 (pred(pred(X6!49)) = pred(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4420])).
% 5.59/5.56 tff(4422,plain,
% 5.59/5.56 (pred(pred(X6!49)) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4421, 18])).
% 5.59/5.56 tff(4423,plain,
% 5.59/5.56 (pred(pred(pred(X6!49))) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4422])).
% 5.59/5.56 tff(4424,plain,
% 5.59/5.56 (pred(pred(pred(X6!49))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4423, 17])).
% 5.59/5.56 tff(4425,plain,
% 5.59/5.56 (pred(pred(pred(pred(X6!49)))) = pred(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4424])).
% 5.59/5.56 tff(4426,plain,
% 5.59/5.56 (pred(pred(pred(pred(X6!49)))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4425, 16])).
% 5.59/5.56 tff(4427,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(X6!49))))) = pred(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4426])).
% 5.59/5.56 tff(4428,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(X6!49))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4427, 15])).
% 5.59/5.56 tff(4429,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4428])).
% 5.59/5.56 tff(4430,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4429, 25])).
% 5.59/5.56 tff(4431,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4430])).
% 5.59/5.56 tff(4432,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4431, 24])).
% 5.59/5.56 tff(4433,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4432])).
% 5.59/5.56 tff(4434,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4433, 23])).
% 5.59/5.56 tff(4435,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4434])).
% 5.59/5.56 tff(4436,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4435, 22])).
% 5.59/5.56 tff(4437,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4436])).
% 5.59/5.56 tff(4438,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4437, 21])).
% 5.59/5.56 tff(4439,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4438])).
% 5.59/5.56 tff(4440,plain,
% 5.59/5.56 (NPX6!15 = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[1523, 4439, 20])).
% 5.59/5.56 tff(4441,plain,
% 5.59/5.56 (succ(NPX6!15) = succ(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4440])).
% 5.59/5.56 tff(4442,plain,
% 5.59/5.56 (succ(NPX6!15) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4441, 45])).
% 5.59/5.56 tff(4443,plain,
% 5.59/5.56 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n9, n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4442, 4412])).
% 5.59/5.56 tff(4444,plain,
% 5.59/5.56 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4443, 790])).
% 5.59/5.56 tff(4445,plain,
% 5.59/5.56 (succ(X6!49) = succ(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4418])).
% 5.59/5.56 tff(4446,plain,
% 5.59/5.56 (succ(X6!49) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4445, 45])).
% 5.59/5.56 tff(4447,plain,
% 5.59/5.56 (succ(succ(X6!49)) = succ(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4446])).
% 5.59/5.56 tff(4448,plain,
% 5.59/5.56 (succ(succ(X6!49)) = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[4447, 28])).
% 5.59/5.56 tff(4449,plain,
% 5.59/5.56 (succ(succ(succ(X6!49))) = succ(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4448])).
% 5.59/5.56 tff(4450,plain,
% 5.59/5.56 (succ(succ(succ(X6!49))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4449, 42])).
% 5.59/5.56 tff(4451,plain,
% 5.59/5.56 (succ(succ(succ(succ(X6!49)))) = succ(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4450])).
% 5.59/5.56 tff(4452,plain,
% 5.59/5.56 (succ(succ(succ(succ(X6!49)))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4451, 58])).
% 5.59/5.56 tff(4453,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(X6!49))))) = succ(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4452])).
% 5.59/5.56 tff(4454,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(X6!49))))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4453, 36])).
% 5.59/5.56 tff(4455,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4454])).
% 5.59/5.56 tff(4456,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4455, 48])).
% 5.59/5.56 tff(4457,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4456])).
% 5.59/5.56 tff(4458,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4457, 14])).
% 5.59/5.56 tff(4459,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4458])).
% 5.59/5.56 tff(4460,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4459, 33])).
% 5.59/5.56 tff(4461,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4460])).
% 5.59/5.56 tff(4462,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4461, 30])).
% 5.59/5.56 tff(4463,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4462])).
% 5.59/5.56 tff(4464,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4463, 39])).
% 5.59/5.56 tff(4465,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4464])).
% 5.59/5.56 tff(4466,plain,
% 5.59/5.56 (NSX6!13 = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[1550, 4465, 53])).
% 5.59/5.56 tff(4467,plain,
% 5.59/5.56 (pred(NSX6!13) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4466])).
% 5.59/5.56 tff(4468,plain,
% 5.59/5.56 (pred(NSX6!13) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4467, 19])).
% 5.59/5.56 tff(4469,plain,
% 5.59/5.56 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n7, n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4468, 4444])).
% 5.59/5.56 tff(4470,plain,
% 5.59/5.56 (sum(n7, n3) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.59/5.56 inference(symmetry,[status(thm)],[4469])).
% 5.59/5.56 tff(4471,plain,
% 5.59/5.56 (n10 = sum(n7, n3)),
% 5.59/5.56 inference(symmetry,[status(thm)],[789])).
% 5.59/5.56 tff(4472,plain,
% 5.59/5.56 (sum(pred(Y6!48), succ(X6!49)) = sum(n7, n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4364, 4446])).
% 5.59/5.56 tff(4473,plain,
% 5.59/5.56 (sum(pred(Y6!48), succ(X6!49)) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4472, 44])).
% 5.59/5.56 tff(4474,plain,
% 5.59/5.56 (sum(pred(X6!49), succ(Y6!48)) = sum(n7, n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4420, 4388])).
% 5.59/5.56 tff(4475,plain,
% 5.59/5.56 (sum(pred(X6!49), succ(Y6!48)) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4474, 44])).
% 5.59/5.56 tff(4476,plain,
% 5.59/5.56 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n5, n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4475, 4473])).
% 5.59/5.56 tff(4477,plain,
% 5.59/5.56 (X7!47 = Y7!46),
% 5.59/5.56 inference(transitivity,[status(thm)],[785, 4476, 43, 4471, 4470, 794])).
% 5.59/5.56 tff(4478,plain,
% 5.59/5.56 ($false),
% 5.59/5.56 inference(unit_resolution,[status(thm)],[792, 4477])).
% 5.59/5.56 tff(4479,plain,((~(Y0!60 = n5)) | (X7!47 = Y7!46) | (~(X0!61 = n10))), inference(lemma,lemma(discharge,[]))).
% 5.59/5.56 tff(4480,plain,
% 5.59/5.56 (~(Y0!60 = n5)),
% 5.59/5.56 inference(unit_resolution,[status(thm)],[4479, 3715, 792])).
% 5.59/5.56 tff(4481,plain,
% 5.59/5.56 (sum(n9, n1) = n10),
% 5.59/5.56 inference(and_elim,[status(thm)],[9])).
% 5.59/5.56 tff(4482,plain,
% 5.59/5.56 (sum(n0, n1) = n1),
% 5.59/5.56 inference(and_elim,[status(thm)],[9])).
% 5.59/5.56 tff(4483,plain,
% 5.59/5.56 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n0, n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[3792, 1622])).
% 5.59/5.56 tff(4484,plain,
% 5.59/5.56 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4483, 4482])).
% 5.59/5.56 tff(4485,plain,
% 5.59/5.56 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n9, n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[3818, 4484])).
% 5.59/5.56 tff(4486,plain,
% 5.59/5.56 (Y1!58 = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[196, 4485, 4481])).
% 5.59/5.56 tff(4487,plain,
% 5.59/5.56 (pred(Y1!58) = pred(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4486])).
% 5.59/5.56 tff(4488,plain,
% 5.59/5.56 (pred(Y1!58) = n9),
% 5.59/5.56 inference(transitivity,[status(thm)],[4487, 21])).
% 5.59/5.56 tff(4489,plain,
% 5.59/5.56 (pred(pred(Y1!58)) = pred(n9)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4488])).
% 5.59/5.56 tff(4490,plain,
% 5.59/5.56 (pred(pred(Y1!58)) = n8),
% 5.59/5.56 inference(transitivity,[status(thm)],[4489, 20])).
% 5.59/5.56 tff(4491,plain,
% 5.59/5.56 (pred(pred(pred(Y1!58))) = pred(n8)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4490])).
% 5.59/5.56 tff(4492,plain,
% 5.59/5.56 (pred(pred(pred(Y1!58))) = n7),
% 5.59/5.56 inference(transitivity,[status(thm)],[4491, 19])).
% 5.59/5.56 tff(4493,plain,
% 5.59/5.56 (pred(pred(pred(pred(Y1!58)))) = pred(n7)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4492])).
% 5.59/5.56 tff(4494,plain,
% 5.59/5.56 (pred(pred(pred(pred(Y1!58)))) = n6),
% 5.59/5.56 inference(transitivity,[status(thm)],[4493, 18])).
% 5.59/5.56 tff(4495,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n6)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4494])).
% 5.59/5.56 tff(4496,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(Y1!58))))) = n5),
% 5.59/5.56 inference(transitivity,[status(thm)],[4495, 17])).
% 5.59/5.56 tff(4497,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n5)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4496])).
% 5.59/5.56 tff(4498,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4497, 16])).
% 5.59/5.56 tff(4499,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n4)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4498])).
% 5.59/5.56 tff(4500,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4499, 15])).
% 5.59/5.56 tff(4501,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4500])).
% 5.59/5.56 tff(4502,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4501, 25])).
% 5.59/5.56 tff(4503,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4502])).
% 5.59/5.56 tff(4504,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4503, 24])).
% 5.59/5.56 tff(4505,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4504])).
% 5.59/5.56 tff(4506,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4505, 23])).
% 5.59/5.56 tff(4507,plain,
% 5.59/5.56 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4506])).
% 5.59/5.56 tff(4508,plain,
% 5.59/5.56 (NPY1!34 = n10),
% 5.59/5.56 inference(transitivity,[status(thm)],[232, 4507, 22])).
% 5.59/5.56 tff(4509,plain,
% 5.59/5.56 (succ(NPY1!34) = succ(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4508])).
% 5.59/5.56 tff(4510,plain,
% 5.59/5.56 (succ(NPY1!34) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4509, 42])).
% 5.59/5.56 tff(4511,plain,
% 5.59/5.56 (succ(Y1!58) = succ(n10)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4486])).
% 5.59/5.56 tff(4512,plain,
% 5.59/5.56 (succ(Y1!58) = n0),
% 5.59/5.56 inference(transitivity,[status(thm)],[4511, 42])).
% 5.59/5.56 tff(4513,plain,
% 5.59/5.56 (succ(succ(Y1!58)) = succ(n0)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4512])).
% 5.59/5.56 tff(4514,plain,
% 5.59/5.56 (succ(succ(Y1!58)) = n1),
% 5.59/5.56 inference(transitivity,[status(thm)],[4513, 58])).
% 5.59/5.56 tff(4515,plain,
% 5.59/5.56 (succ(succ(succ(Y1!58))) = succ(n1)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4514])).
% 5.59/5.56 tff(4516,plain,
% 5.59/5.56 (succ(succ(succ(Y1!58))) = n2),
% 5.59/5.56 inference(transitivity,[status(thm)],[4515, 36])).
% 5.59/5.56 tff(4517,plain,
% 5.59/5.56 (succ(succ(succ(succ(Y1!58)))) = succ(n2)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4516])).
% 5.59/5.56 tff(4518,plain,
% 5.59/5.56 (succ(succ(succ(succ(Y1!58)))) = n3),
% 5.59/5.56 inference(transitivity,[status(thm)],[4517, 48])).
% 5.59/5.56 tff(4519,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n3)),
% 5.59/5.56 inference(monotonicity,[status(thm)],[4518])).
% 5.59/5.56 tff(4520,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(Y1!58))))) = n4),
% 5.59/5.56 inference(transitivity,[status(thm)],[4519, 14])).
% 5.59/5.56 tff(4521,plain,
% 5.59/5.56 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4520])).
% 5.59/5.57 tff(4522,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4521, 33])).
% 5.59/5.57 tff(4523,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4522])).
% 5.59/5.57 tff(4524,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4523, 30])).
% 5.59/5.57 tff(4525,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4524])).
% 5.59/5.57 tff(4526,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4525, 39])).
% 5.59/5.57 tff(4527,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4526])).
% 5.59/5.57 tff(4528,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4527, 53])).
% 5.59/5.57 tff(4529,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4528])).
% 5.59/5.57 tff(4530,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4529, 45])).
% 5.59/5.57 tff(4531,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4530])).
% 5.59/5.57 tff(4532,plain,
% 5.59/5.57 (NSY1!32 = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[255, 4531, 28])).
% 5.59/5.57 tff(4533,plain,
% 5.59/5.57 (pred(NSY1!32) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4532])).
% 5.59/5.57 tff(4534,plain,
% 5.59/5.57 (pred(NSY1!32) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4533, 21])).
% 5.59/5.57 tff(4535,plain,
% 5.59/5.57 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n9, n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4534, 4510])).
% 5.59/5.57 tff(4536,plain,
% 5.59/5.57 (sum(pred(NSY1!32), succ(NPY1!34)) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4535, 41])).
% 5.59/5.57 tff(4537,plain,
% 5.59/5.57 (sum(n5, n0) = n5),
% 5.59/5.57 inference(and_elim,[status(thm)],[9])).
% 5.59/5.57 tff(4538,plain,
% 5.59/5.57 (sum(pred(Y0!60), succ(X0!61)) = sum(n5, n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[1574, 3796])).
% 5.59/5.57 tff(4539,plain,
% 5.59/5.57 (sum(pred(Y0!60), succ(X0!61)) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4538, 4537])).
% 5.59/5.57 tff(4540,plain,
% 5.59/5.57 (sum(n9, n7) = n5),
% 5.59/5.57 inference(and_elim,[status(thm)],[9])).
% 5.59/5.57 tff(4541,plain,
% 5.59/5.57 (sum(pred(X0!61), succ(Y0!60)) = sum(n9, n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[3770, 1598])).
% 5.59/5.57 tff(4542,plain,
% 5.59/5.57 (sum(pred(X0!61), succ(Y0!60)) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4541, 4540])).
% 5.59/5.57 tff(4543,plain,
% 5.59/5.57 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n5, n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4542, 4539])).
% 5.59/5.57 tff(4544,plain,
% 5.59/5.57 (X1!59 = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[93, 4543, 43])).
% 5.59/5.57 tff(4545,plain,
% 5.59/5.57 (pred(X1!59) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4544])).
% 5.59/5.57 tff(4546,plain,
% 5.59/5.57 (pred(X1!59) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4545, 21])).
% 5.59/5.57 tff(4547,plain,
% 5.59/5.57 (pred(pred(X1!59)) = pred(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4546])).
% 5.59/5.57 tff(4548,plain,
% 5.59/5.57 (pred(pred(X1!59)) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4547, 20])).
% 5.59/5.57 tff(4549,plain,
% 5.59/5.57 (pred(pred(pred(X1!59))) = pred(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4548])).
% 5.59/5.57 tff(4550,plain,
% 5.59/5.57 (pred(pred(pred(X1!59))) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4549, 19])).
% 5.59/5.57 tff(4551,plain,
% 5.59/5.57 (pred(pred(pred(pred(X1!59)))) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4550])).
% 5.59/5.57 tff(4552,plain,
% 5.59/5.57 (pred(pred(pred(pred(X1!59)))) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4551, 18])).
% 5.59/5.57 tff(4553,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(X1!59))))) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4552])).
% 5.59/5.57 tff(4554,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(X1!59))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4553, 17])).
% 5.59/5.57 tff(4555,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4554])).
% 5.59/5.57 tff(4556,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4555, 16])).
% 5.59/5.57 tff(4557,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4556])).
% 5.59/5.57 tff(4558,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4557, 15])).
% 5.59/5.57 tff(4559,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4558])).
% 5.59/5.57 tff(4560,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4559, 25])).
% 5.59/5.57 tff(4561,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4560])).
% 5.59/5.57 tff(4562,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4561, 24])).
% 5.59/5.57 tff(4563,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4562])).
% 5.59/5.57 tff(4564,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4563, 23])).
% 5.59/5.57 tff(4565,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4564])).
% 5.59/5.57 tff(4566,plain,
% 5.59/5.57 (NPX1!35 = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[280, 4565, 22])).
% 5.59/5.57 tff(4567,plain,
% 5.59/5.57 (succ(NPX1!35) = succ(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4566])).
% 5.59/5.57 tff(4568,plain,
% 5.59/5.57 (succ(NPX1!35) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4567, 42])).
% 5.59/5.57 tff(4569,plain,
% 5.59/5.57 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n0, n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4568, 4536])).
% 5.59/5.57 tff(4570,plain,
% 5.59/5.57 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4569, 40])).
% 5.59/5.57 tff(4571,plain,
% 5.59/5.57 (succ(X1!59) = succ(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4544])).
% 5.59/5.57 tff(4572,plain,
% 5.59/5.57 (succ(X1!59) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4571, 42])).
% 5.59/5.57 tff(4573,plain,
% 5.59/5.57 (succ(succ(X1!59)) = succ(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4572])).
% 5.59/5.57 tff(4574,plain,
% 5.59/5.57 (succ(succ(X1!59)) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4573, 58])).
% 5.59/5.57 tff(4575,plain,
% 5.59/5.57 (succ(succ(succ(X1!59))) = succ(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4574])).
% 5.59/5.57 tff(4576,plain,
% 5.59/5.57 (succ(succ(succ(X1!59))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4575, 36])).
% 5.59/5.57 tff(4577,plain,
% 5.59/5.57 (succ(succ(succ(succ(X1!59)))) = succ(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4576])).
% 5.59/5.57 tff(4578,plain,
% 5.59/5.57 (succ(succ(succ(succ(X1!59)))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4577, 48])).
% 5.59/5.57 tff(4579,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(X1!59))))) = succ(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4578])).
% 5.59/5.57 tff(4580,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(X1!59))))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4579, 14])).
% 5.59/5.57 tff(4581,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4580])).
% 5.59/5.57 tff(4582,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4581, 33])).
% 5.59/5.57 tff(4583,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4582])).
% 5.59/5.57 tff(4584,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4583, 30])).
% 5.59/5.57 tff(4585,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4584])).
% 5.59/5.57 tff(4586,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4585, 39])).
% 5.59/5.57 tff(4587,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4586])).
% 5.59/5.57 tff(4588,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4587, 53])).
% 5.59/5.57 tff(4589,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4588])).
% 5.59/5.57 tff(4590,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4589, 45])).
% 5.59/5.57 tff(4591,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4590])).
% 5.59/5.57 tff(4592,plain,
% 5.59/5.57 (NSX1!33 = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[305, 4591, 28])).
% 5.59/5.57 tff(4593,plain,
% 5.59/5.57 (pred(NSX1!33) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4592])).
% 5.59/5.57 tff(4594,plain,
% 5.59/5.57 (pred(NSX1!33) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4593, 21])).
% 5.59/5.57 tff(4595,plain,
% 5.59/5.57 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n9, n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4594, 4570])).
% 5.59/5.57 tff(4596,plain,
% 5.59/5.57 (Y2!56 = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[310, 4595, 54])).
% 5.59/5.57 tff(4597,plain,
% 5.59/5.57 (pred(Y2!56) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4596])).
% 5.59/5.57 tff(4598,plain,
% 5.59/5.57 (pred(Y2!56) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4597, 18])).
% 5.59/5.57 tff(4599,plain,
% 5.59/5.57 (pred(pred(Y2!56)) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4598])).
% 5.59/5.57 tff(4600,plain,
% 5.59/5.57 (pred(pred(Y2!56)) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4599, 17])).
% 5.59/5.57 tff(4601,plain,
% 5.59/5.57 (pred(pred(pred(Y2!56))) = pred(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4600])).
% 5.59/5.57 tff(4602,plain,
% 5.59/5.57 (pred(pred(pred(Y2!56))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4601, 16])).
% 5.59/5.57 tff(4603,plain,
% 5.59/5.57 (pred(pred(pred(pred(Y2!56)))) = pred(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4602])).
% 5.59/5.57 tff(4604,plain,
% 5.59/5.57 (pred(pred(pred(pred(Y2!56)))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4603, 15])).
% 5.59/5.57 tff(4605,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4604])).
% 5.59/5.57 tff(4606,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(Y2!56))))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4605, 25])).
% 5.59/5.57 tff(4607,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4606])).
% 5.59/5.57 tff(4608,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4607, 24])).
% 5.59/5.57 tff(4609,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4608])).
% 5.59/5.57 tff(4610,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4609, 23])).
% 5.59/5.57 tff(4611,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4610])).
% 5.59/5.57 tff(4612,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4611, 22])).
% 5.59/5.57 tff(4613,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4612])).
% 5.59/5.57 tff(4614,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4613, 21])).
% 5.59/5.57 tff(4615,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4614])).
% 5.59/5.57 tff(4616,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4615, 20])).
% 5.59/5.57 tff(4617,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4616])).
% 5.59/5.57 tff(4618,plain,
% 5.59/5.57 (NPY2!30 = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[347, 4617, 19])).
% 5.59/5.57 tff(4619,plain,
% 5.59/5.57 (succ(NPY2!30) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4618])).
% 5.59/5.57 tff(4620,plain,
% 5.59/5.57 (succ(NPY2!30) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4619, 53])).
% 5.59/5.57 tff(4621,plain,
% 5.59/5.57 (succ(Y2!56) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4596])).
% 5.59/5.57 tff(4622,plain,
% 5.59/5.57 (succ(Y2!56) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4621, 53])).
% 5.59/5.57 tff(4623,plain,
% 5.59/5.57 (succ(succ(Y2!56)) = succ(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4622])).
% 5.59/5.57 tff(4624,plain,
% 5.59/5.57 (succ(succ(Y2!56)) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4623, 45])).
% 5.59/5.57 tff(4625,plain,
% 5.59/5.57 (succ(succ(succ(Y2!56))) = succ(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4624])).
% 5.59/5.57 tff(4626,plain,
% 5.59/5.57 (succ(succ(succ(Y2!56))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4625, 28])).
% 5.59/5.57 tff(4627,plain,
% 5.59/5.57 (succ(succ(succ(succ(Y2!56)))) = succ(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4626])).
% 5.59/5.57 tff(4628,plain,
% 5.59/5.57 (succ(succ(succ(succ(Y2!56)))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4627, 42])).
% 5.59/5.57 tff(4629,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4628])).
% 5.59/5.57 tff(4630,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(Y2!56))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4629, 58])).
% 5.59/5.57 tff(4631,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4630])).
% 5.59/5.57 tff(4632,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4631, 36])).
% 5.59/5.57 tff(4633,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4632])).
% 5.59/5.57 tff(4634,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4633, 48])).
% 5.59/5.57 tff(4635,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4634])).
% 5.59/5.57 tff(4636,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4635, 14])).
% 5.59/5.57 tff(4637,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4636])).
% 5.59/5.57 tff(4638,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4637, 33])).
% 5.59/5.57 tff(4639,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4638])).
% 5.59/5.57 tff(4640,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4639, 30])).
% 5.59/5.57 tff(4641,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4640])).
% 5.59/5.57 tff(4642,plain,
% 5.59/5.57 (NSY2!28 = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[370, 4641, 39])).
% 5.59/5.57 tff(4643,plain,
% 5.59/5.57 (pred(NSY2!28) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4642])).
% 5.59/5.57 tff(4644,plain,
% 5.59/5.57 (pred(NSY2!28) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4643, 18])).
% 5.59/5.57 tff(4645,plain,
% 5.59/5.57 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n6, n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4644, 4620])).
% 5.59/5.57 tff(4646,plain,
% 5.59/5.57 (sum(pred(NSY2!28), succ(NPY2!30)) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4645, 52])).
% 5.59/5.57 tff(4647,plain,
% 5.59/5.57 (sum(pred(Y1!58), succ(X1!59)) = sum(n9, n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4488, 4572])).
% 5.59/5.57 tff(4648,plain,
% 5.59/5.57 (sum(pred(Y1!58), succ(X1!59)) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4647, 41])).
% 5.59/5.57 tff(4649,plain,
% 5.59/5.57 (sum(pred(X1!59), succ(Y1!58)) = sum(n9, n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4546, 4512])).
% 5.59/5.57 tff(4650,plain,
% 5.59/5.57 (sum(pred(X1!59), succ(Y1!58)) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4649, 41])).
% 5.59/5.57 tff(4651,plain,
% 5.59/5.57 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n9, n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4650, 4648])).
% 5.59/5.57 tff(4652,plain,
% 5.59/5.57 (X2!57 = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[209, 4651, 54])).
% 5.59/5.57 tff(4653,plain,
% 5.59/5.57 (pred(X2!57) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4652])).
% 5.59/5.57 tff(4654,plain,
% 5.59/5.57 (pred(X2!57) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4653, 18])).
% 5.59/5.57 tff(4655,plain,
% 5.59/5.57 (pred(pred(X2!57)) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4654])).
% 5.59/5.57 tff(4656,plain,
% 5.59/5.57 (pred(pred(X2!57)) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4655, 17])).
% 5.59/5.57 tff(4657,plain,
% 5.59/5.57 (pred(pred(pred(X2!57))) = pred(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4656])).
% 5.59/5.57 tff(4658,plain,
% 5.59/5.57 (pred(pred(pred(X2!57))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4657, 16])).
% 5.59/5.57 tff(4659,plain,
% 5.59/5.57 (pred(pred(pred(pred(X2!57)))) = pred(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4658])).
% 5.59/5.57 tff(4660,plain,
% 5.59/5.57 (pred(pred(pred(pred(X2!57)))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4659, 15])).
% 5.59/5.57 tff(4661,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(X2!57))))) = pred(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4660])).
% 5.59/5.57 tff(4662,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(X2!57))))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4661, 25])).
% 5.59/5.57 tff(4663,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4662])).
% 5.59/5.57 tff(4664,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4663, 24])).
% 5.59/5.57 tff(4665,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4664])).
% 5.59/5.57 tff(4666,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4665, 23])).
% 5.59/5.57 tff(4667,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4666])).
% 5.59/5.57 tff(4668,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4667, 22])).
% 5.59/5.57 tff(4669,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4668])).
% 5.59/5.57 tff(4670,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4669, 21])).
% 5.59/5.57 tff(4671,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4670])).
% 5.59/5.57 tff(4672,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4671, 20])).
% 5.59/5.57 tff(4673,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4672])).
% 5.59/5.57 tff(4674,plain,
% 5.59/5.57 (NPX2!31 = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[395, 4673, 19])).
% 5.59/5.57 tff(4675,plain,
% 5.59/5.57 (succ(NPX2!31) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4674])).
% 5.59/5.57 tff(4676,plain,
% 5.59/5.57 (succ(NPX2!31) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4675, 53])).
% 5.59/5.57 tff(4677,plain,
% 5.59/5.57 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n8, n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4676, 4646])).
% 5.59/5.57 tff(4678,plain,
% 5.59/5.57 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4677, 64])).
% 5.59/5.57 tff(4679,plain,
% 5.59/5.57 (succ(X2!57) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4652])).
% 5.59/5.57 tff(4680,plain,
% 5.59/5.57 (succ(X2!57) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4679, 53])).
% 5.59/5.57 tff(4681,plain,
% 5.59/5.57 (succ(succ(X2!57)) = succ(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4680])).
% 5.59/5.57 tff(4682,plain,
% 5.59/5.57 (succ(succ(X2!57)) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4681, 45])).
% 5.59/5.57 tff(4683,plain,
% 5.59/5.57 (succ(succ(succ(X2!57))) = succ(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4682])).
% 5.59/5.57 tff(4684,plain,
% 5.59/5.57 (succ(succ(succ(X2!57))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4683, 28])).
% 5.59/5.57 tff(4685,plain,
% 5.59/5.57 (succ(succ(succ(succ(X2!57)))) = succ(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4684])).
% 5.59/5.57 tff(4686,plain,
% 5.59/5.57 (succ(succ(succ(succ(X2!57)))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4685, 42])).
% 5.59/5.57 tff(4687,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(X2!57))))) = succ(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4686])).
% 5.59/5.57 tff(4688,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(X2!57))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4687, 58])).
% 5.59/5.57 tff(4689,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4688])).
% 5.59/5.57 tff(4690,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4689, 36])).
% 5.59/5.57 tff(4691,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4690])).
% 5.59/5.57 tff(4692,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4691, 48])).
% 5.59/5.57 tff(4693,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4692])).
% 5.59/5.57 tff(4694,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4693, 14])).
% 5.59/5.57 tff(4695,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4694])).
% 5.59/5.57 tff(4696,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4695, 33])).
% 5.59/5.57 tff(4697,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4696])).
% 5.59/5.57 tff(4698,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4697, 30])).
% 5.59/5.57 tff(4699,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4698])).
% 5.59/5.57 tff(4700,plain,
% 5.59/5.57 (NSX2!29 = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[420, 4699, 39])).
% 5.59/5.57 tff(4701,plain,
% 5.59/5.57 (pred(NSX2!29) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4700])).
% 5.59/5.57 tff(4702,plain,
% 5.59/5.57 (pred(NSX2!29) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4701, 18])).
% 5.59/5.57 tff(4703,plain,
% 5.59/5.57 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n6, n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4702, 4678])).
% 5.59/5.57 tff(4704,plain,
% 5.59/5.57 (Y3!54 = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[425, 4703, 788])).
% 5.59/5.57 tff(4705,plain,
% 5.59/5.57 (pred(Y3!54) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4704])).
% 5.59/5.57 tff(4706,plain,
% 5.59/5.57 (pred(Y3!54) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4705, 17])).
% 5.59/5.57 tff(4707,plain,
% 5.59/5.57 (pred(pred(Y3!54)) = pred(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4706])).
% 5.59/5.57 tff(4708,plain,
% 5.59/5.57 (pred(pred(Y3!54)) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4707, 16])).
% 5.59/5.57 tff(4709,plain,
% 5.59/5.57 (pred(pred(pred(Y3!54))) = pred(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4708])).
% 5.59/5.57 tff(4710,plain,
% 5.59/5.57 (pred(pred(pred(Y3!54))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4709, 15])).
% 5.59/5.57 tff(4711,plain,
% 5.59/5.57 (pred(pred(pred(pred(Y3!54)))) = pred(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4710])).
% 5.59/5.57 tff(4712,plain,
% 5.59/5.57 (pred(pred(pred(pred(Y3!54)))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4711, 25])).
% 5.59/5.57 tff(4713,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4712])).
% 5.59/5.57 tff(4714,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(Y3!54))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4713, 24])).
% 5.59/5.57 tff(4715,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4714])).
% 5.59/5.57 tff(4716,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4715, 23])).
% 5.59/5.57 tff(4717,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4716])).
% 5.59/5.57 tff(4718,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4717, 22])).
% 5.59/5.57 tff(4719,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4718])).
% 5.59/5.57 tff(4720,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4719, 21])).
% 5.59/5.57 tff(4721,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4720])).
% 5.59/5.57 tff(4722,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4721, 20])).
% 5.59/5.57 tff(4723,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4722])).
% 5.59/5.57 tff(4724,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4723, 19])).
% 5.59/5.57 tff(4725,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4724])).
% 5.59/5.57 tff(4726,plain,
% 5.59/5.57 (NPY3!26 = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[462, 4725, 18])).
% 5.59/5.57 tff(4727,plain,
% 5.59/5.57 (succ(NPY3!26) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4726])).
% 5.59/5.57 tff(4728,plain,
% 5.59/5.57 (succ(NPY3!26) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4727, 39])).
% 5.59/5.57 tff(4729,plain,
% 5.59/5.57 (succ(Y3!54) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4704])).
% 5.59/5.57 tff(4730,plain,
% 5.59/5.57 (succ(Y3!54) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4729, 39])).
% 5.59/5.57 tff(4731,plain,
% 5.59/5.57 (succ(succ(Y3!54)) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4730])).
% 5.59/5.57 tff(4732,plain,
% 5.59/5.57 (succ(succ(Y3!54)) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4731, 53])).
% 5.59/5.57 tff(4733,plain,
% 5.59/5.57 (succ(succ(succ(Y3!54))) = succ(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4732])).
% 5.59/5.57 tff(4734,plain,
% 5.59/5.57 (succ(succ(succ(Y3!54))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4733, 45])).
% 5.59/5.57 tff(4735,plain,
% 5.59/5.57 (succ(succ(succ(succ(Y3!54)))) = succ(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4734])).
% 5.59/5.57 tff(4736,plain,
% 5.59/5.57 (succ(succ(succ(succ(Y3!54)))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4735, 28])).
% 5.59/5.57 tff(4737,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4736])).
% 5.59/5.57 tff(4738,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(Y3!54))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4737, 42])).
% 5.59/5.57 tff(4739,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4738])).
% 5.59/5.57 tff(4740,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4739, 58])).
% 5.59/5.57 tff(4741,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4740])).
% 5.59/5.57 tff(4742,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4741, 36])).
% 5.59/5.57 tff(4743,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4742])).
% 5.59/5.57 tff(4744,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4743, 48])).
% 5.59/5.57 tff(4745,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4744])).
% 5.59/5.57 tff(4746,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4745, 14])).
% 5.59/5.57 tff(4747,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4746])).
% 5.59/5.57 tff(4748,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4747, 33])).
% 5.59/5.57 tff(4749,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4748])).
% 5.59/5.57 tff(4750,plain,
% 5.59/5.57 (NSY3!24 = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[485, 4749, 30])).
% 5.59/5.57 tff(4751,plain,
% 5.59/5.57 (pred(NSY3!24) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4750])).
% 5.59/5.57 tff(4752,plain,
% 5.59/5.57 (pred(NSY3!24) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4751, 17])).
% 5.59/5.57 tff(4753,plain,
% 5.59/5.57 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n5, n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4752, 4728])).
% 5.59/5.57 tff(4754,plain,
% 5.59/5.57 (sum(pred(NSY3!24), succ(NPY3!26)) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4753, 50])).
% 5.59/5.57 tff(4755,plain,
% 5.59/5.57 (sum(pred(Y2!56), succ(X2!57)) = sum(n6, n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4598, 4680])).
% 5.59/5.57 tff(4756,plain,
% 5.59/5.57 (sum(pred(Y2!56), succ(X2!57)) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4755, 52])).
% 5.59/5.57 tff(4757,plain,
% 5.59/5.57 (sum(pred(X2!57), succ(Y2!56)) = sum(n6, n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4654, 4622])).
% 5.59/5.57 tff(4758,plain,
% 5.59/5.57 (sum(pred(X2!57), succ(Y2!56)) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4757, 52])).
% 5.59/5.57 tff(4759,plain,
% 5.59/5.57 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n3, n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4758, 4756])).
% 5.59/5.57 tff(4760,plain,
% 5.59/5.57 (X3!55 = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[323, 4759, 51])).
% 5.59/5.57 tff(4761,plain,
% 5.59/5.57 (pred(X3!55) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4760])).
% 5.59/5.57 tff(4762,plain,
% 5.59/5.57 (pred(X3!55) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4761, 17])).
% 5.59/5.57 tff(4763,plain,
% 5.59/5.57 (pred(pred(X3!55)) = pred(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4762])).
% 5.59/5.57 tff(4764,plain,
% 5.59/5.57 (pred(pred(X3!55)) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4763, 16])).
% 5.59/5.57 tff(4765,plain,
% 5.59/5.57 (pred(pred(pred(X3!55))) = pred(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4764])).
% 5.59/5.57 tff(4766,plain,
% 5.59/5.57 (pred(pred(pred(X3!55))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4765, 15])).
% 5.59/5.57 tff(4767,plain,
% 5.59/5.57 (pred(pred(pred(pred(X3!55)))) = pred(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4766])).
% 5.59/5.57 tff(4768,plain,
% 5.59/5.57 (pred(pred(pred(pred(X3!55)))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4767, 25])).
% 5.59/5.57 tff(4769,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(X3!55))))) = pred(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4768])).
% 5.59/5.57 tff(4770,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(X3!55))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4769, 24])).
% 5.59/5.57 tff(4771,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4770])).
% 5.59/5.57 tff(4772,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4771, 23])).
% 5.59/5.57 tff(4773,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4772])).
% 5.59/5.57 tff(4774,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4773, 22])).
% 5.59/5.57 tff(4775,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4774])).
% 5.59/5.57 tff(4776,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4775, 21])).
% 5.59/5.57 tff(4777,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4776])).
% 5.59/5.57 tff(4778,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4777, 20])).
% 5.59/5.57 tff(4779,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4778])).
% 5.59/5.57 tff(4780,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4779, 19])).
% 5.59/5.57 tff(4781,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4780])).
% 5.59/5.57 tff(4782,plain,
% 5.59/5.57 (NPX3!27 = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[510, 4781, 18])).
% 5.59/5.57 tff(4783,plain,
% 5.59/5.57 (succ(NPX3!27) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4782])).
% 5.59/5.57 tff(4784,plain,
% 5.59/5.57 (succ(NPX3!27) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4783, 39])).
% 5.59/5.57 tff(4785,plain,
% 5.59/5.57 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n7, n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4784, 4754])).
% 5.59/5.57 tff(4786,plain,
% 5.59/5.57 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4785, 787])).
% 5.59/5.57 tff(4787,plain,
% 5.59/5.57 (succ(X3!55) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4760])).
% 5.59/5.57 tff(4788,plain,
% 5.59/5.57 (succ(X3!55) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4787, 39])).
% 5.59/5.57 tff(4789,plain,
% 5.59/5.57 (succ(succ(X3!55)) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4788])).
% 5.59/5.57 tff(4790,plain,
% 5.59/5.57 (succ(succ(X3!55)) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4789, 53])).
% 5.59/5.57 tff(4791,plain,
% 5.59/5.57 (succ(succ(succ(X3!55))) = succ(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4790])).
% 5.59/5.57 tff(4792,plain,
% 5.59/5.57 (succ(succ(succ(X3!55))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4791, 45])).
% 5.59/5.57 tff(4793,plain,
% 5.59/5.57 (succ(succ(succ(succ(X3!55)))) = succ(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4792])).
% 5.59/5.57 tff(4794,plain,
% 5.59/5.57 (succ(succ(succ(succ(X3!55)))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4793, 28])).
% 5.59/5.57 tff(4795,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(X3!55))))) = succ(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4794])).
% 5.59/5.57 tff(4796,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(X3!55))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4795, 42])).
% 5.59/5.57 tff(4797,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4796])).
% 5.59/5.57 tff(4798,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4797, 58])).
% 5.59/5.57 tff(4799,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4798])).
% 5.59/5.57 tff(4800,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[4799, 36])).
% 5.59/5.57 tff(4801,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4800])).
% 5.59/5.57 tff(4802,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4801, 48])).
% 5.59/5.57 tff(4803,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4802])).
% 5.59/5.57 tff(4804,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4803, 14])).
% 5.59/5.57 tff(4805,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4804])).
% 5.59/5.57 tff(4806,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4805, 33])).
% 5.59/5.57 tff(4807,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4806])).
% 5.59/5.57 tff(4808,plain,
% 5.59/5.57 (NSX3!25 = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[535, 4807, 30])).
% 5.59/5.57 tff(4809,plain,
% 5.59/5.57 (pred(NSX3!25) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4808])).
% 5.59/5.57 tff(4810,plain,
% 5.59/5.57 (pred(NSX3!25) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4809, 17])).
% 5.59/5.57 tff(4811,plain,
% 5.59/5.57 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n5, n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4810, 4786])).
% 5.59/5.57 tff(4812,plain,
% 5.59/5.57 (Y4!52 = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[540, 4811, 558])).
% 5.59/5.57 tff(4813,plain,
% 5.59/5.57 (pred(Y4!52) = pred(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4812])).
% 5.59/5.57 tff(4814,plain,
% 5.59/5.57 (pred(Y4!52) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4813, 24])).
% 5.59/5.57 tff(4815,plain,
% 5.59/5.57 (pred(pred(Y4!52)) = pred(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4814])).
% 5.59/5.57 tff(4816,plain,
% 5.59/5.57 (pred(pred(Y4!52)) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4815, 23])).
% 5.59/5.57 tff(4817,plain,
% 5.59/5.57 (pred(pred(pred(Y4!52))) = pred(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4816])).
% 5.59/5.57 tff(4818,plain,
% 5.59/5.57 (pred(pred(pred(Y4!52))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4817, 22])).
% 5.59/5.57 tff(4819,plain,
% 5.59/5.57 (pred(pred(pred(pred(Y4!52)))) = pred(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4818])).
% 5.59/5.57 tff(4820,plain,
% 5.59/5.57 (pred(pred(pred(pred(Y4!52)))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4819, 21])).
% 5.59/5.57 tff(4821,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4820])).
% 5.59/5.57 tff(4822,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(Y4!52))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4821, 20])).
% 5.59/5.57 tff(4823,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4822])).
% 5.59/5.57 tff(4824,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4823, 19])).
% 5.59/5.57 tff(4825,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4824])).
% 5.59/5.57 tff(4826,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4825, 18])).
% 5.59/5.57 tff(4827,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4826])).
% 5.59/5.57 tff(4828,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4827, 17])).
% 5.59/5.57 tff(4829,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4828])).
% 5.59/5.57 tff(4830,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4829, 16])).
% 5.59/5.57 tff(4831,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4830])).
% 5.59/5.57 tff(4832,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4831, 15])).
% 5.59/5.57 tff(4833,plain,
% 5.59/5.57 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4832])).
% 5.59/5.57 tff(4834,plain,
% 5.59/5.57 (NPY4!22 = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[578, 4833, 25])).
% 5.59/5.57 tff(4835,plain,
% 5.59/5.57 (succ(NPY4!22) = succ(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4834])).
% 5.59/5.57 tff(4836,plain,
% 5.59/5.57 (succ(NPY4!22) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4835, 48])).
% 5.59/5.57 tff(4837,plain,
% 5.59/5.57 (succ(Y4!52) = succ(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4812])).
% 5.59/5.57 tff(4838,plain,
% 5.59/5.57 (succ(Y4!52) = n3),
% 5.59/5.57 inference(transitivity,[status(thm)],[4837, 48])).
% 5.59/5.57 tff(4839,plain,
% 5.59/5.57 (succ(succ(Y4!52)) = succ(n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4838])).
% 5.59/5.57 tff(4840,plain,
% 5.59/5.57 (succ(succ(Y4!52)) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4839, 14])).
% 5.59/5.57 tff(4841,plain,
% 5.59/5.57 (succ(succ(succ(Y4!52))) = succ(n4)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4840])).
% 5.59/5.57 tff(4842,plain,
% 5.59/5.57 (succ(succ(succ(Y4!52))) = n5),
% 5.59/5.57 inference(transitivity,[status(thm)],[4841, 33])).
% 5.59/5.57 tff(4843,plain,
% 5.59/5.57 (succ(succ(succ(succ(Y4!52)))) = succ(n5)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4842])).
% 5.59/5.57 tff(4844,plain,
% 5.59/5.57 (succ(succ(succ(succ(Y4!52)))) = n6),
% 5.59/5.57 inference(transitivity,[status(thm)],[4843, 30])).
% 5.59/5.57 tff(4845,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n6)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4844])).
% 5.59/5.57 tff(4846,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(Y4!52))))) = n7),
% 5.59/5.57 inference(transitivity,[status(thm)],[4845, 39])).
% 5.59/5.57 tff(4847,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4846])).
% 5.59/5.57 tff(4848,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n8),
% 5.59/5.57 inference(transitivity,[status(thm)],[4847, 53])).
% 5.59/5.57 tff(4849,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n8)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4848])).
% 5.59/5.57 tff(4850,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n9),
% 5.59/5.57 inference(transitivity,[status(thm)],[4849, 45])).
% 5.59/5.57 tff(4851,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n9)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4850])).
% 5.59/5.57 tff(4852,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n10),
% 5.59/5.57 inference(transitivity,[status(thm)],[4851, 28])).
% 5.59/5.57 tff(4853,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n10)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4852])).
% 5.59/5.57 tff(4854,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n0),
% 5.59/5.57 inference(transitivity,[status(thm)],[4853, 42])).
% 5.59/5.57 tff(4855,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n0)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4854])).
% 5.59/5.57 tff(4856,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4855, 58])).
% 5.59/5.57 tff(4857,plain,
% 5.59/5.57 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n1)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4856])).
% 5.59/5.57 tff(4858,plain,
% 5.59/5.57 (NSY4!20 = n2),
% 5.59/5.57 inference(transitivity,[status(thm)],[601, 4857, 36])).
% 5.59/5.57 tff(4859,plain,
% 5.59/5.57 (pred(NSY4!20) = pred(n2)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4858])).
% 5.59/5.57 tff(4860,plain,
% 5.59/5.57 (pred(NSY4!20) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4859, 24])).
% 5.59/5.57 tff(4861,plain,
% 5.59/5.57 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n1, n3)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4860, 4836])).
% 5.59/5.57 tff(4862,plain,
% 5.59/5.57 (sum(pred(NSY4!20), succ(NPY4!22)) = n4),
% 5.59/5.57 inference(transitivity,[status(thm)],[4861, 47])).
% 5.59/5.57 tff(4863,plain,
% 5.59/5.57 (sum(pred(Y3!54), succ(X3!55)) = sum(n5, n7)),
% 5.59/5.57 inference(monotonicity,[status(thm)],[4706, 4788])).
% 5.59/5.57 tff(4864,plain,
% 5.59/5.57 (sum(pred(Y3!54), succ(X3!55)) = n1),
% 5.59/5.57 inference(transitivity,[status(thm)],[4863, 50])).
% 5.59/5.57 tff(4865,plain,
% 5.59/5.57 (sum(pred(X3!55), succ(Y3!54)) = sum(n5, n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4762, 4730])).
% 5.59/5.58 tff(4866,plain,
% 5.59/5.58 (sum(pred(X3!55), succ(Y3!54)) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[4865, 50])).
% 5.59/5.58 tff(4867,plain,
% 5.59/5.58 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n1, n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4866, 4864])).
% 5.59/5.58 tff(4868,plain,
% 5.59/5.58 (X4!53 = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[438, 4867, 49])).
% 5.59/5.58 tff(4869,plain,
% 5.59/5.58 (pred(X4!53) = pred(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4868])).
% 5.59/5.58 tff(4870,plain,
% 5.59/5.58 (pred(X4!53) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[4869, 24])).
% 5.59/5.58 tff(4871,plain,
% 5.59/5.58 (pred(pred(X4!53)) = pred(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4870])).
% 5.59/5.58 tff(4872,plain,
% 5.59/5.58 (pred(pred(X4!53)) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[4871, 23])).
% 5.59/5.58 tff(4873,plain,
% 5.59/5.58 (pred(pred(pred(X4!53))) = pred(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4872])).
% 5.59/5.58 tff(4874,plain,
% 5.59/5.58 (pred(pred(pred(X4!53))) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[4873, 22])).
% 5.59/5.58 tff(4875,plain,
% 5.59/5.58 (pred(pred(pred(pred(X4!53)))) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4874])).
% 5.59/5.58 tff(4876,plain,
% 5.59/5.58 (pred(pred(pred(pred(X4!53)))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[4875, 21])).
% 5.59/5.58 tff(4877,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X4!53))))) = pred(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4876])).
% 5.59/5.58 tff(4878,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X4!53))))) = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[4877, 20])).
% 5.59/5.58 tff(4879,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4878])).
% 5.59/5.58 tff(4880,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[4879, 19])).
% 5.59/5.58 tff(4881,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4880])).
% 5.59/5.58 tff(4882,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[4881, 18])).
% 5.59/5.58 tff(4883,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4882])).
% 5.59/5.58 tff(4884,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[4883, 17])).
% 5.59/5.58 tff(4885,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4884])).
% 5.59/5.58 tff(4886,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[4885, 16])).
% 5.59/5.58 tff(4887,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4886])).
% 5.59/5.58 tff(4888,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[4887, 15])).
% 5.59/5.58 tff(4889,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4888])).
% 5.59/5.58 tff(4890,plain,
% 5.59/5.58 (NPX4!23 = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[626, 4889, 25])).
% 5.59/5.58 tff(4891,plain,
% 5.59/5.58 (succ(NPX4!23) = succ(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4890])).
% 5.59/5.58 tff(4892,plain,
% 5.59/5.58 (succ(NPX4!23) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[4891, 48])).
% 5.59/5.58 tff(4893,plain,
% 5.59/5.58 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n3, n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4892, 4862])).
% 5.59/5.58 tff(4894,plain,
% 5.59/5.58 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[4893, 786])).
% 5.59/5.58 tff(4895,plain,
% 5.59/5.58 (succ(X4!53) = succ(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4868])).
% 5.59/5.58 tff(4896,plain,
% 5.59/5.58 (succ(X4!53) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[4895, 48])).
% 5.59/5.58 tff(4897,plain,
% 5.59/5.58 (succ(succ(X4!53)) = succ(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4896])).
% 5.59/5.58 tff(4898,plain,
% 5.59/5.58 (succ(succ(X4!53)) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[4897, 14])).
% 5.59/5.58 tff(4899,plain,
% 5.59/5.58 (succ(succ(succ(X4!53))) = succ(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4898])).
% 5.59/5.58 tff(4900,plain,
% 5.59/5.58 (succ(succ(succ(X4!53))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[4899, 33])).
% 5.59/5.58 tff(4901,plain,
% 5.59/5.58 (succ(succ(succ(succ(X4!53)))) = succ(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4900])).
% 5.59/5.58 tff(4902,plain,
% 5.59/5.58 (succ(succ(succ(succ(X4!53)))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[4901, 30])).
% 5.59/5.58 tff(4903,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X4!53))))) = succ(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4902])).
% 5.59/5.58 tff(4904,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X4!53))))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[4903, 39])).
% 5.59/5.58 tff(4905,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4904])).
% 5.59/5.58 tff(4906,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[4905, 53])).
% 5.59/5.58 tff(4907,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4906])).
% 5.59/5.58 tff(4908,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[4907, 45])).
% 5.59/5.58 tff(4909,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4908])).
% 5.59/5.58 tff(4910,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[4909, 28])).
% 5.59/5.58 tff(4911,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4910])).
% 5.59/5.58 tff(4912,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[4911, 42])).
% 5.59/5.58 tff(4913,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4912])).
% 5.59/5.58 tff(4914,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[4913, 58])).
% 5.59/5.58 tff(4915,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4914])).
% 5.59/5.58 tff(4916,plain,
% 5.59/5.58 (NSX4!21 = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[651, 4915, 36])).
% 5.59/5.58 tff(4917,plain,
% 5.59/5.58 (pred(NSX4!21) = pred(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4916])).
% 5.59/5.58 tff(4918,plain,
% 5.59/5.58 (pred(NSX4!21) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[4917, 24])).
% 5.59/5.58 tff(4919,plain,
% 5.59/5.58 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n1, n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4918, 4894])).
% 5.59/5.58 tff(4920,plain,
% 5.59/5.58 (Y5!50 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[656, 4919, 791])).
% 5.59/5.58 tff(4921,plain,
% 5.59/5.58 (pred(Y5!50) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4920])).
% 5.59/5.58 tff(4922,plain,
% 5.59/5.58 (pred(Y5!50) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[4921, 19])).
% 5.59/5.58 tff(4923,plain,
% 5.59/5.58 (pred(pred(Y5!50)) = pred(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4922])).
% 5.59/5.58 tff(4924,plain,
% 5.59/5.58 (pred(pred(Y5!50)) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[4923, 18])).
% 5.59/5.58 tff(4925,plain,
% 5.59/5.58 (pred(pred(pred(Y5!50))) = pred(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4924])).
% 5.59/5.58 tff(4926,plain,
% 5.59/5.58 (pred(pred(pred(Y5!50))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[4925, 17])).
% 5.59/5.58 tff(4927,plain,
% 5.59/5.58 (pred(pred(pred(pred(Y5!50)))) = pred(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4926])).
% 5.59/5.58 tff(4928,plain,
% 5.59/5.58 (pred(pred(pred(pred(Y5!50)))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[4927, 16])).
% 5.59/5.58 tff(4929,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4928])).
% 5.59/5.58 tff(4930,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(Y5!50))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[4929, 15])).
% 5.59/5.58 tff(4931,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4930])).
% 5.59/5.58 tff(4932,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[4931, 25])).
% 5.59/5.58 tff(4933,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4932])).
% 5.59/5.58 tff(4934,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[4933, 24])).
% 5.59/5.58 tff(4935,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4934])).
% 5.59/5.58 tff(4936,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[4935, 23])).
% 5.59/5.58 tff(4937,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4936])).
% 5.59/5.58 tff(4938,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[4937, 22])).
% 5.59/5.58 tff(4939,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4938])).
% 5.59/5.58 tff(4940,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[4939, 21])).
% 5.59/5.58 tff(4941,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4940])).
% 5.59/5.58 tff(4942,plain,
% 5.59/5.58 (NPY5!18 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[694, 4941, 20])).
% 5.59/5.58 tff(4943,plain,
% 5.59/5.58 (succ(NPY5!18) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4942])).
% 5.59/5.58 tff(4944,plain,
% 5.59/5.58 (succ(NPY5!18) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[4943, 45])).
% 5.59/5.58 tff(4945,plain,
% 5.59/5.58 (succ(Y5!50) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4920])).
% 5.59/5.58 tff(4946,plain,
% 5.59/5.58 (succ(Y5!50) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[4945, 45])).
% 5.59/5.58 tff(4947,plain,
% 5.59/5.58 (succ(succ(Y5!50)) = succ(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4946])).
% 5.59/5.58 tff(4948,plain,
% 5.59/5.58 (succ(succ(Y5!50)) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[4947, 28])).
% 5.59/5.58 tff(4949,plain,
% 5.59/5.58 (succ(succ(succ(Y5!50))) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4948])).
% 5.59/5.58 tff(4950,plain,
% 5.59/5.58 (succ(succ(succ(Y5!50))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[4949, 42])).
% 5.59/5.58 tff(4951,plain,
% 5.59/5.58 (succ(succ(succ(succ(Y5!50)))) = succ(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4950])).
% 5.59/5.58 tff(4952,plain,
% 5.59/5.58 (succ(succ(succ(succ(Y5!50)))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[4951, 58])).
% 5.59/5.58 tff(4953,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4952])).
% 5.59/5.58 tff(4954,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(Y5!50))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[4953, 36])).
% 5.59/5.58 tff(4955,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4954])).
% 5.59/5.58 tff(4956,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[4955, 48])).
% 5.59/5.58 tff(4957,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4956])).
% 5.59/5.58 tff(4958,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[4957, 14])).
% 5.59/5.58 tff(4959,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4958])).
% 5.59/5.58 tff(4960,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[4959, 33])).
% 5.59/5.58 tff(4961,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4960])).
% 5.59/5.58 tff(4962,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[4961, 30])).
% 5.59/5.58 tff(4963,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4962])).
% 5.59/5.58 tff(4964,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[4963, 39])).
% 5.59/5.58 tff(4965,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4964])).
% 5.59/5.58 tff(4966,plain,
% 5.59/5.58 (NSY5!16 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[717, 4965, 53])).
% 5.59/5.58 tff(4967,plain,
% 5.59/5.58 (pred(NSY5!16) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4966])).
% 5.59/5.58 tff(4968,plain,
% 5.59/5.58 (pred(NSY5!16) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[4967, 19])).
% 5.59/5.58 tff(4969,plain,
% 5.59/5.58 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n7, n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4968, 4944])).
% 5.59/5.58 tff(4970,plain,
% 5.59/5.58 (sum(pred(NSY5!16), succ(NPY5!18)) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[4969, 44])).
% 5.59/5.58 tff(4971,plain,
% 5.59/5.58 (sum(pred(Y4!52), succ(X4!53)) = sum(n1, n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4814, 4896])).
% 5.59/5.58 tff(4972,plain,
% 5.59/5.58 (sum(pred(Y4!52), succ(X4!53)) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[4971, 47])).
% 5.59/5.58 tff(4973,plain,
% 5.59/5.58 (sum(pred(X4!53), succ(Y4!52)) = sum(n1, n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4870, 4838])).
% 5.59/5.58 tff(4974,plain,
% 5.59/5.58 (sum(pred(X4!53), succ(Y4!52)) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[4973, 47])).
% 5.59/5.58 tff(4975,plain,
% 5.59/5.58 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n4, n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4974, 4972])).
% 5.59/5.58 tff(4976,plain,
% 5.59/5.58 (X5!51 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[553, 4975, 46])).
% 5.59/5.58 tff(4977,plain,
% 5.59/5.58 (pred(X5!51) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4976])).
% 5.59/5.58 tff(4978,plain,
% 5.59/5.58 (pred(X5!51) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[4977, 19])).
% 5.59/5.58 tff(4979,plain,
% 5.59/5.58 (pred(pred(X5!51)) = pred(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4978])).
% 5.59/5.58 tff(4980,plain,
% 5.59/5.58 (pred(pred(X5!51)) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[4979, 18])).
% 5.59/5.58 tff(4981,plain,
% 5.59/5.58 (pred(pred(pred(X5!51))) = pred(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4980])).
% 5.59/5.58 tff(4982,plain,
% 5.59/5.58 (pred(pred(pred(X5!51))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[4981, 17])).
% 5.59/5.58 tff(4983,plain,
% 5.59/5.58 (pred(pred(pred(pred(X5!51)))) = pred(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4982])).
% 5.59/5.58 tff(4984,plain,
% 5.59/5.58 (pred(pred(pred(pred(X5!51)))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[4983, 16])).
% 5.59/5.58 tff(4985,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X5!51))))) = pred(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4984])).
% 5.59/5.58 tff(4986,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X5!51))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[4985, 15])).
% 5.59/5.58 tff(4987,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4986])).
% 5.59/5.58 tff(4988,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[4987, 25])).
% 5.59/5.58 tff(4989,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4988])).
% 5.59/5.58 tff(4990,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[4989, 24])).
% 5.59/5.58 tff(4991,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4990])).
% 5.59/5.58 tff(4992,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[4991, 23])).
% 5.59/5.58 tff(4993,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4992])).
% 5.59/5.58 tff(4994,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[4993, 22])).
% 5.59/5.58 tff(4995,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4994])).
% 5.59/5.58 tff(4996,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[4995, 21])).
% 5.59/5.58 tff(4997,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4996])).
% 5.59/5.58 tff(4998,plain,
% 5.59/5.58 (NPX5!19 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[742, 4997, 20])).
% 5.59/5.58 tff(4999,plain,
% 5.59/5.58 (succ(NPX5!19) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4998])).
% 5.59/5.58 tff(5000,plain,
% 5.59/5.58 (succ(NPX5!19) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[4999, 45])).
% 5.59/5.58 tff(5001,plain,
% 5.59/5.58 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n9, n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5000, 4970])).
% 5.59/5.58 tff(5002,plain,
% 5.59/5.58 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5001, 790])).
% 5.59/5.58 tff(5003,plain,
% 5.59/5.58 (succ(X5!51) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4976])).
% 5.59/5.58 tff(5004,plain,
% 5.59/5.58 (succ(X5!51) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5003, 45])).
% 5.59/5.58 tff(5005,plain,
% 5.59/5.58 (succ(succ(X5!51)) = succ(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5004])).
% 5.59/5.58 tff(5006,plain,
% 5.59/5.58 (succ(succ(X5!51)) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[5005, 28])).
% 5.59/5.58 tff(5007,plain,
% 5.59/5.58 (succ(succ(succ(X5!51))) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5006])).
% 5.59/5.58 tff(5008,plain,
% 5.59/5.58 (succ(succ(succ(X5!51))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5007, 42])).
% 5.59/5.58 tff(5009,plain,
% 5.59/5.58 (succ(succ(succ(succ(X5!51)))) = succ(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5008])).
% 5.59/5.58 tff(5010,plain,
% 5.59/5.58 (succ(succ(succ(succ(X5!51)))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[5009, 58])).
% 5.59/5.58 tff(5011,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X5!51))))) = succ(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5010])).
% 5.59/5.58 tff(5012,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X5!51))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5011, 36])).
% 5.59/5.58 tff(5013,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5012])).
% 5.59/5.58 tff(5014,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5013, 48])).
% 5.59/5.58 tff(5015,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5014])).
% 5.59/5.58 tff(5016,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5015, 14])).
% 5.59/5.58 tff(5017,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5016])).
% 5.59/5.58 tff(5018,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5017, 33])).
% 5.59/5.58 tff(5019,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5018])).
% 5.59/5.58 tff(5020,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5019, 30])).
% 5.59/5.58 tff(5021,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5020])).
% 5.59/5.58 tff(5022,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5021, 39])).
% 5.59/5.58 tff(5023,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5022])).
% 5.59/5.58 tff(5024,plain,
% 5.59/5.58 (NSX5!17 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[767, 5023, 53])).
% 5.59/5.58 tff(5025,plain,
% 5.59/5.58 (pred(NSX5!17) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5024])).
% 5.59/5.58 tff(5026,plain,
% 5.59/5.58 (pred(NSX5!17) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5025, 19])).
% 5.59/5.58 tff(5027,plain,
% 5.59/5.58 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n7, n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5026, 5002])).
% 5.59/5.58 tff(5028,plain,
% 5.59/5.58 (Y6!48 = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[772, 5027, 789])).
% 5.59/5.58 tff(5029,plain,
% 5.59/5.58 (pred(Y6!48) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5028])).
% 5.59/5.58 tff(5030,plain,
% 5.59/5.58 (pred(Y6!48) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5029, 21])).
% 5.59/5.58 tff(5031,plain,
% 5.59/5.58 (pred(pred(Y6!48)) = pred(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5030])).
% 5.59/5.58 tff(5032,plain,
% 5.59/5.58 (pred(pred(Y6!48)) = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[5031, 20])).
% 5.59/5.58 tff(5033,plain,
% 5.59/5.58 (pred(pred(pred(Y6!48))) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5032])).
% 5.59/5.58 tff(5034,plain,
% 5.59/5.58 (pred(pred(pred(Y6!48))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5033, 19])).
% 5.59/5.58 tff(5035,plain,
% 5.59/5.58 (pred(pred(pred(pred(Y6!48)))) = pred(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5034])).
% 5.59/5.58 tff(5036,plain,
% 5.59/5.58 (pred(pred(pred(pred(Y6!48)))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5035, 18])).
% 5.59/5.58 tff(5037,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5036])).
% 5.59/5.58 tff(5038,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(Y6!48))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5037, 17])).
% 5.59/5.58 tff(5039,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5038])).
% 5.59/5.58 tff(5040,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5039, 16])).
% 5.59/5.58 tff(5041,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5040])).
% 5.59/5.58 tff(5042,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5041, 15])).
% 5.59/5.58 tff(5043,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5042])).
% 5.59/5.58 tff(5044,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5043, 25])).
% 5.59/5.58 tff(5045,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5044])).
% 5.59/5.58 tff(5046,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[5045, 24])).
% 5.59/5.58 tff(5047,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5046])).
% 5.59/5.58 tff(5048,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5047, 23])).
% 5.59/5.58 tff(5049,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5048])).
% 5.59/5.58 tff(5050,plain,
% 5.59/5.58 (NPY6!14 = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[1465, 5049, 22])).
% 5.59/5.58 tff(5051,plain,
% 5.59/5.58 (succ(NPY6!14) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5050])).
% 5.59/5.58 tff(5052,plain,
% 5.59/5.58 (succ(NPY6!14) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5051, 42])).
% 5.59/5.58 tff(5053,plain,
% 5.59/5.58 (succ(Y6!48) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5028])).
% 5.59/5.58 tff(5054,plain,
% 5.59/5.58 (succ(Y6!48) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5053, 42])).
% 5.59/5.58 tff(5055,plain,
% 5.59/5.58 (succ(succ(Y6!48)) = succ(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5054])).
% 5.59/5.58 tff(5056,plain,
% 5.59/5.58 (succ(succ(Y6!48)) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[5055, 58])).
% 5.59/5.58 tff(5057,plain,
% 5.59/5.58 (succ(succ(succ(Y6!48))) = succ(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5056])).
% 5.59/5.58 tff(5058,plain,
% 5.59/5.58 (succ(succ(succ(Y6!48))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5057, 36])).
% 5.59/5.58 tff(5059,plain,
% 5.59/5.58 (succ(succ(succ(succ(Y6!48)))) = succ(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5058])).
% 5.59/5.58 tff(5060,plain,
% 5.59/5.58 (succ(succ(succ(succ(Y6!48)))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5059, 48])).
% 5.59/5.58 tff(5061,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5060])).
% 5.59/5.58 tff(5062,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(Y6!48))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5061, 14])).
% 5.59/5.58 tff(5063,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5062])).
% 5.59/5.58 tff(5064,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5063, 33])).
% 5.59/5.58 tff(5065,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5064])).
% 5.59/5.58 tff(5066,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5065, 30])).
% 5.59/5.58 tff(5067,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5066])).
% 5.59/5.58 tff(5068,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5067, 39])).
% 5.59/5.58 tff(5069,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5068])).
% 5.59/5.58 tff(5070,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[5069, 53])).
% 5.59/5.58 tff(5071,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5070])).
% 5.59/5.58 tff(5072,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5071, 45])).
% 5.59/5.58 tff(5073,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5072])).
% 5.59/5.58 tff(5074,plain,
% 5.59/5.58 (NSY6!12 = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[1490, 5073, 28])).
% 5.59/5.58 tff(5075,plain,
% 5.59/5.58 (pred(NSY6!12) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5074])).
% 5.59/5.58 tff(5076,plain,
% 5.59/5.58 (pred(NSY6!12) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5075, 21])).
% 5.59/5.58 tff(5077,plain,
% 5.59/5.58 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n9, n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5076, 5052])).
% 5.59/5.58 tff(5078,plain,
% 5.59/5.58 (sum(pred(NSY6!12), succ(NPY6!14)) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5077, 41])).
% 5.59/5.58 tff(5079,plain,
% 5.59/5.58 (sum(pred(Y5!50), succ(X5!51)) = sum(n7, n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4922, 5004])).
% 5.59/5.58 tff(5080,plain,
% 5.59/5.58 (sum(pred(Y5!50), succ(X5!51)) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5079, 44])).
% 5.59/5.58 tff(5081,plain,
% 5.59/5.58 (sum(pred(X5!51), succ(Y5!50)) = sum(n7, n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[4978, 4946])).
% 5.59/5.58 tff(5082,plain,
% 5.59/5.58 (sum(pred(X5!51), succ(Y5!50)) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5081, 44])).
% 5.59/5.58 tff(5083,plain,
% 5.59/5.58 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n5, n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5082, 5080])).
% 5.59/5.58 tff(5084,plain,
% 5.59/5.58 (X6!49 = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[669, 5083, 43])).
% 5.59/5.58 tff(5085,plain,
% 5.59/5.58 (pred(X6!49) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5084])).
% 5.59/5.58 tff(5086,plain,
% 5.59/5.58 (pred(X6!49) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5085, 21])).
% 5.59/5.58 tff(5087,plain,
% 5.59/5.58 (pred(pred(X6!49)) = pred(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5086])).
% 5.59/5.58 tff(5088,plain,
% 5.59/5.58 (pred(pred(X6!49)) = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[5087, 20])).
% 5.59/5.58 tff(5089,plain,
% 5.59/5.58 (pred(pred(pred(X6!49))) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5088])).
% 5.59/5.58 tff(5090,plain,
% 5.59/5.58 (pred(pred(pred(X6!49))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5089, 19])).
% 5.59/5.58 tff(5091,plain,
% 5.59/5.58 (pred(pred(pred(pred(X6!49)))) = pred(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5090])).
% 5.59/5.58 tff(5092,plain,
% 5.59/5.58 (pred(pred(pred(pred(X6!49)))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5091, 18])).
% 5.59/5.58 tff(5093,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X6!49))))) = pred(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5092])).
% 5.59/5.58 tff(5094,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X6!49))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5093, 17])).
% 5.59/5.58 tff(5095,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5094])).
% 5.59/5.58 tff(5096,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5095, 16])).
% 5.59/5.58 tff(5097,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5096])).
% 5.59/5.58 tff(5098,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5097, 15])).
% 5.59/5.58 tff(5099,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5098])).
% 5.59/5.58 tff(5100,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5099, 25])).
% 5.59/5.58 tff(5101,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5100])).
% 5.59/5.58 tff(5102,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[5101, 24])).
% 5.59/5.58 tff(5103,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5102])).
% 5.59/5.58 tff(5104,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5103, 23])).
% 5.59/5.58 tff(5105,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5104])).
% 5.59/5.58 tff(5106,plain,
% 5.59/5.58 (NPX6!15 = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[1523, 5105, 22])).
% 5.59/5.58 tff(5107,plain,
% 5.59/5.58 (succ(NPX6!15) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5106])).
% 5.59/5.58 tff(5108,plain,
% 5.59/5.58 (succ(NPX6!15) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5107, 42])).
% 5.59/5.58 tff(5109,plain,
% 5.59/5.58 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n0, n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5108, 5078])).
% 5.59/5.58 tff(5110,plain,
% 5.59/5.58 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5109, 40])).
% 5.59/5.58 tff(5111,plain,
% 5.59/5.58 (succ(X6!49) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5084])).
% 5.59/5.58 tff(5112,plain,
% 5.59/5.58 (succ(X6!49) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5111, 42])).
% 5.59/5.58 tff(5113,plain,
% 5.59/5.58 (succ(succ(X6!49)) = succ(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5112])).
% 5.59/5.58 tff(5114,plain,
% 5.59/5.58 (succ(succ(X6!49)) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[5113, 58])).
% 5.59/5.58 tff(5115,plain,
% 5.59/5.58 (succ(succ(succ(X6!49))) = succ(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5114])).
% 5.59/5.58 tff(5116,plain,
% 5.59/5.58 (succ(succ(succ(X6!49))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5115, 36])).
% 5.59/5.58 tff(5117,plain,
% 5.59/5.58 (succ(succ(succ(succ(X6!49)))) = succ(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5116])).
% 5.59/5.58 tff(5118,plain,
% 5.59/5.58 (succ(succ(succ(succ(X6!49)))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5117, 48])).
% 5.59/5.58 tff(5119,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X6!49))))) = succ(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5118])).
% 5.59/5.58 tff(5120,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X6!49))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5119, 14])).
% 5.59/5.58 tff(5121,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5120])).
% 5.59/5.58 tff(5122,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5121, 33])).
% 5.59/5.58 tff(5123,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5122])).
% 5.59/5.58 tff(5124,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5123, 30])).
% 5.59/5.58 tff(5125,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5124])).
% 5.59/5.58 tff(5126,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5125, 39])).
% 5.59/5.58 tff(5127,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5126])).
% 5.59/5.58 tff(5128,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[5127, 53])).
% 5.59/5.58 tff(5129,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5128])).
% 5.59/5.58 tff(5130,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5129, 45])).
% 5.59/5.58 tff(5131,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5130])).
% 5.59/5.58 tff(5132,plain,
% 5.59/5.58 (NSX6!13 = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[1550, 5131, 28])).
% 5.59/5.58 tff(5133,plain,
% 5.59/5.58 (pred(NSX6!13) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5132])).
% 5.59/5.58 tff(5134,plain,
% 5.59/5.58 (pred(NSX6!13) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5133, 21])).
% 5.59/5.58 tff(5135,plain,
% 5.59/5.58 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n9, n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5134, 5110])).
% 5.59/5.58 tff(5136,plain,
% 5.59/5.58 (sum(n9, n9) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.59/5.58 inference(symmetry,[status(thm)],[5135])).
% 5.59/5.58 tff(5137,plain,
% 5.59/5.58 (sum(pred(Y6!48), succ(X6!49)) = sum(n9, n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5030, 5112])).
% 5.59/5.58 tff(5138,plain,
% 5.59/5.58 (sum(pred(Y6!48), succ(X6!49)) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5137, 41])).
% 5.59/5.58 tff(5139,plain,
% 5.59/5.58 (sum(pred(X6!49), succ(Y6!48)) = sum(n9, n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5086, 5054])).
% 5.59/5.58 tff(5140,plain,
% 5.59/5.58 (sum(pred(X6!49), succ(Y6!48)) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5139, 41])).
% 5.59/5.58 tff(5141,plain,
% 5.59/5.58 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n9, n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5140, 5138])).
% 5.59/5.58 tff(5142,plain,
% 5.59/5.58 (X7!47 = Y7!46),
% 5.59/5.58 inference(transitivity,[status(thm)],[785, 5141, 5136, 794])).
% 5.59/5.58 tff(5143,plain,
% 5.59/5.58 ($false),
% 5.59/5.58 inference(unit_resolution,[status(thm)],[792, 5142])).
% 5.59/5.58 tff(5144,plain,((~(Y0!60 = n6)) | (X7!47 = Y7!46) | (~(X0!61 = n10))), inference(lemma,lemma(discharge,[]))).
% 5.59/5.58 tff(5145,plain,
% 5.59/5.58 (~(Y0!60 = n6)),
% 5.59/5.58 inference(unit_resolution,[status(thm)],[5144, 3715, 792])).
% 5.59/5.58 tff(5146,plain,
% 5.59/5.58 (sum(n5, n2) = n7),
% 5.59/5.58 inference(and_elim,[status(thm)],[9])).
% 5.59/5.58 tff(5147,plain,
% 5.59/5.58 (sum(n7, n4) = n0),
% 5.59/5.58 inference(and_elim,[status(thm)],[9])).
% 5.59/5.58 tff(5148,assumption,(X0!61 = n8), introduced(assumption)).
% 5.59/5.58 tff(5149,plain,
% 5.59/5.58 (pred(X0!61) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5148])).
% 5.59/5.58 tff(5150,plain,
% 5.59/5.58 (pred(X0!61) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5149, 19])).
% 5.59/5.58 tff(5151,plain,
% 5.59/5.58 (pred(pred(X0!61)) = pred(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5150])).
% 5.59/5.58 tff(5152,plain,
% 5.59/5.58 (pred(pred(X0!61)) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5151, 18])).
% 5.59/5.58 tff(5153,plain,
% 5.59/5.58 (pred(pred(pred(X0!61))) = pred(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5152])).
% 5.59/5.58 tff(5154,plain,
% 5.59/5.58 (pred(pred(pred(X0!61))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5153, 17])).
% 5.59/5.58 tff(5155,plain,
% 5.59/5.58 (pred(pred(pred(pred(X0!61)))) = pred(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5154])).
% 5.59/5.58 tff(5156,plain,
% 5.59/5.58 (pred(pred(pred(pred(X0!61)))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5155, 16])).
% 5.59/5.58 tff(5157,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X0!61))))) = pred(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5156])).
% 5.59/5.58 tff(5158,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(X0!61))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5157, 15])).
% 5.59/5.58 tff(5159,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5158])).
% 5.59/5.58 tff(5160,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5159, 25])).
% 5.59/5.58 tff(5161,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5160])).
% 5.59/5.58 tff(5162,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[5161, 24])).
% 5.59/5.58 tff(5163,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5162])).
% 5.59/5.58 tff(5164,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5163, 23])).
% 5.59/5.58 tff(5165,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5164])).
% 5.59/5.58 tff(5166,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[5165, 22])).
% 5.59/5.58 tff(5167,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5166])).
% 5.59/5.58 tff(5168,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5167, 21])).
% 5.59/5.58 tff(5169,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5168])).
% 5.59/5.58 tff(5170,plain,
% 5.59/5.58 (NPX0!39 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[166, 5169, 20])).
% 5.59/5.58 tff(5171,plain,
% 5.59/5.58 (succ(NPX0!39) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5170])).
% 5.59/5.58 tff(5172,plain,
% 5.59/5.58 (succ(NPX0!39) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5171, 45])).
% 5.59/5.58 tff(5173,plain,
% 5.59/5.58 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n9, n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5172, 146])).
% 5.59/5.58 tff(5174,plain,
% 5.59/5.58 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5173, 3874])).
% 5.59/5.58 tff(5175,plain,
% 5.59/5.58 (succ(X0!61) = succ(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5148])).
% 5.59/5.58 tff(5176,plain,
% 5.59/5.58 (succ(X0!61) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5175, 45])).
% 5.59/5.58 tff(5177,plain,
% 5.59/5.58 (succ(succ(X0!61)) = succ(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5176])).
% 5.59/5.58 tff(5178,plain,
% 5.59/5.58 (succ(succ(X0!61)) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[5177, 28])).
% 5.59/5.58 tff(5179,plain,
% 5.59/5.58 (succ(succ(succ(X0!61))) = succ(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5178])).
% 5.59/5.58 tff(5180,plain,
% 5.59/5.58 (succ(succ(succ(X0!61))) = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[5179, 42])).
% 5.59/5.58 tff(5181,plain,
% 5.59/5.58 (succ(succ(succ(succ(X0!61)))) = succ(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5180])).
% 5.59/5.58 tff(5182,plain,
% 5.59/5.58 (succ(succ(succ(succ(X0!61)))) = n1),
% 5.59/5.58 inference(transitivity,[status(thm)],[5181, 58])).
% 5.59/5.58 tff(5183,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X0!61))))) = succ(n1)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5182])).
% 5.59/5.58 tff(5184,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(X0!61))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5183, 36])).
% 5.59/5.58 tff(5185,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n2)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5184])).
% 5.59/5.58 tff(5186,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5185, 48])).
% 5.59/5.58 tff(5187,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5186])).
% 5.59/5.58 tff(5188,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5187, 14])).
% 5.59/5.58 tff(5189,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5188])).
% 5.59/5.58 tff(5190,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5189, 33])).
% 5.59/5.58 tff(5191,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5190])).
% 5.59/5.58 tff(5192,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5191, 30])).
% 5.59/5.58 tff(5193,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5192])).
% 5.59/5.58 tff(5194,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5193, 39])).
% 5.59/5.58 tff(5195,plain,
% 5.59/5.58 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5194])).
% 5.59/5.58 tff(5196,plain,
% 5.59/5.58 (NSX0!37 = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[191, 5195, 53])).
% 5.59/5.58 tff(5197,plain,
% 5.59/5.58 (pred(NSX0!37) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5196])).
% 5.59/5.58 tff(5198,plain,
% 5.59/5.58 (pred(NSX0!37) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5197, 19])).
% 5.59/5.58 tff(5199,plain,
% 5.59/5.58 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n7, n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5198, 5174])).
% 5.59/5.58 tff(5200,plain,
% 5.59/5.58 (Y1!58 = n0),
% 5.59/5.58 inference(transitivity,[status(thm)],[196, 5199, 5147])).
% 5.59/5.58 tff(5201,plain,
% 5.59/5.58 (pred(Y1!58) = pred(n0)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5200])).
% 5.59/5.58 tff(5202,plain,
% 5.59/5.58 (pred(Y1!58) = n10),
% 5.59/5.58 inference(transitivity,[status(thm)],[5201, 22])).
% 5.59/5.58 tff(5203,plain,
% 5.59/5.58 (pred(pred(Y1!58)) = pred(n10)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5202])).
% 5.59/5.58 tff(5204,plain,
% 5.59/5.58 (pred(pred(Y1!58)) = n9),
% 5.59/5.58 inference(transitivity,[status(thm)],[5203, 21])).
% 5.59/5.58 tff(5205,plain,
% 5.59/5.58 (pred(pred(pred(Y1!58))) = pred(n9)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5204])).
% 5.59/5.58 tff(5206,plain,
% 5.59/5.58 (pred(pred(pred(Y1!58))) = n8),
% 5.59/5.58 inference(transitivity,[status(thm)],[5205, 20])).
% 5.59/5.58 tff(5207,plain,
% 5.59/5.58 (pred(pred(pred(pred(Y1!58)))) = pred(n8)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5206])).
% 5.59/5.58 tff(5208,plain,
% 5.59/5.58 (pred(pred(pred(pred(Y1!58)))) = n7),
% 5.59/5.58 inference(transitivity,[status(thm)],[5207, 19])).
% 5.59/5.58 tff(5209,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n7)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5208])).
% 5.59/5.58 tff(5210,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(Y1!58))))) = n6),
% 5.59/5.58 inference(transitivity,[status(thm)],[5209, 18])).
% 5.59/5.58 tff(5211,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n6)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5210])).
% 5.59/5.58 tff(5212,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n5),
% 5.59/5.58 inference(transitivity,[status(thm)],[5211, 17])).
% 5.59/5.58 tff(5213,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n5)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5212])).
% 5.59/5.58 tff(5214,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n4),
% 5.59/5.58 inference(transitivity,[status(thm)],[5213, 16])).
% 5.59/5.58 tff(5215,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n4)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5214])).
% 5.59/5.58 tff(5216,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n3),
% 5.59/5.58 inference(transitivity,[status(thm)],[5215, 15])).
% 5.59/5.58 tff(5217,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n3)),
% 5.59/5.58 inference(monotonicity,[status(thm)],[5216])).
% 5.59/5.58 tff(5218,plain,
% 5.59/5.58 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n2),
% 5.59/5.58 inference(transitivity,[status(thm)],[5217, 25])).
% 5.59/5.59 tff(5219,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5218])).
% 5.59/5.59 tff(5220,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5219, 24])).
% 5.59/5.59 tff(5221,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5220])).
% 5.59/5.59 tff(5222,plain,
% 5.59/5.59 (NPY1!34 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[232, 5221, 23])).
% 5.59/5.59 tff(5223,plain,
% 5.59/5.59 (succ(NPY1!34) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5222])).
% 5.59/5.59 tff(5224,plain,
% 5.59/5.59 (succ(NPY1!34) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5223, 58])).
% 5.59/5.59 tff(5225,plain,
% 5.59/5.59 (succ(Y1!58) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5200])).
% 5.59/5.59 tff(5226,plain,
% 5.59/5.59 (succ(Y1!58) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5225, 58])).
% 5.59/5.59 tff(5227,plain,
% 5.59/5.59 (succ(succ(Y1!58)) = succ(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5226])).
% 5.59/5.59 tff(5228,plain,
% 5.59/5.59 (succ(succ(Y1!58)) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5227, 36])).
% 5.59/5.59 tff(5229,plain,
% 5.59/5.59 (succ(succ(succ(Y1!58))) = succ(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5228])).
% 5.59/5.59 tff(5230,plain,
% 5.59/5.59 (succ(succ(succ(Y1!58))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5229, 48])).
% 5.59/5.59 tff(5231,plain,
% 5.59/5.59 (succ(succ(succ(succ(Y1!58)))) = succ(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5230])).
% 5.59/5.59 tff(5232,plain,
% 5.59/5.59 (succ(succ(succ(succ(Y1!58)))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5231, 14])).
% 5.59/5.59 tff(5233,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5232])).
% 5.59/5.59 tff(5234,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(Y1!58))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5233, 33])).
% 5.59/5.59 tff(5235,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5234])).
% 5.59/5.59 tff(5236,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5235, 30])).
% 5.59/5.59 tff(5237,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5236])).
% 5.59/5.59 tff(5238,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5237, 39])).
% 5.59/5.59 tff(5239,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5238])).
% 5.59/5.59 tff(5240,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5239, 53])).
% 5.59/5.59 tff(5241,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5240])).
% 5.59/5.59 tff(5242,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5241, 45])).
% 5.59/5.59 tff(5243,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5242])).
% 5.59/5.59 tff(5244,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5243, 28])).
% 5.59/5.59 tff(5245,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5244])).
% 5.59/5.59 tff(5246,plain,
% 5.59/5.59 (NSY1!32 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[255, 5245, 42])).
% 5.59/5.59 tff(5247,plain,
% 5.59/5.59 (pred(NSY1!32) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5246])).
% 5.59/5.59 tff(5248,plain,
% 5.59/5.59 (pred(NSY1!32) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5247, 22])).
% 5.59/5.59 tff(5249,plain,
% 5.59/5.59 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5248, 5224])).
% 5.59/5.59 tff(5250,plain,
% 5.59/5.59 (sum(pred(NSY1!32), succ(NPY1!34)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5249, 57])).
% 5.59/5.59 tff(5251,plain,
% 5.59/5.59 (sum(n2, n9) = n0),
% 5.59/5.59 inference(and_elim,[status(thm)],[9])).
% 5.59/5.59 tff(5252,plain,
% 5.59/5.59 (sum(pred(Y0!60), succ(X0!61)) = sum(n2, n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[82, 5176])).
% 5.59/5.59 tff(5253,plain,
% 5.59/5.59 (sum(pred(Y0!60), succ(X0!61)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5252, 5251])).
% 5.59/5.59 tff(5254,plain,
% 5.59/5.59 (sum(pred(X0!61), succ(Y0!60)) = sum(n7, n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5150, 87])).
% 5.59/5.59 tff(5255,plain,
% 5.59/5.59 (sum(pred(X0!61), succ(Y0!60)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5254, 5147])).
% 5.59/5.59 tff(5256,plain,
% 5.59/5.59 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n0, n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5255, 5253])).
% 5.59/5.59 tff(5257,plain,
% 5.59/5.59 (X1!59 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[93, 5256, 59])).
% 5.59/5.59 tff(5258,plain,
% 5.59/5.59 (pred(X1!59) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5257])).
% 5.59/5.59 tff(5259,plain,
% 5.59/5.59 (pred(X1!59) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5258, 22])).
% 5.59/5.59 tff(5260,plain,
% 5.59/5.59 (pred(pred(X1!59)) = pred(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5259])).
% 5.59/5.59 tff(5261,plain,
% 5.59/5.59 (pred(pred(X1!59)) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5260, 21])).
% 5.59/5.59 tff(5262,plain,
% 5.59/5.59 (pred(pred(pred(X1!59))) = pred(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5261])).
% 5.59/5.59 tff(5263,plain,
% 5.59/5.59 (pred(pred(pred(X1!59))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5262, 20])).
% 5.59/5.59 tff(5264,plain,
% 5.59/5.59 (pred(pred(pred(pred(X1!59)))) = pred(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5263])).
% 5.59/5.59 tff(5265,plain,
% 5.59/5.59 (pred(pred(pred(pred(X1!59)))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5264, 19])).
% 5.59/5.59 tff(5266,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(X1!59))))) = pred(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5265])).
% 5.59/5.59 tff(5267,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(X1!59))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5266, 18])).
% 5.59/5.59 tff(5268,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5267])).
% 5.59/5.59 tff(5269,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5268, 17])).
% 5.59/5.59 tff(5270,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5269])).
% 5.59/5.59 tff(5271,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5270, 16])).
% 5.59/5.59 tff(5272,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5271])).
% 5.59/5.59 tff(5273,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5272, 15])).
% 5.59/5.59 tff(5274,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5273])).
% 5.59/5.59 tff(5275,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5274, 25])).
% 5.59/5.59 tff(5276,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5275])).
% 5.59/5.59 tff(5277,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5276, 24])).
% 5.59/5.59 tff(5278,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5277])).
% 5.59/5.59 tff(5279,plain,
% 5.59/5.59 (NPX1!35 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[280, 5278, 23])).
% 5.59/5.59 tff(5280,plain,
% 5.59/5.59 (succ(NPX1!35) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5279])).
% 5.59/5.59 tff(5281,plain,
% 5.59/5.59 (succ(NPX1!35) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5280, 58])).
% 5.59/5.59 tff(5282,plain,
% 5.59/5.59 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n1, n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5281, 5250])).
% 5.59/5.59 tff(5283,plain,
% 5.59/5.59 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5282, 56])).
% 5.59/5.59 tff(5284,plain,
% 5.59/5.59 (succ(X1!59) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5257])).
% 5.59/5.59 tff(5285,plain,
% 5.59/5.59 (succ(X1!59) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5284, 58])).
% 5.59/5.59 tff(5286,plain,
% 5.59/5.59 (succ(succ(X1!59)) = succ(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5285])).
% 5.59/5.59 tff(5287,plain,
% 5.59/5.59 (succ(succ(X1!59)) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5286, 36])).
% 5.59/5.59 tff(5288,plain,
% 5.59/5.59 (succ(succ(succ(X1!59))) = succ(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5287])).
% 5.59/5.59 tff(5289,plain,
% 5.59/5.59 (succ(succ(succ(X1!59))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5288, 48])).
% 5.59/5.59 tff(5290,plain,
% 5.59/5.59 (succ(succ(succ(succ(X1!59)))) = succ(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5289])).
% 5.59/5.59 tff(5291,plain,
% 5.59/5.59 (succ(succ(succ(succ(X1!59)))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5290, 14])).
% 5.59/5.59 tff(5292,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(X1!59))))) = succ(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5291])).
% 5.59/5.59 tff(5293,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(X1!59))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5292, 33])).
% 5.59/5.59 tff(5294,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5293])).
% 5.59/5.59 tff(5295,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5294, 30])).
% 5.59/5.59 tff(5296,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5295])).
% 5.59/5.59 tff(5297,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5296, 39])).
% 5.59/5.59 tff(5298,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5297])).
% 5.59/5.59 tff(5299,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5298, 53])).
% 5.59/5.59 tff(5300,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5299])).
% 5.59/5.59 tff(5301,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5300, 45])).
% 5.59/5.59 tff(5302,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5301])).
% 5.59/5.59 tff(5303,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5302, 28])).
% 5.59/5.59 tff(5304,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5303])).
% 5.59/5.59 tff(5305,plain,
% 5.59/5.59 (NSX1!33 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[305, 5304, 42])).
% 5.59/5.59 tff(5306,plain,
% 5.59/5.59 (pred(NSX1!33) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5305])).
% 5.59/5.59 tff(5307,plain,
% 5.59/5.59 (pred(NSX1!33) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5306, 22])).
% 5.59/5.59 tff(5308,plain,
% 5.59/5.59 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5307, 5283])).
% 5.59/5.59 tff(5309,plain,
% 5.59/5.59 (Y2!56 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[310, 5308, 57])).
% 5.59/5.59 tff(5310,plain,
% 5.59/5.59 (pred(Y2!56) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5309])).
% 5.59/5.59 tff(5311,plain,
% 5.59/5.59 (pred(Y2!56) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5310, 22])).
% 5.59/5.59 tff(5312,plain,
% 5.59/5.59 (pred(pred(Y2!56)) = pred(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5311])).
% 5.59/5.59 tff(5313,plain,
% 5.59/5.59 (pred(pred(Y2!56)) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5312, 21])).
% 5.59/5.59 tff(5314,plain,
% 5.59/5.59 (pred(pred(pred(Y2!56))) = pred(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5313])).
% 5.59/5.59 tff(5315,plain,
% 5.59/5.59 (pred(pred(pred(Y2!56))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5314, 20])).
% 5.59/5.59 tff(5316,plain,
% 5.59/5.59 (pred(pred(pred(pred(Y2!56)))) = pred(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5315])).
% 5.59/5.59 tff(5317,plain,
% 5.59/5.59 (pred(pred(pred(pred(Y2!56)))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5316, 19])).
% 5.59/5.59 tff(5318,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5317])).
% 5.59/5.59 tff(5319,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(Y2!56))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5318, 18])).
% 5.59/5.59 tff(5320,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5319])).
% 5.59/5.59 tff(5321,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5320, 17])).
% 5.59/5.59 tff(5322,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5321])).
% 5.59/5.59 tff(5323,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5322, 16])).
% 5.59/5.59 tff(5324,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5323])).
% 5.59/5.59 tff(5325,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5324, 15])).
% 5.59/5.59 tff(5326,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5325])).
% 5.59/5.59 tff(5327,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5326, 25])).
% 5.59/5.59 tff(5328,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5327])).
% 5.59/5.59 tff(5329,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5328, 24])).
% 5.59/5.59 tff(5330,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5329])).
% 5.59/5.59 tff(5331,plain,
% 5.59/5.59 (NPY2!30 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[347, 5330, 23])).
% 5.59/5.59 tff(5332,plain,
% 5.59/5.59 (succ(NPY2!30) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5331])).
% 5.59/5.59 tff(5333,plain,
% 5.59/5.59 (succ(NPY2!30) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5332, 58])).
% 5.59/5.59 tff(5334,plain,
% 5.59/5.59 (succ(Y2!56) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5309])).
% 5.59/5.59 tff(5335,plain,
% 5.59/5.59 (succ(Y2!56) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5334, 58])).
% 5.59/5.59 tff(5336,plain,
% 5.59/5.59 (succ(succ(Y2!56)) = succ(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5335])).
% 5.59/5.59 tff(5337,plain,
% 5.59/5.59 (succ(succ(Y2!56)) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5336, 36])).
% 5.59/5.59 tff(5338,plain,
% 5.59/5.59 (succ(succ(succ(Y2!56))) = succ(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5337])).
% 5.59/5.59 tff(5339,plain,
% 5.59/5.59 (succ(succ(succ(Y2!56))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5338, 48])).
% 5.59/5.59 tff(5340,plain,
% 5.59/5.59 (succ(succ(succ(succ(Y2!56)))) = succ(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5339])).
% 5.59/5.59 tff(5341,plain,
% 5.59/5.59 (succ(succ(succ(succ(Y2!56)))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5340, 14])).
% 5.59/5.59 tff(5342,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5341])).
% 5.59/5.59 tff(5343,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(Y2!56))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5342, 33])).
% 5.59/5.59 tff(5344,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5343])).
% 5.59/5.59 tff(5345,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5344, 30])).
% 5.59/5.59 tff(5346,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5345])).
% 5.59/5.59 tff(5347,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5346, 39])).
% 5.59/5.59 tff(5348,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5347])).
% 5.59/5.59 tff(5349,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5348, 53])).
% 5.59/5.59 tff(5350,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5349])).
% 5.59/5.59 tff(5351,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5350, 45])).
% 5.59/5.59 tff(5352,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5351])).
% 5.59/5.59 tff(5353,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5352, 28])).
% 5.59/5.59 tff(5354,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5353])).
% 5.59/5.59 tff(5355,plain,
% 5.59/5.59 (NSY2!28 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[370, 5354, 42])).
% 5.59/5.59 tff(5356,plain,
% 5.59/5.59 (pred(NSY2!28) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5355])).
% 5.59/5.59 tff(5357,plain,
% 5.59/5.59 (pred(NSY2!28) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5356, 22])).
% 5.59/5.59 tff(5358,plain,
% 5.59/5.59 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5357, 5333])).
% 5.59/5.59 tff(5359,plain,
% 5.59/5.59 (sum(pred(NSY2!28), succ(NPY2!30)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5358, 57])).
% 5.59/5.59 tff(5360,plain,
% 5.59/5.59 (sum(pred(Y1!58), succ(X1!59)) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5202, 5285])).
% 5.59/5.59 tff(5361,plain,
% 5.59/5.59 (sum(pred(Y1!58), succ(X1!59)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5360, 57])).
% 5.59/5.59 tff(5362,plain,
% 5.59/5.59 (sum(pred(X1!59), succ(Y1!58)) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5259, 5226])).
% 5.59/5.59 tff(5363,plain,
% 5.59/5.59 (sum(pred(X1!59), succ(Y1!58)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5362, 57])).
% 5.59/5.59 tff(5364,plain,
% 5.59/5.59 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n0, n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5363, 5361])).
% 5.59/5.59 tff(5365,plain,
% 5.59/5.59 (X2!57 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[209, 5364, 59])).
% 5.59/5.59 tff(5366,plain,
% 5.59/5.59 (pred(X2!57) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5365])).
% 5.59/5.59 tff(5367,plain,
% 5.59/5.59 (pred(X2!57) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5366, 22])).
% 5.59/5.59 tff(5368,plain,
% 5.59/5.59 (pred(pred(X2!57)) = pred(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5367])).
% 5.59/5.59 tff(5369,plain,
% 5.59/5.59 (pred(pred(X2!57)) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5368, 21])).
% 5.59/5.59 tff(5370,plain,
% 5.59/5.59 (pred(pred(pred(X2!57))) = pred(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5369])).
% 5.59/5.59 tff(5371,plain,
% 5.59/5.59 (pred(pred(pred(X2!57))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5370, 20])).
% 5.59/5.59 tff(5372,plain,
% 5.59/5.59 (pred(pred(pred(pred(X2!57)))) = pred(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5371])).
% 5.59/5.59 tff(5373,plain,
% 5.59/5.59 (pred(pred(pred(pred(X2!57)))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5372, 19])).
% 5.59/5.59 tff(5374,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(X2!57))))) = pred(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5373])).
% 5.59/5.59 tff(5375,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(X2!57))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5374, 18])).
% 5.59/5.59 tff(5376,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5375])).
% 5.59/5.59 tff(5377,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5376, 17])).
% 5.59/5.59 tff(5378,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5377])).
% 5.59/5.59 tff(5379,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5378, 16])).
% 5.59/5.59 tff(5380,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5379])).
% 5.59/5.59 tff(5381,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5380, 15])).
% 5.59/5.59 tff(5382,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5381])).
% 5.59/5.59 tff(5383,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5382, 25])).
% 5.59/5.59 tff(5384,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5383])).
% 5.59/5.59 tff(5385,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5384, 24])).
% 5.59/5.59 tff(5386,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5385])).
% 5.59/5.59 tff(5387,plain,
% 5.59/5.59 (NPX2!31 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[395, 5386, 23])).
% 5.59/5.59 tff(5388,plain,
% 5.59/5.59 (succ(NPX2!31) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5387])).
% 5.59/5.59 tff(5389,plain,
% 5.59/5.59 (succ(NPX2!31) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5388, 58])).
% 5.59/5.59 tff(5390,plain,
% 5.59/5.59 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n1, n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5389, 5359])).
% 5.59/5.59 tff(5391,plain,
% 5.59/5.59 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5390, 56])).
% 5.59/5.59 tff(5392,plain,
% 5.59/5.59 (succ(X2!57) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5365])).
% 5.59/5.59 tff(5393,plain,
% 5.59/5.59 (succ(X2!57) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5392, 58])).
% 5.59/5.59 tff(5394,plain,
% 5.59/5.59 (succ(succ(X2!57)) = succ(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5393])).
% 5.59/5.59 tff(5395,plain,
% 5.59/5.59 (succ(succ(X2!57)) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5394, 36])).
% 5.59/5.59 tff(5396,plain,
% 5.59/5.59 (succ(succ(succ(X2!57))) = succ(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5395])).
% 5.59/5.59 tff(5397,plain,
% 5.59/5.59 (succ(succ(succ(X2!57))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5396, 48])).
% 5.59/5.59 tff(5398,plain,
% 5.59/5.59 (succ(succ(succ(succ(X2!57)))) = succ(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5397])).
% 5.59/5.59 tff(5399,plain,
% 5.59/5.59 (succ(succ(succ(succ(X2!57)))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5398, 14])).
% 5.59/5.59 tff(5400,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(X2!57))))) = succ(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5399])).
% 5.59/5.59 tff(5401,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(X2!57))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5400, 33])).
% 5.59/5.59 tff(5402,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5401])).
% 5.59/5.59 tff(5403,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5402, 30])).
% 5.59/5.59 tff(5404,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5403])).
% 5.59/5.59 tff(5405,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5404, 39])).
% 5.59/5.59 tff(5406,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5405])).
% 5.59/5.59 tff(5407,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5406, 53])).
% 5.59/5.59 tff(5408,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5407])).
% 5.59/5.59 tff(5409,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5408, 45])).
% 5.59/5.59 tff(5410,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5409])).
% 5.59/5.59 tff(5411,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5410, 28])).
% 5.59/5.59 tff(5412,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5411])).
% 5.59/5.59 tff(5413,plain,
% 5.59/5.59 (NSX2!29 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[420, 5412, 42])).
% 5.59/5.59 tff(5414,plain,
% 5.59/5.59 (pred(NSX2!29) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5413])).
% 5.59/5.59 tff(5415,plain,
% 5.59/5.59 (pred(NSX2!29) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5414, 22])).
% 5.59/5.59 tff(5416,plain,
% 5.59/5.59 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5415, 5391])).
% 5.59/5.59 tff(5417,plain,
% 5.59/5.59 (Y3!54 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[425, 5416, 57])).
% 5.59/5.59 tff(5418,plain,
% 5.59/5.59 (pred(Y3!54) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5417])).
% 5.59/5.59 tff(5419,plain,
% 5.59/5.59 (pred(Y3!54) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5418, 22])).
% 5.59/5.59 tff(5420,plain,
% 5.59/5.59 (pred(pred(Y3!54)) = pred(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5419])).
% 5.59/5.59 tff(5421,plain,
% 5.59/5.59 (pred(pred(Y3!54)) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5420, 21])).
% 5.59/5.59 tff(5422,plain,
% 5.59/5.59 (pred(pred(pred(Y3!54))) = pred(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5421])).
% 5.59/5.59 tff(5423,plain,
% 5.59/5.59 (pred(pred(pred(Y3!54))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5422, 20])).
% 5.59/5.59 tff(5424,plain,
% 5.59/5.59 (pred(pred(pred(pred(Y3!54)))) = pred(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5423])).
% 5.59/5.59 tff(5425,plain,
% 5.59/5.59 (pred(pred(pred(pred(Y3!54)))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5424, 19])).
% 5.59/5.59 tff(5426,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5425])).
% 5.59/5.59 tff(5427,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(Y3!54))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5426, 18])).
% 5.59/5.59 tff(5428,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5427])).
% 5.59/5.59 tff(5429,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5428, 17])).
% 5.59/5.59 tff(5430,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5429])).
% 5.59/5.59 tff(5431,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5430, 16])).
% 5.59/5.59 tff(5432,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5431])).
% 5.59/5.59 tff(5433,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5432, 15])).
% 5.59/5.59 tff(5434,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5433])).
% 5.59/5.59 tff(5435,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5434, 25])).
% 5.59/5.59 tff(5436,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5435])).
% 5.59/5.59 tff(5437,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5436, 24])).
% 5.59/5.59 tff(5438,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5437])).
% 5.59/5.59 tff(5439,plain,
% 5.59/5.59 (NPY3!26 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[462, 5438, 23])).
% 5.59/5.59 tff(5440,plain,
% 5.59/5.59 (succ(NPY3!26) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5439])).
% 5.59/5.59 tff(5441,plain,
% 5.59/5.59 (succ(NPY3!26) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5440, 58])).
% 5.59/5.59 tff(5442,plain,
% 5.59/5.59 (succ(Y3!54) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5417])).
% 5.59/5.59 tff(5443,plain,
% 5.59/5.59 (succ(Y3!54) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5442, 58])).
% 5.59/5.59 tff(5444,plain,
% 5.59/5.59 (succ(succ(Y3!54)) = succ(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5443])).
% 5.59/5.59 tff(5445,plain,
% 5.59/5.59 (succ(succ(Y3!54)) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5444, 36])).
% 5.59/5.59 tff(5446,plain,
% 5.59/5.59 (succ(succ(succ(Y3!54))) = succ(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5445])).
% 5.59/5.59 tff(5447,plain,
% 5.59/5.59 (succ(succ(succ(Y3!54))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5446, 48])).
% 5.59/5.59 tff(5448,plain,
% 5.59/5.59 (succ(succ(succ(succ(Y3!54)))) = succ(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5447])).
% 5.59/5.59 tff(5449,plain,
% 5.59/5.59 (succ(succ(succ(succ(Y3!54)))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5448, 14])).
% 5.59/5.59 tff(5450,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5449])).
% 5.59/5.59 tff(5451,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(Y3!54))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5450, 33])).
% 5.59/5.59 tff(5452,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5451])).
% 5.59/5.59 tff(5453,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5452, 30])).
% 5.59/5.59 tff(5454,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5453])).
% 5.59/5.59 tff(5455,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5454, 39])).
% 5.59/5.59 tff(5456,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5455])).
% 5.59/5.59 tff(5457,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5456, 53])).
% 5.59/5.59 tff(5458,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5457])).
% 5.59/5.59 tff(5459,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5458, 45])).
% 5.59/5.59 tff(5460,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5459])).
% 5.59/5.59 tff(5461,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5460, 28])).
% 5.59/5.59 tff(5462,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5461])).
% 5.59/5.59 tff(5463,plain,
% 5.59/5.59 (NSY3!24 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[485, 5462, 42])).
% 5.59/5.59 tff(5464,plain,
% 5.59/5.59 (pred(NSY3!24) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5463])).
% 5.59/5.59 tff(5465,plain,
% 5.59/5.59 (pred(NSY3!24) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5464, 22])).
% 5.59/5.59 tff(5466,plain,
% 5.59/5.59 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5465, 5441])).
% 5.59/5.59 tff(5467,plain,
% 5.59/5.59 (sum(pred(NSY3!24), succ(NPY3!26)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5466, 57])).
% 5.59/5.59 tff(5468,plain,
% 5.59/5.59 (sum(pred(Y2!56), succ(X2!57)) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5311, 5393])).
% 5.59/5.59 tff(5469,plain,
% 5.59/5.59 (sum(pred(Y2!56), succ(X2!57)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5468, 57])).
% 5.59/5.59 tff(5470,plain,
% 5.59/5.59 (sum(pred(X2!57), succ(Y2!56)) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5367, 5335])).
% 5.59/5.59 tff(5471,plain,
% 5.59/5.59 (sum(pred(X2!57), succ(Y2!56)) = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[5470, 57])).
% 5.59/5.59 tff(5472,plain,
% 5.59/5.59 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n0, n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5471, 5469])).
% 5.59/5.59 tff(5473,plain,
% 5.59/5.59 (X3!55 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[323, 5472, 59])).
% 5.59/5.59 tff(5474,plain,
% 5.59/5.59 (pred(X3!55) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5473])).
% 5.59/5.59 tff(5475,plain,
% 5.59/5.59 (pred(X3!55) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5474, 22])).
% 5.59/5.59 tff(5476,plain,
% 5.59/5.59 (pred(pred(X3!55)) = pred(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5475])).
% 5.59/5.59 tff(5477,plain,
% 5.59/5.59 (pred(pred(X3!55)) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5476, 21])).
% 5.59/5.59 tff(5478,plain,
% 5.59/5.59 (pred(pred(pred(X3!55))) = pred(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5477])).
% 5.59/5.59 tff(5479,plain,
% 5.59/5.59 (pred(pred(pred(X3!55))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5478, 20])).
% 5.59/5.59 tff(5480,plain,
% 5.59/5.59 (pred(pred(pred(pred(X3!55)))) = pred(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5479])).
% 5.59/5.59 tff(5481,plain,
% 5.59/5.59 (pred(pred(pred(pred(X3!55)))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5480, 19])).
% 5.59/5.59 tff(5482,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(X3!55))))) = pred(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5481])).
% 5.59/5.59 tff(5483,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(X3!55))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5482, 18])).
% 5.59/5.59 tff(5484,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5483])).
% 5.59/5.59 tff(5485,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5484, 17])).
% 5.59/5.59 tff(5486,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5485])).
% 5.59/5.59 tff(5487,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5486, 16])).
% 5.59/5.59 tff(5488,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5487])).
% 5.59/5.59 tff(5489,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5488, 15])).
% 5.59/5.59 tff(5490,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5489])).
% 5.59/5.59 tff(5491,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5490, 25])).
% 5.59/5.59 tff(5492,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5491])).
% 5.59/5.59 tff(5493,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5492, 24])).
% 5.59/5.59 tff(5494,plain,
% 5.59/5.59 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5493])).
% 5.59/5.59 tff(5495,plain,
% 5.59/5.59 (NPX3!27 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[510, 5494, 23])).
% 5.59/5.59 tff(5496,plain,
% 5.59/5.59 (succ(NPX3!27) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5495])).
% 5.59/5.59 tff(5497,plain,
% 5.59/5.59 (succ(NPX3!27) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5496, 58])).
% 5.59/5.59 tff(5498,plain,
% 5.59/5.59 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n1, n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5497, 5467])).
% 5.59/5.59 tff(5499,plain,
% 5.59/5.59 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5498, 56])).
% 5.59/5.59 tff(5500,plain,
% 5.59/5.59 (succ(X3!55) = succ(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5473])).
% 5.59/5.59 tff(5501,plain,
% 5.59/5.59 (succ(X3!55) = n1),
% 5.59/5.59 inference(transitivity,[status(thm)],[5500, 58])).
% 5.59/5.59 tff(5502,plain,
% 5.59/5.59 (succ(succ(X3!55)) = succ(n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5501])).
% 5.59/5.59 tff(5503,plain,
% 5.59/5.59 (succ(succ(X3!55)) = n2),
% 5.59/5.59 inference(transitivity,[status(thm)],[5502, 36])).
% 5.59/5.59 tff(5504,plain,
% 5.59/5.59 (succ(succ(succ(X3!55))) = succ(n2)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5503])).
% 5.59/5.59 tff(5505,plain,
% 5.59/5.59 (succ(succ(succ(X3!55))) = n3),
% 5.59/5.59 inference(transitivity,[status(thm)],[5504, 48])).
% 5.59/5.59 tff(5506,plain,
% 5.59/5.59 (succ(succ(succ(succ(X3!55)))) = succ(n3)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5505])).
% 5.59/5.59 tff(5507,plain,
% 5.59/5.59 (succ(succ(succ(succ(X3!55)))) = n4),
% 5.59/5.59 inference(transitivity,[status(thm)],[5506, 14])).
% 5.59/5.59 tff(5508,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(X3!55))))) = succ(n4)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5507])).
% 5.59/5.59 tff(5509,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(X3!55))))) = n5),
% 5.59/5.59 inference(transitivity,[status(thm)],[5508, 33])).
% 5.59/5.59 tff(5510,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n5)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5509])).
% 5.59/5.59 tff(5511,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n6),
% 5.59/5.59 inference(transitivity,[status(thm)],[5510, 30])).
% 5.59/5.59 tff(5512,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n6)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5511])).
% 5.59/5.59 tff(5513,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n7),
% 5.59/5.59 inference(transitivity,[status(thm)],[5512, 39])).
% 5.59/5.59 tff(5514,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n7)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5513])).
% 5.59/5.59 tff(5515,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n8),
% 5.59/5.59 inference(transitivity,[status(thm)],[5514, 53])).
% 5.59/5.59 tff(5516,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n8)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5515])).
% 5.59/5.59 tff(5517,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5516, 45])).
% 5.59/5.59 tff(5518,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n9)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5517])).
% 5.59/5.59 tff(5519,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5518, 28])).
% 5.59/5.59 tff(5520,plain,
% 5.59/5.59 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5519])).
% 5.59/5.59 tff(5521,plain,
% 5.59/5.59 (NSX3!25 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[535, 5520, 42])).
% 5.59/5.59 tff(5522,plain,
% 5.59/5.59 (pred(NSX3!25) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5521])).
% 5.59/5.59 tff(5523,plain,
% 5.59/5.59 (pred(NSX3!25) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5522, 22])).
% 5.59/5.59 tff(5524,plain,
% 5.59/5.59 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n10, n1)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5523, 5499])).
% 5.59/5.59 tff(5525,plain,
% 5.59/5.59 (Y4!52 = n0),
% 5.59/5.59 inference(transitivity,[status(thm)],[540, 5524, 57])).
% 5.59/5.59 tff(5526,plain,
% 5.59/5.59 (pred(Y4!52) = pred(n0)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5525])).
% 5.59/5.59 tff(5527,plain,
% 5.59/5.59 (pred(Y4!52) = n10),
% 5.59/5.59 inference(transitivity,[status(thm)],[5526, 22])).
% 5.59/5.59 tff(5528,plain,
% 5.59/5.59 (pred(pred(Y4!52)) = pred(n10)),
% 5.59/5.59 inference(monotonicity,[status(thm)],[5527])).
% 5.59/5.59 tff(5529,plain,
% 5.59/5.59 (pred(pred(Y4!52)) = n9),
% 5.59/5.59 inference(transitivity,[status(thm)],[5528, 21])).
% 5.59/5.59 tff(5530,plain,
% 5.59/5.59 (pred(pred(pred(Y4!52))) = pred(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5529])).
% 5.59/5.60 tff(5531,plain,
% 5.59/5.60 (pred(pred(pred(Y4!52))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5530, 20])).
% 5.59/5.60 tff(5532,plain,
% 5.59/5.60 (pred(pred(pred(pred(Y4!52)))) = pred(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5531])).
% 5.59/5.60 tff(5533,plain,
% 5.59/5.60 (pred(pred(pred(pred(Y4!52)))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5532, 19])).
% 5.59/5.60 tff(5534,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5533])).
% 5.59/5.60 tff(5535,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(Y4!52))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5534, 18])).
% 5.59/5.60 tff(5536,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5535])).
% 5.59/5.60 tff(5537,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5536, 17])).
% 5.59/5.60 tff(5538,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5537])).
% 5.59/5.60 tff(5539,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5538, 16])).
% 5.59/5.60 tff(5540,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5539])).
% 5.59/5.60 tff(5541,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5540, 15])).
% 5.59/5.60 tff(5542,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5541])).
% 5.59/5.60 tff(5543,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5542, 25])).
% 5.59/5.60 tff(5544,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5543])).
% 5.59/5.60 tff(5545,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5544, 24])).
% 5.59/5.60 tff(5546,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5545])).
% 5.59/5.60 tff(5547,plain,
% 5.59/5.60 (NPY4!22 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[578, 5546, 23])).
% 5.59/5.60 tff(5548,plain,
% 5.59/5.60 (succ(NPY4!22) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5547])).
% 5.59/5.60 tff(5549,plain,
% 5.59/5.60 (succ(NPY4!22) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5548, 58])).
% 5.59/5.60 tff(5550,plain,
% 5.59/5.60 (succ(Y4!52) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5525])).
% 5.59/5.60 tff(5551,plain,
% 5.59/5.60 (succ(Y4!52) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5550, 58])).
% 5.59/5.60 tff(5552,plain,
% 5.59/5.60 (succ(succ(Y4!52)) = succ(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5551])).
% 5.59/5.60 tff(5553,plain,
% 5.59/5.60 (succ(succ(Y4!52)) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5552, 36])).
% 5.59/5.60 tff(5554,plain,
% 5.59/5.60 (succ(succ(succ(Y4!52))) = succ(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5553])).
% 5.59/5.60 tff(5555,plain,
% 5.59/5.60 (succ(succ(succ(Y4!52))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5554, 48])).
% 5.59/5.60 tff(5556,plain,
% 5.59/5.60 (succ(succ(succ(succ(Y4!52)))) = succ(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5555])).
% 5.59/5.60 tff(5557,plain,
% 5.59/5.60 (succ(succ(succ(succ(Y4!52)))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5556, 14])).
% 5.59/5.60 tff(5558,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5557])).
% 5.59/5.60 tff(5559,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(Y4!52))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5558, 33])).
% 5.59/5.60 tff(5560,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5559])).
% 5.59/5.60 tff(5561,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5560, 30])).
% 5.59/5.60 tff(5562,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5561])).
% 5.59/5.60 tff(5563,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5562, 39])).
% 5.59/5.60 tff(5564,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5563])).
% 5.59/5.60 tff(5565,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5564, 53])).
% 5.59/5.60 tff(5566,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5565])).
% 5.59/5.60 tff(5567,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5566, 45])).
% 5.59/5.60 tff(5568,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5567])).
% 5.59/5.60 tff(5569,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5568, 28])).
% 5.59/5.60 tff(5570,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5569])).
% 5.59/5.60 tff(5571,plain,
% 5.59/5.60 (NSY4!20 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[601, 5570, 42])).
% 5.59/5.60 tff(5572,plain,
% 5.59/5.60 (pred(NSY4!20) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5571])).
% 5.59/5.60 tff(5573,plain,
% 5.59/5.60 (pred(NSY4!20) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5572, 22])).
% 5.59/5.60 tff(5574,plain,
% 5.59/5.60 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5573, 5549])).
% 5.59/5.60 tff(5575,plain,
% 5.59/5.60 (sum(pred(NSY4!20), succ(NPY4!22)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5574, 57])).
% 5.59/5.60 tff(5576,plain,
% 5.59/5.60 (sum(pred(Y3!54), succ(X3!55)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5419, 5501])).
% 5.59/5.60 tff(5577,plain,
% 5.59/5.60 (sum(pred(Y3!54), succ(X3!55)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5576, 57])).
% 5.59/5.60 tff(5578,plain,
% 5.59/5.60 (sum(pred(X3!55), succ(Y3!54)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5475, 5443])).
% 5.59/5.60 tff(5579,plain,
% 5.59/5.60 (sum(pred(X3!55), succ(Y3!54)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5578, 57])).
% 5.59/5.60 tff(5580,plain,
% 5.59/5.60 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n0, n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5579, 5577])).
% 5.59/5.60 tff(5581,plain,
% 5.59/5.60 (X4!53 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[438, 5580, 59])).
% 5.59/5.60 tff(5582,plain,
% 5.59/5.60 (pred(X4!53) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5581])).
% 5.59/5.60 tff(5583,plain,
% 5.59/5.60 (pred(X4!53) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5582, 22])).
% 5.59/5.60 tff(5584,plain,
% 5.59/5.60 (pred(pred(X4!53)) = pred(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5583])).
% 5.59/5.60 tff(5585,plain,
% 5.59/5.60 (pred(pred(X4!53)) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5584, 21])).
% 5.59/5.60 tff(5586,plain,
% 5.59/5.60 (pred(pred(pred(X4!53))) = pred(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5585])).
% 5.59/5.60 tff(5587,plain,
% 5.59/5.60 (pred(pred(pred(X4!53))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5586, 20])).
% 5.59/5.60 tff(5588,plain,
% 5.59/5.60 (pred(pred(pred(pred(X4!53)))) = pred(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5587])).
% 5.59/5.60 tff(5589,plain,
% 5.59/5.60 (pred(pred(pred(pred(X4!53)))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5588, 19])).
% 5.59/5.60 tff(5590,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(X4!53))))) = pred(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5589])).
% 5.59/5.60 tff(5591,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(X4!53))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5590, 18])).
% 5.59/5.60 tff(5592,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5591])).
% 5.59/5.60 tff(5593,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5592, 17])).
% 5.59/5.60 tff(5594,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5593])).
% 5.59/5.60 tff(5595,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5594, 16])).
% 5.59/5.60 tff(5596,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5595])).
% 5.59/5.60 tff(5597,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5596, 15])).
% 5.59/5.60 tff(5598,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5597])).
% 5.59/5.60 tff(5599,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5598, 25])).
% 5.59/5.60 tff(5600,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5599])).
% 5.59/5.60 tff(5601,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5600, 24])).
% 5.59/5.60 tff(5602,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5601])).
% 5.59/5.60 tff(5603,plain,
% 5.59/5.60 (NPX4!23 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[626, 5602, 23])).
% 5.59/5.60 tff(5604,plain,
% 5.59/5.60 (succ(NPX4!23) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5603])).
% 5.59/5.60 tff(5605,plain,
% 5.59/5.60 (succ(NPX4!23) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5604, 58])).
% 5.59/5.60 tff(5606,plain,
% 5.59/5.60 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n1, n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5605, 5575])).
% 5.59/5.60 tff(5607,plain,
% 5.59/5.60 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5606, 56])).
% 5.59/5.60 tff(5608,plain,
% 5.59/5.60 (succ(X4!53) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5581])).
% 5.59/5.60 tff(5609,plain,
% 5.59/5.60 (succ(X4!53) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5608, 58])).
% 5.59/5.60 tff(5610,plain,
% 5.59/5.60 (succ(succ(X4!53)) = succ(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5609])).
% 5.59/5.60 tff(5611,plain,
% 5.59/5.60 (succ(succ(X4!53)) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5610, 36])).
% 5.59/5.60 tff(5612,plain,
% 5.59/5.60 (succ(succ(succ(X4!53))) = succ(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5611])).
% 5.59/5.60 tff(5613,plain,
% 5.59/5.60 (succ(succ(succ(X4!53))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5612, 48])).
% 5.59/5.60 tff(5614,plain,
% 5.59/5.60 (succ(succ(succ(succ(X4!53)))) = succ(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5613])).
% 5.59/5.60 tff(5615,plain,
% 5.59/5.60 (succ(succ(succ(succ(X4!53)))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5614, 14])).
% 5.59/5.60 tff(5616,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(X4!53))))) = succ(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5615])).
% 5.59/5.60 tff(5617,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(X4!53))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5616, 33])).
% 5.59/5.60 tff(5618,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5617])).
% 5.59/5.60 tff(5619,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5618, 30])).
% 5.59/5.60 tff(5620,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5619])).
% 5.59/5.60 tff(5621,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5620, 39])).
% 5.59/5.60 tff(5622,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5621])).
% 5.59/5.60 tff(5623,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5622, 53])).
% 5.59/5.60 tff(5624,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5623])).
% 5.59/5.60 tff(5625,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5624, 45])).
% 5.59/5.60 tff(5626,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5625])).
% 5.59/5.60 tff(5627,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5626, 28])).
% 5.59/5.60 tff(5628,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5627])).
% 5.59/5.60 tff(5629,plain,
% 5.59/5.60 (NSX4!21 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[651, 5628, 42])).
% 5.59/5.60 tff(5630,plain,
% 5.59/5.60 (pred(NSX4!21) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5629])).
% 5.59/5.60 tff(5631,plain,
% 5.59/5.60 (pred(NSX4!21) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5630, 22])).
% 5.59/5.60 tff(5632,plain,
% 5.59/5.60 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5631, 5607])).
% 5.59/5.60 tff(5633,plain,
% 5.59/5.60 (Y5!50 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[656, 5632, 57])).
% 5.59/5.60 tff(5634,plain,
% 5.59/5.60 (pred(Y5!50) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5633])).
% 5.59/5.60 tff(5635,plain,
% 5.59/5.60 (pred(Y5!50) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5634, 22])).
% 5.59/5.60 tff(5636,plain,
% 5.59/5.60 (pred(pred(Y5!50)) = pred(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5635])).
% 5.59/5.60 tff(5637,plain,
% 5.59/5.60 (pred(pred(Y5!50)) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5636, 21])).
% 5.59/5.60 tff(5638,plain,
% 5.59/5.60 (pred(pred(pred(Y5!50))) = pred(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5637])).
% 5.59/5.60 tff(5639,plain,
% 5.59/5.60 (pred(pred(pred(Y5!50))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5638, 20])).
% 5.59/5.60 tff(5640,plain,
% 5.59/5.60 (pred(pred(pred(pred(Y5!50)))) = pred(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5639])).
% 5.59/5.60 tff(5641,plain,
% 5.59/5.60 (pred(pred(pred(pred(Y5!50)))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5640, 19])).
% 5.59/5.60 tff(5642,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5641])).
% 5.59/5.60 tff(5643,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(Y5!50))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5642, 18])).
% 5.59/5.60 tff(5644,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5643])).
% 5.59/5.60 tff(5645,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5644, 17])).
% 5.59/5.60 tff(5646,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5645])).
% 5.59/5.60 tff(5647,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5646, 16])).
% 5.59/5.60 tff(5648,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5647])).
% 5.59/5.60 tff(5649,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5648, 15])).
% 5.59/5.60 tff(5650,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5649])).
% 5.59/5.60 tff(5651,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5650, 25])).
% 5.59/5.60 tff(5652,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5651])).
% 5.59/5.60 tff(5653,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5652, 24])).
% 5.59/5.60 tff(5654,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5653])).
% 5.59/5.60 tff(5655,plain,
% 5.59/5.60 (NPY5!18 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[694, 5654, 23])).
% 5.59/5.60 tff(5656,plain,
% 5.59/5.60 (succ(NPY5!18) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5655])).
% 5.59/5.60 tff(5657,plain,
% 5.59/5.60 (succ(NPY5!18) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5656, 58])).
% 5.59/5.60 tff(5658,plain,
% 5.59/5.60 (succ(Y5!50) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5633])).
% 5.59/5.60 tff(5659,plain,
% 5.59/5.60 (succ(Y5!50) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5658, 58])).
% 5.59/5.60 tff(5660,plain,
% 5.59/5.60 (succ(succ(Y5!50)) = succ(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5659])).
% 5.59/5.60 tff(5661,plain,
% 5.59/5.60 (succ(succ(Y5!50)) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5660, 36])).
% 5.59/5.60 tff(5662,plain,
% 5.59/5.60 (succ(succ(succ(Y5!50))) = succ(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5661])).
% 5.59/5.60 tff(5663,plain,
% 5.59/5.60 (succ(succ(succ(Y5!50))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5662, 48])).
% 5.59/5.60 tff(5664,plain,
% 5.59/5.60 (succ(succ(succ(succ(Y5!50)))) = succ(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5663])).
% 5.59/5.60 tff(5665,plain,
% 5.59/5.60 (succ(succ(succ(succ(Y5!50)))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5664, 14])).
% 5.59/5.60 tff(5666,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5665])).
% 5.59/5.60 tff(5667,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(Y5!50))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5666, 33])).
% 5.59/5.60 tff(5668,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5667])).
% 5.59/5.60 tff(5669,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5668, 30])).
% 5.59/5.60 tff(5670,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5669])).
% 5.59/5.60 tff(5671,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5670, 39])).
% 5.59/5.60 tff(5672,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5671])).
% 5.59/5.60 tff(5673,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5672, 53])).
% 5.59/5.60 tff(5674,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5673])).
% 5.59/5.60 tff(5675,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5674, 45])).
% 5.59/5.60 tff(5676,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5675])).
% 5.59/5.60 tff(5677,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5676, 28])).
% 5.59/5.60 tff(5678,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5677])).
% 5.59/5.60 tff(5679,plain,
% 5.59/5.60 (NSY5!16 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[717, 5678, 42])).
% 5.59/5.60 tff(5680,plain,
% 5.59/5.60 (pred(NSY5!16) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5679])).
% 5.59/5.60 tff(5681,plain,
% 5.59/5.60 (pred(NSY5!16) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5680, 22])).
% 5.59/5.60 tff(5682,plain,
% 5.59/5.60 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5681, 5657])).
% 5.59/5.60 tff(5683,plain,
% 5.59/5.60 (sum(pred(NSY5!16), succ(NPY5!18)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5682, 57])).
% 5.59/5.60 tff(5684,plain,
% 5.59/5.60 (sum(pred(Y4!52), succ(X4!53)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5527, 5609])).
% 5.59/5.60 tff(5685,plain,
% 5.59/5.60 (sum(pred(Y4!52), succ(X4!53)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5684, 57])).
% 5.59/5.60 tff(5686,plain,
% 5.59/5.60 (sum(pred(X4!53), succ(Y4!52)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5583, 5551])).
% 5.59/5.60 tff(5687,plain,
% 5.59/5.60 (sum(pred(X4!53), succ(Y4!52)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5686, 57])).
% 5.59/5.60 tff(5688,plain,
% 5.59/5.60 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n0, n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5687, 5685])).
% 5.59/5.60 tff(5689,plain,
% 5.59/5.60 (X5!51 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[553, 5688, 59])).
% 5.59/5.60 tff(5690,plain,
% 5.59/5.60 (pred(X5!51) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5689])).
% 5.59/5.60 tff(5691,plain,
% 5.59/5.60 (pred(X5!51) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5690, 22])).
% 5.59/5.60 tff(5692,plain,
% 5.59/5.60 (pred(pred(X5!51)) = pred(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5691])).
% 5.59/5.60 tff(5693,plain,
% 5.59/5.60 (pred(pred(X5!51)) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5692, 21])).
% 5.59/5.60 tff(5694,plain,
% 5.59/5.60 (pred(pred(pred(X5!51))) = pred(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5693])).
% 5.59/5.60 tff(5695,plain,
% 5.59/5.60 (pred(pred(pred(X5!51))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5694, 20])).
% 5.59/5.60 tff(5696,plain,
% 5.59/5.60 (pred(pred(pred(pred(X5!51)))) = pred(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5695])).
% 5.59/5.60 tff(5697,plain,
% 5.59/5.60 (pred(pred(pred(pred(X5!51)))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5696, 19])).
% 5.59/5.60 tff(5698,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(X5!51))))) = pred(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5697])).
% 5.59/5.60 tff(5699,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(X5!51))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5698, 18])).
% 5.59/5.60 tff(5700,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5699])).
% 5.59/5.60 tff(5701,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5700, 17])).
% 5.59/5.60 tff(5702,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5701])).
% 5.59/5.60 tff(5703,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5702, 16])).
% 5.59/5.60 tff(5704,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5703])).
% 5.59/5.60 tff(5705,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5704, 15])).
% 5.59/5.60 tff(5706,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5705])).
% 5.59/5.60 tff(5707,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5706, 25])).
% 5.59/5.60 tff(5708,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5707])).
% 5.59/5.60 tff(5709,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5708, 24])).
% 5.59/5.60 tff(5710,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5709])).
% 5.59/5.60 tff(5711,plain,
% 5.59/5.60 (NPX5!19 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[742, 5710, 23])).
% 5.59/5.60 tff(5712,plain,
% 5.59/5.60 (succ(NPX5!19) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5711])).
% 5.59/5.60 tff(5713,plain,
% 5.59/5.60 (succ(NPX5!19) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5712, 58])).
% 5.59/5.60 tff(5714,plain,
% 5.59/5.60 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n1, n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5713, 5683])).
% 5.59/5.60 tff(5715,plain,
% 5.59/5.60 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5714, 56])).
% 5.59/5.60 tff(5716,plain,
% 5.59/5.60 (succ(X5!51) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5689])).
% 5.59/5.60 tff(5717,plain,
% 5.59/5.60 (succ(X5!51) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5716, 58])).
% 5.59/5.60 tff(5718,plain,
% 5.59/5.60 (succ(succ(X5!51)) = succ(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5717])).
% 5.59/5.60 tff(5719,plain,
% 5.59/5.60 (succ(succ(X5!51)) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5718, 36])).
% 5.59/5.60 tff(5720,plain,
% 5.59/5.60 (succ(succ(succ(X5!51))) = succ(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5719])).
% 5.59/5.60 tff(5721,plain,
% 5.59/5.60 (succ(succ(succ(X5!51))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5720, 48])).
% 5.59/5.60 tff(5722,plain,
% 5.59/5.60 (succ(succ(succ(succ(X5!51)))) = succ(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5721])).
% 5.59/5.60 tff(5723,plain,
% 5.59/5.60 (succ(succ(succ(succ(X5!51)))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5722, 14])).
% 5.59/5.60 tff(5724,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(X5!51))))) = succ(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5723])).
% 5.59/5.60 tff(5725,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(X5!51))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5724, 33])).
% 5.59/5.60 tff(5726,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5725])).
% 5.59/5.60 tff(5727,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5726, 30])).
% 5.59/5.60 tff(5728,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5727])).
% 5.59/5.60 tff(5729,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5728, 39])).
% 5.59/5.60 tff(5730,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5729])).
% 5.59/5.60 tff(5731,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5730, 53])).
% 5.59/5.60 tff(5732,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5731])).
% 5.59/5.60 tff(5733,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5732, 45])).
% 5.59/5.60 tff(5734,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5733])).
% 5.59/5.60 tff(5735,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5734, 28])).
% 5.59/5.60 tff(5736,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5735])).
% 5.59/5.60 tff(5737,plain,
% 5.59/5.60 (NSX5!17 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[767, 5736, 42])).
% 5.59/5.60 tff(5738,plain,
% 5.59/5.60 (pred(NSX5!17) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5737])).
% 5.59/5.60 tff(5739,plain,
% 5.59/5.60 (pred(NSX5!17) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5738, 22])).
% 5.59/5.60 tff(5740,plain,
% 5.59/5.60 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5739, 5715])).
% 5.59/5.60 tff(5741,plain,
% 5.59/5.60 (Y6!48 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[772, 5740, 57])).
% 5.59/5.60 tff(5742,plain,
% 5.59/5.60 (pred(Y6!48) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5741])).
% 5.59/5.60 tff(5743,plain,
% 5.59/5.60 (pred(Y6!48) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5742, 22])).
% 5.59/5.60 tff(5744,plain,
% 5.59/5.60 (pred(pred(Y6!48)) = pred(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5743])).
% 5.59/5.60 tff(5745,plain,
% 5.59/5.60 (pred(pred(Y6!48)) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5744, 21])).
% 5.59/5.60 tff(5746,plain,
% 5.59/5.60 (pred(pred(pred(Y6!48))) = pred(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5745])).
% 5.59/5.60 tff(5747,plain,
% 5.59/5.60 (pred(pred(pred(Y6!48))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5746, 20])).
% 5.59/5.60 tff(5748,plain,
% 5.59/5.60 (pred(pred(pred(pred(Y6!48)))) = pred(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5747])).
% 5.59/5.60 tff(5749,plain,
% 5.59/5.60 (pred(pred(pred(pred(Y6!48)))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5748, 19])).
% 5.59/5.60 tff(5750,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5749])).
% 5.59/5.60 tff(5751,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(Y6!48))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5750, 18])).
% 5.59/5.60 tff(5752,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5751])).
% 5.59/5.60 tff(5753,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5752, 17])).
% 5.59/5.60 tff(5754,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5753])).
% 5.59/5.60 tff(5755,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5754, 16])).
% 5.59/5.60 tff(5756,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5755])).
% 5.59/5.60 tff(5757,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5756, 15])).
% 5.59/5.60 tff(5758,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5757])).
% 5.59/5.60 tff(5759,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5758, 25])).
% 5.59/5.60 tff(5760,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5759])).
% 5.59/5.60 tff(5761,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5760, 24])).
% 5.59/5.60 tff(5762,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5761])).
% 5.59/5.60 tff(5763,plain,
% 5.59/5.60 (NPY6!14 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[1465, 5762, 23])).
% 5.59/5.60 tff(5764,plain,
% 5.59/5.60 (succ(NPY6!14) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5763])).
% 5.59/5.60 tff(5765,plain,
% 5.59/5.60 (succ(NPY6!14) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5764, 58])).
% 5.59/5.60 tff(5766,plain,
% 5.59/5.60 (succ(Y6!48) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5741])).
% 5.59/5.60 tff(5767,plain,
% 5.59/5.60 (succ(Y6!48) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5766, 58])).
% 5.59/5.60 tff(5768,plain,
% 5.59/5.60 (succ(succ(Y6!48)) = succ(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5767])).
% 5.59/5.60 tff(5769,plain,
% 5.59/5.60 (succ(succ(Y6!48)) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5768, 36])).
% 5.59/5.60 tff(5770,plain,
% 5.59/5.60 (succ(succ(succ(Y6!48))) = succ(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5769])).
% 5.59/5.60 tff(5771,plain,
% 5.59/5.60 (succ(succ(succ(Y6!48))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5770, 48])).
% 5.59/5.60 tff(5772,plain,
% 5.59/5.60 (succ(succ(succ(succ(Y6!48)))) = succ(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5771])).
% 5.59/5.60 tff(5773,plain,
% 5.59/5.60 (succ(succ(succ(succ(Y6!48)))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5772, 14])).
% 5.59/5.60 tff(5774,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5773])).
% 5.59/5.60 tff(5775,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(Y6!48))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5774, 33])).
% 5.59/5.60 tff(5776,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5775])).
% 5.59/5.60 tff(5777,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5776, 30])).
% 5.59/5.60 tff(5778,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5777])).
% 5.59/5.60 tff(5779,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5778, 39])).
% 5.59/5.60 tff(5780,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5779])).
% 5.59/5.60 tff(5781,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5780, 53])).
% 5.59/5.60 tff(5782,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5781])).
% 5.59/5.60 tff(5783,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5782, 45])).
% 5.59/5.60 tff(5784,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5783])).
% 5.59/5.60 tff(5785,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5784, 28])).
% 5.59/5.60 tff(5786,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5785])).
% 5.59/5.60 tff(5787,plain,
% 5.59/5.60 (NSY6!12 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[1490, 5786, 42])).
% 5.59/5.60 tff(5788,plain,
% 5.59/5.60 (pred(NSY6!12) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5787])).
% 5.59/5.60 tff(5789,plain,
% 5.59/5.60 (pred(NSY6!12) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5788, 22])).
% 5.59/5.60 tff(5790,plain,
% 5.59/5.60 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5789, 5765])).
% 5.59/5.60 tff(5791,plain,
% 5.59/5.60 (sum(pred(NSY6!12), succ(NPY6!14)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5790, 57])).
% 5.59/5.60 tff(5792,plain,
% 5.59/5.60 (sum(pred(Y5!50), succ(X5!51)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5635, 5717])).
% 5.59/5.60 tff(5793,plain,
% 5.59/5.60 (sum(pred(Y5!50), succ(X5!51)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5792, 57])).
% 5.59/5.60 tff(5794,plain,
% 5.59/5.60 (sum(pred(X5!51), succ(Y5!50)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5691, 5659])).
% 5.59/5.60 tff(5795,plain,
% 5.59/5.60 (sum(pred(X5!51), succ(Y5!50)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5794, 57])).
% 5.59/5.60 tff(5796,plain,
% 5.59/5.60 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n0, n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5795, 5793])).
% 5.59/5.60 tff(5797,plain,
% 5.59/5.60 (X6!49 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[669, 5796, 59])).
% 5.59/5.60 tff(5798,plain,
% 5.59/5.60 (pred(X6!49) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5797])).
% 5.59/5.60 tff(5799,plain,
% 5.59/5.60 (pred(X6!49) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5798, 22])).
% 5.59/5.60 tff(5800,plain,
% 5.59/5.60 (pred(pred(X6!49)) = pred(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5799])).
% 5.59/5.60 tff(5801,plain,
% 5.59/5.60 (pred(pred(X6!49)) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5800, 21])).
% 5.59/5.60 tff(5802,plain,
% 5.59/5.60 (pred(pred(pred(X6!49))) = pred(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5801])).
% 5.59/5.60 tff(5803,plain,
% 5.59/5.60 (pred(pred(pred(X6!49))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5802, 20])).
% 5.59/5.60 tff(5804,plain,
% 5.59/5.60 (pred(pred(pred(pred(X6!49)))) = pred(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5803])).
% 5.59/5.60 tff(5805,plain,
% 5.59/5.60 (pred(pred(pred(pred(X6!49)))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5804, 19])).
% 5.59/5.60 tff(5806,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(X6!49))))) = pred(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5805])).
% 5.59/5.60 tff(5807,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(X6!49))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5806, 18])).
% 5.59/5.60 tff(5808,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5807])).
% 5.59/5.60 tff(5809,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5808, 17])).
% 5.59/5.60 tff(5810,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5809])).
% 5.59/5.60 tff(5811,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5810, 16])).
% 5.59/5.60 tff(5812,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5811])).
% 5.59/5.60 tff(5813,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5812, 15])).
% 5.59/5.60 tff(5814,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5813])).
% 5.59/5.60 tff(5815,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5814, 25])).
% 5.59/5.60 tff(5816,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5815])).
% 5.59/5.60 tff(5817,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5816, 24])).
% 5.59/5.60 tff(5818,plain,
% 5.59/5.60 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5817])).
% 5.59/5.60 tff(5819,plain,
% 5.59/5.60 (NPX6!15 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[1523, 5818, 23])).
% 5.59/5.60 tff(5820,plain,
% 5.59/5.60 (succ(NPX6!15) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5819])).
% 5.59/5.60 tff(5821,plain,
% 5.59/5.60 (succ(NPX6!15) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5820, 58])).
% 5.59/5.60 tff(5822,plain,
% 5.59/5.60 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n1, n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5821, 5791])).
% 5.59/5.60 tff(5823,plain,
% 5.59/5.60 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5822, 56])).
% 5.59/5.60 tff(5824,plain,
% 5.59/5.60 (succ(X6!49) = succ(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5797])).
% 5.59/5.60 tff(5825,plain,
% 5.59/5.60 (succ(X6!49) = n1),
% 5.59/5.60 inference(transitivity,[status(thm)],[5824, 58])).
% 5.59/5.60 tff(5826,plain,
% 5.59/5.60 (succ(succ(X6!49)) = succ(n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5825])).
% 5.59/5.60 tff(5827,plain,
% 5.59/5.60 (succ(succ(X6!49)) = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[5826, 36])).
% 5.59/5.60 tff(5828,plain,
% 5.59/5.60 (succ(succ(succ(X6!49))) = succ(n2)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5827])).
% 5.59/5.60 tff(5829,plain,
% 5.59/5.60 (succ(succ(succ(X6!49))) = n3),
% 5.59/5.60 inference(transitivity,[status(thm)],[5828, 48])).
% 5.59/5.60 tff(5830,plain,
% 5.59/5.60 (succ(succ(succ(succ(X6!49)))) = succ(n3)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5829])).
% 5.59/5.60 tff(5831,plain,
% 5.59/5.60 (succ(succ(succ(succ(X6!49)))) = n4),
% 5.59/5.60 inference(transitivity,[status(thm)],[5830, 14])).
% 5.59/5.60 tff(5832,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(X6!49))))) = succ(n4)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5831])).
% 5.59/5.60 tff(5833,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(X6!49))))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5832, 33])).
% 5.59/5.60 tff(5834,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5833])).
% 5.59/5.60 tff(5835,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n6),
% 5.59/5.60 inference(transitivity,[status(thm)],[5834, 30])).
% 5.59/5.60 tff(5836,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5835])).
% 5.59/5.60 tff(5837,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n7),
% 5.59/5.60 inference(transitivity,[status(thm)],[5836, 39])).
% 5.59/5.60 tff(5838,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n7)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5837])).
% 5.59/5.60 tff(5839,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n8),
% 5.59/5.60 inference(transitivity,[status(thm)],[5838, 53])).
% 5.59/5.60 tff(5840,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n8)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5839])).
% 5.59/5.60 tff(5841,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n9),
% 5.59/5.60 inference(transitivity,[status(thm)],[5840, 45])).
% 5.59/5.60 tff(5842,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n9)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5841])).
% 5.59/5.60 tff(5843,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5842, 28])).
% 5.59/5.60 tff(5844,plain,
% 5.59/5.60 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n10)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5843])).
% 5.59/5.60 tff(5845,plain,
% 5.59/5.60 (NSX6!13 = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[1550, 5844, 42])).
% 5.59/5.60 tff(5846,plain,
% 5.59/5.60 (pred(NSX6!13) = pred(n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5845])).
% 5.59/5.60 tff(5847,plain,
% 5.59/5.60 (pred(NSX6!13) = n10),
% 5.59/5.60 inference(transitivity,[status(thm)],[5846, 22])).
% 5.59/5.60 tff(5848,plain,
% 5.59/5.60 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5847, 5823])).
% 5.59/5.60 tff(5849,plain,
% 5.59/5.60 (sum(n10, n1) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.59/5.60 inference(symmetry,[status(thm)],[5848])).
% 5.59/5.60 tff(5850,plain,
% 5.59/5.60 (n0 = sum(n10, n1)),
% 5.59/5.60 inference(symmetry,[status(thm)],[57])).
% 5.59/5.60 tff(5851,plain,
% 5.59/5.60 (sum(pred(Y6!48), succ(X6!49)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5743, 5825])).
% 5.59/5.60 tff(5852,plain,
% 5.59/5.60 (sum(pred(Y6!48), succ(X6!49)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5851, 57])).
% 5.59/5.60 tff(5853,plain,
% 5.59/5.60 (sum(pred(X6!49), succ(Y6!48)) = sum(n10, n1)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5799, 5767])).
% 5.59/5.60 tff(5854,plain,
% 5.59/5.60 (sum(pred(X6!49), succ(Y6!48)) = n0),
% 5.59/5.60 inference(transitivity,[status(thm)],[5853, 57])).
% 5.59/5.60 tff(5855,plain,
% 5.59/5.60 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n0, n0)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[5854, 5852])).
% 5.59/5.60 tff(5856,plain,
% 5.59/5.60 (X7!47 = Y7!46),
% 5.59/5.60 inference(transitivity,[status(thm)],[785, 5855, 59, 5850, 5849, 794])).
% 5.59/5.60 tff(5857,plain,
% 5.59/5.60 ($false),
% 5.59/5.60 inference(unit_resolution,[status(thm)],[792, 5856])).
% 5.59/5.60 tff(5858,plain,((~(X0!61 = n8)) | (X7!47 = Y7!46) | (~(Y0!60 = n3))), inference(lemma,lemma(discharge,[]))).
% 5.59/5.60 tff(5859,plain,
% 5.59/5.60 (~(X0!61 = n8)),
% 5.59/5.60 inference(unit_resolution,[status(thm)],[5858, 80, 792])).
% 5.59/5.60 tff(5860,plain,
% 5.59/5.60 (sum(n8, n5) = n2),
% 5.59/5.60 inference(and_elim,[status(thm)],[9])).
% 5.59/5.60 tff(5861,plain,
% 5.59/5.60 (sum(n10, n6) = n5),
% 5.59/5.60 inference(and_elim,[status(thm)],[9])).
% 5.59/5.60 tff(5862,plain,
% 5.59/5.60 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n10, n6)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[2362, 146])).
% 5.59/5.60 tff(5863,plain,
% 5.59/5.60 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n5),
% 5.59/5.60 inference(transitivity,[status(thm)],[5862, 5861])).
% 5.59/5.60 tff(5864,plain,
% 5.59/5.60 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n8, n5)),
% 5.59/5.60 inference(monotonicity,[status(thm)],[2388, 5863])).
% 5.59/5.60 tff(5865,plain,
% 5.59/5.60 (Y1!58 = n2),
% 5.59/5.60 inference(transitivity,[status(thm)],[196, 5864, 5860])).
% 5.59/5.61 tff(5866,plain,
% 5.59/5.61 (pred(Y1!58) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5865])).
% 5.59/5.61 tff(5867,plain,
% 5.59/5.61 (pred(Y1!58) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5866, 24])).
% 5.59/5.61 tff(5868,plain,
% 5.59/5.61 (pred(pred(Y1!58)) = pred(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5867])).
% 5.59/5.61 tff(5869,plain,
% 5.59/5.61 (pred(pred(Y1!58)) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[5868, 23])).
% 5.59/5.61 tff(5870,plain,
% 5.59/5.61 (pred(pred(pred(Y1!58))) = pred(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5869])).
% 5.59/5.61 tff(5871,plain,
% 5.59/5.61 (pred(pred(pred(Y1!58))) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[5870, 22])).
% 5.59/5.61 tff(5872,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y1!58)))) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5871])).
% 5.59/5.61 tff(5873,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y1!58)))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[5872, 21])).
% 5.59/5.61 tff(5874,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5873])).
% 5.59/5.61 tff(5875,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y1!58))))) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[5874, 20])).
% 5.59/5.61 tff(5876,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5875])).
% 5.59/5.61 tff(5877,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[5876, 19])).
% 5.59/5.61 tff(5878,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5877])).
% 5.59/5.61 tff(5879,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[5878, 18])).
% 5.59/5.61 tff(5880,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5879])).
% 5.59/5.61 tff(5881,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[5880, 17])).
% 5.59/5.61 tff(5882,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5881])).
% 5.59/5.61 tff(5883,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[5882, 16])).
% 5.59/5.61 tff(5884,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5883])).
% 5.59/5.61 tff(5885,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[5884, 15])).
% 5.59/5.61 tff(5886,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5885])).
% 5.59/5.61 tff(5887,plain,
% 5.59/5.61 (NPY1!34 = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[232, 5886, 25])).
% 5.59/5.61 tff(5888,plain,
% 5.59/5.61 (succ(NPY1!34) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5887])).
% 5.59/5.61 tff(5889,plain,
% 5.59/5.61 (succ(NPY1!34) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[5888, 48])).
% 5.59/5.61 tff(5890,plain,
% 5.59/5.61 (succ(Y1!58) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5865])).
% 5.59/5.61 tff(5891,plain,
% 5.59/5.61 (succ(Y1!58) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[5890, 48])).
% 5.59/5.61 tff(5892,plain,
% 5.59/5.61 (succ(succ(Y1!58)) = succ(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5891])).
% 5.59/5.61 tff(5893,plain,
% 5.59/5.61 (succ(succ(Y1!58)) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[5892, 14])).
% 5.59/5.61 tff(5894,plain,
% 5.59/5.61 (succ(succ(succ(Y1!58))) = succ(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5893])).
% 5.59/5.61 tff(5895,plain,
% 5.59/5.61 (succ(succ(succ(Y1!58))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[5894, 33])).
% 5.59/5.61 tff(5896,plain,
% 5.59/5.61 (succ(succ(succ(succ(Y1!58)))) = succ(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5895])).
% 5.59/5.61 tff(5897,plain,
% 5.59/5.61 (succ(succ(succ(succ(Y1!58)))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[5896, 30])).
% 5.59/5.61 tff(5898,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5897])).
% 5.59/5.61 tff(5899,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(Y1!58))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[5898, 39])).
% 5.59/5.61 tff(5900,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5899])).
% 5.59/5.61 tff(5901,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[5900, 53])).
% 5.59/5.61 tff(5902,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5901])).
% 5.59/5.61 tff(5903,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[5902, 45])).
% 5.59/5.61 tff(5904,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5903])).
% 5.59/5.61 tff(5905,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[5904, 28])).
% 5.59/5.61 tff(5906,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5905])).
% 5.59/5.61 tff(5907,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[5906, 42])).
% 5.59/5.61 tff(5908,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5907])).
% 5.59/5.61 tff(5909,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5908, 58])).
% 5.59/5.61 tff(5910,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5909])).
% 5.59/5.61 tff(5911,plain,
% 5.59/5.61 (NSY1!32 = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[255, 5910, 36])).
% 5.59/5.61 tff(5912,plain,
% 5.59/5.61 (pred(NSY1!32) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5911])).
% 5.59/5.61 tff(5913,plain,
% 5.59/5.61 (pred(NSY1!32) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5912, 24])).
% 5.59/5.61 tff(5914,plain,
% 5.59/5.61 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n1, n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5913, 5889])).
% 5.59/5.61 tff(5915,plain,
% 5.59/5.61 (sum(pred(NSY1!32), succ(NPY1!34)) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[5914, 47])).
% 5.59/5.61 tff(5916,plain,
% 5.59/5.61 (sum(pred(Y0!60), succ(X0!61)) = sum(n2, n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[82, 2366])).
% 5.59/5.61 tff(5917,plain,
% 5.59/5.61 (sum(pred(Y0!60), succ(X0!61)) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5916, 327])).
% 5.59/5.61 tff(5918,plain,
% 5.59/5.61 (sum(n8, n4) = n1),
% 5.59/5.61 inference(and_elim,[status(thm)],[9])).
% 5.59/5.61 tff(5919,plain,
% 5.59/5.61 (sum(pred(X0!61), succ(Y0!60)) = sum(n8, n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[2340, 87])).
% 5.59/5.61 tff(5920,plain,
% 5.59/5.61 (sum(pred(X0!61), succ(Y0!60)) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5919, 5918])).
% 5.59/5.61 tff(5921,plain,
% 5.59/5.61 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n1, n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5920, 5917])).
% 5.59/5.61 tff(5922,plain,
% 5.59/5.61 (X1!59 = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[93, 5921, 49])).
% 5.59/5.61 tff(5923,plain,
% 5.59/5.61 (pred(X1!59) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5922])).
% 5.59/5.61 tff(5924,plain,
% 5.59/5.61 (pred(X1!59) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5923, 24])).
% 5.59/5.61 tff(5925,plain,
% 5.59/5.61 (pred(pred(X1!59)) = pred(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5924])).
% 5.59/5.61 tff(5926,plain,
% 5.59/5.61 (pred(pred(X1!59)) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[5925, 23])).
% 5.59/5.61 tff(5927,plain,
% 5.59/5.61 (pred(pred(pred(X1!59))) = pred(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5926])).
% 5.59/5.61 tff(5928,plain,
% 5.59/5.61 (pred(pred(pred(X1!59))) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[5927, 22])).
% 5.59/5.61 tff(5929,plain,
% 5.59/5.61 (pred(pred(pred(pred(X1!59)))) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5928])).
% 5.59/5.61 tff(5930,plain,
% 5.59/5.61 (pred(pred(pred(pred(X1!59)))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[5929, 21])).
% 5.59/5.61 tff(5931,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(X1!59))))) = pred(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5930])).
% 5.59/5.61 tff(5932,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(X1!59))))) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[5931, 20])).
% 5.59/5.61 tff(5933,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5932])).
% 5.59/5.61 tff(5934,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[5933, 19])).
% 5.59/5.61 tff(5935,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5934])).
% 5.59/5.61 tff(5936,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[5935, 18])).
% 5.59/5.61 tff(5937,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5936])).
% 5.59/5.61 tff(5938,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[5937, 17])).
% 5.59/5.61 tff(5939,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5938])).
% 5.59/5.61 tff(5940,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[5939, 16])).
% 5.59/5.61 tff(5941,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5940])).
% 5.59/5.61 tff(5942,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[5941, 15])).
% 5.59/5.61 tff(5943,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5942])).
% 5.59/5.61 tff(5944,plain,
% 5.59/5.61 (NPX1!35 = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[280, 5943, 25])).
% 5.59/5.61 tff(5945,plain,
% 5.59/5.61 (succ(NPX1!35) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5944])).
% 5.59/5.61 tff(5946,plain,
% 5.59/5.61 (succ(NPX1!35) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[5945, 48])).
% 5.59/5.61 tff(5947,plain,
% 5.59/5.61 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n3, n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5946, 5915])).
% 5.59/5.61 tff(5948,plain,
% 5.59/5.61 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[5947, 786])).
% 5.59/5.61 tff(5949,plain,
% 5.59/5.61 (succ(X1!59) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5922])).
% 5.59/5.61 tff(5950,plain,
% 5.59/5.61 (succ(X1!59) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[5949, 48])).
% 5.59/5.61 tff(5951,plain,
% 5.59/5.61 (succ(succ(X1!59)) = succ(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5950])).
% 5.59/5.61 tff(5952,plain,
% 5.59/5.61 (succ(succ(X1!59)) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[5951, 14])).
% 5.59/5.61 tff(5953,plain,
% 5.59/5.61 (succ(succ(succ(X1!59))) = succ(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5952])).
% 5.59/5.61 tff(5954,plain,
% 5.59/5.61 (succ(succ(succ(X1!59))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[5953, 33])).
% 5.59/5.61 tff(5955,plain,
% 5.59/5.61 (succ(succ(succ(succ(X1!59)))) = succ(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5954])).
% 5.59/5.61 tff(5956,plain,
% 5.59/5.61 (succ(succ(succ(succ(X1!59)))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[5955, 30])).
% 5.59/5.61 tff(5957,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(X1!59))))) = succ(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5956])).
% 5.59/5.61 tff(5958,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(X1!59))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[5957, 39])).
% 5.59/5.61 tff(5959,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5958])).
% 5.59/5.61 tff(5960,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[5959, 53])).
% 5.59/5.61 tff(5961,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5960])).
% 5.59/5.61 tff(5962,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[5961, 45])).
% 5.59/5.61 tff(5963,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5962])).
% 5.59/5.61 tff(5964,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[5963, 28])).
% 5.59/5.61 tff(5965,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5964])).
% 5.59/5.61 tff(5966,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[5965, 42])).
% 5.59/5.61 tff(5967,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5966])).
% 5.59/5.61 tff(5968,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5967, 58])).
% 5.59/5.61 tff(5969,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5968])).
% 5.59/5.61 tff(5970,plain,
% 5.59/5.61 (NSX1!33 = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[305, 5969, 36])).
% 5.59/5.61 tff(5971,plain,
% 5.59/5.61 (pred(NSX1!33) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5970])).
% 5.59/5.61 tff(5972,plain,
% 5.59/5.61 (pred(NSX1!33) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5971, 24])).
% 5.59/5.61 tff(5973,plain,
% 5.59/5.61 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n1, n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5972, 5948])).
% 5.59/5.61 tff(5974,plain,
% 5.59/5.61 (Y2!56 = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[310, 5973, 791])).
% 5.59/5.61 tff(5975,plain,
% 5.59/5.61 (pred(Y2!56) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5974])).
% 5.59/5.61 tff(5976,plain,
% 5.59/5.61 (pred(Y2!56) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[5975, 19])).
% 5.59/5.61 tff(5977,plain,
% 5.59/5.61 (pred(pred(Y2!56)) = pred(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5976])).
% 5.59/5.61 tff(5978,plain,
% 5.59/5.61 (pred(pred(Y2!56)) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[5977, 18])).
% 5.59/5.61 tff(5979,plain,
% 5.59/5.61 (pred(pred(pred(Y2!56))) = pred(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5978])).
% 5.59/5.61 tff(5980,plain,
% 5.59/5.61 (pred(pred(pred(Y2!56))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[5979, 17])).
% 5.59/5.61 tff(5981,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y2!56)))) = pred(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5980])).
% 5.59/5.61 tff(5982,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y2!56)))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[5981, 16])).
% 5.59/5.61 tff(5983,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5982])).
% 5.59/5.61 tff(5984,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y2!56))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[5983, 15])).
% 5.59/5.61 tff(5985,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5984])).
% 5.59/5.61 tff(5986,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[5985, 25])).
% 5.59/5.61 tff(5987,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5986])).
% 5.59/5.61 tff(5988,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[5987, 24])).
% 5.59/5.61 tff(5989,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5988])).
% 5.59/5.61 tff(5990,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[5989, 23])).
% 5.59/5.61 tff(5991,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5990])).
% 5.59/5.61 tff(5992,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[5991, 22])).
% 5.59/5.61 tff(5993,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5992])).
% 5.59/5.61 tff(5994,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[5993, 21])).
% 5.59/5.61 tff(5995,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5994])).
% 5.59/5.61 tff(5996,plain,
% 5.59/5.61 (NPY2!30 = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[347, 5995, 20])).
% 5.59/5.61 tff(5997,plain,
% 5.59/5.61 (succ(NPY2!30) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5996])).
% 5.59/5.61 tff(5998,plain,
% 5.59/5.61 (succ(NPY2!30) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[5997, 45])).
% 5.59/5.61 tff(5999,plain,
% 5.59/5.61 (succ(Y2!56) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5974])).
% 5.59/5.61 tff(6000,plain,
% 5.59/5.61 (succ(Y2!56) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[5999, 45])).
% 5.59/5.61 tff(6001,plain,
% 5.59/5.61 (succ(succ(Y2!56)) = succ(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6000])).
% 5.59/5.61 tff(6002,plain,
% 5.59/5.61 (succ(succ(Y2!56)) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[6001, 28])).
% 5.59/5.61 tff(6003,plain,
% 5.59/5.61 (succ(succ(succ(Y2!56))) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6002])).
% 5.59/5.61 tff(6004,plain,
% 5.59/5.61 (succ(succ(succ(Y2!56))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6003, 42])).
% 5.59/5.61 tff(6005,plain,
% 5.59/5.61 (succ(succ(succ(succ(Y2!56)))) = succ(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6004])).
% 5.59/5.61 tff(6006,plain,
% 5.59/5.61 (succ(succ(succ(succ(Y2!56)))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6005, 58])).
% 5.59/5.61 tff(6007,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6006])).
% 5.59/5.61 tff(6008,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(Y2!56))))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6007, 36])).
% 5.59/5.61 tff(6009,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6008])).
% 5.59/5.61 tff(6010,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6009, 48])).
% 5.59/5.61 tff(6011,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6010])).
% 5.59/5.61 tff(6012,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6011, 14])).
% 5.59/5.61 tff(6013,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6012])).
% 5.59/5.61 tff(6014,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6013, 33])).
% 5.59/5.61 tff(6015,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6014])).
% 5.59/5.61 tff(6016,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6015, 30])).
% 5.59/5.61 tff(6017,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6016])).
% 5.59/5.61 tff(6018,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6017, 39])).
% 5.59/5.61 tff(6019,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6018])).
% 5.59/5.61 tff(6020,plain,
% 5.59/5.61 (NSY2!28 = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[370, 6019, 53])).
% 5.59/5.61 tff(6021,plain,
% 5.59/5.61 (pred(NSY2!28) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6020])).
% 5.59/5.61 tff(6022,plain,
% 5.59/5.61 (pred(NSY2!28) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6021, 19])).
% 5.59/5.61 tff(6023,plain,
% 5.59/5.61 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n7, n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6022, 5998])).
% 5.59/5.61 tff(6024,plain,
% 5.59/5.61 (sum(pred(NSY2!28), succ(NPY2!30)) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6023, 44])).
% 5.59/5.61 tff(6025,plain,
% 5.59/5.61 (sum(pred(Y1!58), succ(X1!59)) = sum(n1, n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5867, 5950])).
% 5.59/5.61 tff(6026,plain,
% 5.59/5.61 (sum(pred(Y1!58), succ(X1!59)) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6025, 47])).
% 5.59/5.61 tff(6027,plain,
% 5.59/5.61 (sum(pred(X1!59), succ(Y1!58)) = sum(n1, n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5924, 5891])).
% 5.59/5.61 tff(6028,plain,
% 5.59/5.61 (sum(pred(X1!59), succ(Y1!58)) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6027, 47])).
% 5.59/5.61 tff(6029,plain,
% 5.59/5.61 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n4, n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6028, 6026])).
% 5.59/5.61 tff(6030,plain,
% 5.59/5.61 (X2!57 = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[209, 6029, 46])).
% 5.59/5.61 tff(6031,plain,
% 5.59/5.61 (pred(X2!57) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6030])).
% 5.59/5.61 tff(6032,plain,
% 5.59/5.61 (pred(X2!57) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6031, 19])).
% 5.59/5.61 tff(6033,plain,
% 5.59/5.61 (pred(pred(X2!57)) = pred(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6032])).
% 5.59/5.61 tff(6034,plain,
% 5.59/5.61 (pred(pred(X2!57)) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6033, 18])).
% 5.59/5.61 tff(6035,plain,
% 5.59/5.61 (pred(pred(pred(X2!57))) = pred(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6034])).
% 5.59/5.61 tff(6036,plain,
% 5.59/5.61 (pred(pred(pred(X2!57))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6035, 17])).
% 5.59/5.61 tff(6037,plain,
% 5.59/5.61 (pred(pred(pred(pred(X2!57)))) = pred(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6036])).
% 5.59/5.61 tff(6038,plain,
% 5.59/5.61 (pred(pred(pred(pred(X2!57)))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6037, 16])).
% 5.59/5.61 tff(6039,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(X2!57))))) = pred(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6038])).
% 5.59/5.61 tff(6040,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(X2!57))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6039, 15])).
% 5.59/5.61 tff(6041,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6040])).
% 5.59/5.61 tff(6042,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6041, 25])).
% 5.59/5.61 tff(6043,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6042])).
% 5.59/5.61 tff(6044,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6043, 24])).
% 5.59/5.61 tff(6045,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6044])).
% 5.59/5.61 tff(6046,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6045, 23])).
% 5.59/5.61 tff(6047,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6046])).
% 5.59/5.61 tff(6048,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[6047, 22])).
% 5.59/5.61 tff(6049,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6048])).
% 5.59/5.61 tff(6050,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6049, 21])).
% 5.59/5.61 tff(6051,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6050])).
% 5.59/5.61 tff(6052,plain,
% 5.59/5.61 (NPX2!31 = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[395, 6051, 20])).
% 5.59/5.61 tff(6053,plain,
% 5.59/5.61 (succ(NPX2!31) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6052])).
% 5.59/5.61 tff(6054,plain,
% 5.59/5.61 (succ(NPX2!31) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6053, 45])).
% 5.59/5.61 tff(6055,plain,
% 5.59/5.61 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n9, n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6054, 6024])).
% 5.59/5.61 tff(6056,plain,
% 5.59/5.61 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6055, 790])).
% 5.59/5.61 tff(6057,plain,
% 5.59/5.61 (succ(X2!57) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6030])).
% 5.59/5.61 tff(6058,plain,
% 5.59/5.61 (succ(X2!57) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6057, 45])).
% 5.59/5.61 tff(6059,plain,
% 5.59/5.61 (succ(succ(X2!57)) = succ(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6058])).
% 5.59/5.61 tff(6060,plain,
% 5.59/5.61 (succ(succ(X2!57)) = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[6059, 28])).
% 5.59/5.61 tff(6061,plain,
% 5.59/5.61 (succ(succ(succ(X2!57))) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6060])).
% 5.59/5.61 tff(6062,plain,
% 5.59/5.61 (succ(succ(succ(X2!57))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6061, 42])).
% 5.59/5.61 tff(6063,plain,
% 5.59/5.61 (succ(succ(succ(succ(X2!57)))) = succ(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6062])).
% 5.59/5.61 tff(6064,plain,
% 5.59/5.61 (succ(succ(succ(succ(X2!57)))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6063, 58])).
% 5.59/5.61 tff(6065,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(X2!57))))) = succ(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6064])).
% 5.59/5.61 tff(6066,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(X2!57))))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6065, 36])).
% 5.59/5.61 tff(6067,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6066])).
% 5.59/5.61 tff(6068,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6067, 48])).
% 5.59/5.61 tff(6069,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6068])).
% 5.59/5.61 tff(6070,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6069, 14])).
% 5.59/5.61 tff(6071,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6070])).
% 5.59/5.61 tff(6072,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6071, 33])).
% 5.59/5.61 tff(6073,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6072])).
% 5.59/5.61 tff(6074,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6073, 30])).
% 5.59/5.61 tff(6075,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6074])).
% 5.59/5.61 tff(6076,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6075, 39])).
% 5.59/5.61 tff(6077,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6076])).
% 5.59/5.61 tff(6078,plain,
% 5.59/5.61 (NSX2!29 = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[420, 6077, 53])).
% 5.59/5.61 tff(6079,plain,
% 5.59/5.61 (pred(NSX2!29) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6078])).
% 5.59/5.61 tff(6080,plain,
% 5.59/5.61 (pred(NSX2!29) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6079, 19])).
% 5.59/5.61 tff(6081,plain,
% 5.59/5.61 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n7, n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6080, 6056])).
% 5.59/5.61 tff(6082,plain,
% 5.59/5.61 (Y3!54 = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[425, 6081, 789])).
% 5.59/5.61 tff(6083,plain,
% 5.59/5.61 (pred(Y3!54) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6082])).
% 5.59/5.61 tff(6084,plain,
% 5.59/5.61 (pred(Y3!54) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6083, 21])).
% 5.59/5.61 tff(6085,plain,
% 5.59/5.61 (pred(pred(Y3!54)) = pred(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6084])).
% 5.59/5.61 tff(6086,plain,
% 5.59/5.61 (pred(pred(Y3!54)) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[6085, 20])).
% 5.59/5.61 tff(6087,plain,
% 5.59/5.61 (pred(pred(pred(Y3!54))) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6086])).
% 5.59/5.61 tff(6088,plain,
% 5.59/5.61 (pred(pred(pred(Y3!54))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6087, 19])).
% 5.59/5.61 tff(6089,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y3!54)))) = pred(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6088])).
% 5.59/5.61 tff(6090,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y3!54)))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6089, 18])).
% 5.59/5.61 tff(6091,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6090])).
% 5.59/5.61 tff(6092,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y3!54))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6091, 17])).
% 5.59/5.61 tff(6093,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6092])).
% 5.59/5.61 tff(6094,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6093, 16])).
% 5.59/5.61 tff(6095,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6094])).
% 5.59/5.61 tff(6096,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6095, 15])).
% 5.59/5.61 tff(6097,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6096])).
% 5.59/5.61 tff(6098,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6097, 25])).
% 5.59/5.61 tff(6099,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6098])).
% 5.59/5.61 tff(6100,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6099, 24])).
% 5.59/5.61 tff(6101,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6100])).
% 5.59/5.61 tff(6102,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6101, 23])).
% 5.59/5.61 tff(6103,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6102])).
% 5.59/5.61 tff(6104,plain,
% 5.59/5.61 (NPY3!26 = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[462, 6103, 22])).
% 5.59/5.61 tff(6105,plain,
% 5.59/5.61 (succ(NPY3!26) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6104])).
% 5.59/5.61 tff(6106,plain,
% 5.59/5.61 (succ(NPY3!26) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6105, 42])).
% 5.59/5.61 tff(6107,plain,
% 5.59/5.61 (succ(Y3!54) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6082])).
% 5.59/5.61 tff(6108,plain,
% 5.59/5.61 (succ(Y3!54) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6107, 42])).
% 5.59/5.61 tff(6109,plain,
% 5.59/5.61 (succ(succ(Y3!54)) = succ(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6108])).
% 5.59/5.61 tff(6110,plain,
% 5.59/5.61 (succ(succ(Y3!54)) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6109, 58])).
% 5.59/5.61 tff(6111,plain,
% 5.59/5.61 (succ(succ(succ(Y3!54))) = succ(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6110])).
% 5.59/5.61 tff(6112,plain,
% 5.59/5.61 (succ(succ(succ(Y3!54))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6111, 36])).
% 5.59/5.61 tff(6113,plain,
% 5.59/5.61 (succ(succ(succ(succ(Y3!54)))) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6112])).
% 5.59/5.61 tff(6114,plain,
% 5.59/5.61 (succ(succ(succ(succ(Y3!54)))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6113, 48])).
% 5.59/5.61 tff(6115,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6114])).
% 5.59/5.61 tff(6116,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(Y3!54))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6115, 14])).
% 5.59/5.61 tff(6117,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6116])).
% 5.59/5.61 tff(6118,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6117, 33])).
% 5.59/5.61 tff(6119,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6118])).
% 5.59/5.61 tff(6120,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6119, 30])).
% 5.59/5.61 tff(6121,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6120])).
% 5.59/5.61 tff(6122,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6121, 39])).
% 5.59/5.61 tff(6123,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6122])).
% 5.59/5.61 tff(6124,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[6123, 53])).
% 5.59/5.61 tff(6125,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6124])).
% 5.59/5.61 tff(6126,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6125, 45])).
% 5.59/5.61 tff(6127,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6126])).
% 5.59/5.61 tff(6128,plain,
% 5.59/5.61 (NSY3!24 = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[485, 6127, 28])).
% 5.59/5.61 tff(6129,plain,
% 5.59/5.61 (pred(NSY3!24) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6128])).
% 5.59/5.61 tff(6130,plain,
% 5.59/5.61 (pred(NSY3!24) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6129, 21])).
% 5.59/5.61 tff(6131,plain,
% 5.59/5.61 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n9, n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6130, 6106])).
% 5.59/5.61 tff(6132,plain,
% 5.59/5.61 (sum(pred(NSY3!24), succ(NPY3!26)) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6131, 41])).
% 5.59/5.61 tff(6133,plain,
% 5.59/5.61 (sum(pred(Y2!56), succ(X2!57)) = sum(n7, n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[5976, 6058])).
% 5.59/5.61 tff(6134,plain,
% 5.59/5.61 (sum(pred(Y2!56), succ(X2!57)) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6133, 44])).
% 5.59/5.61 tff(6135,plain,
% 5.59/5.61 (sum(pred(X2!57), succ(Y2!56)) = sum(n7, n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6032, 6000])).
% 5.59/5.61 tff(6136,plain,
% 5.59/5.61 (sum(pred(X2!57), succ(Y2!56)) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6135, 44])).
% 5.59/5.61 tff(6137,plain,
% 5.59/5.61 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n5, n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6136, 6134])).
% 5.59/5.61 tff(6138,plain,
% 5.59/5.61 (X3!55 = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[323, 6137, 43])).
% 5.59/5.61 tff(6139,plain,
% 5.59/5.61 (pred(X3!55) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6138])).
% 5.59/5.61 tff(6140,plain,
% 5.59/5.61 (pred(X3!55) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6139, 21])).
% 5.59/5.61 tff(6141,plain,
% 5.59/5.61 (pred(pred(X3!55)) = pred(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6140])).
% 5.59/5.61 tff(6142,plain,
% 5.59/5.61 (pred(pred(X3!55)) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[6141, 20])).
% 5.59/5.61 tff(6143,plain,
% 5.59/5.61 (pred(pred(pred(X3!55))) = pred(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6142])).
% 5.59/5.61 tff(6144,plain,
% 5.59/5.61 (pred(pred(pred(X3!55))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6143, 19])).
% 5.59/5.61 tff(6145,plain,
% 5.59/5.61 (pred(pred(pred(pred(X3!55)))) = pred(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6144])).
% 5.59/5.61 tff(6146,plain,
% 5.59/5.61 (pred(pred(pred(pred(X3!55)))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6145, 18])).
% 5.59/5.61 tff(6147,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(X3!55))))) = pred(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6146])).
% 5.59/5.61 tff(6148,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(X3!55))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6147, 17])).
% 5.59/5.61 tff(6149,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6148])).
% 5.59/5.61 tff(6150,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6149, 16])).
% 5.59/5.61 tff(6151,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6150])).
% 5.59/5.61 tff(6152,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6151, 15])).
% 5.59/5.61 tff(6153,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6152])).
% 5.59/5.61 tff(6154,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6153, 25])).
% 5.59/5.61 tff(6155,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6154])).
% 5.59/5.61 tff(6156,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6155, 24])).
% 5.59/5.61 tff(6157,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6156])).
% 5.59/5.61 tff(6158,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6157, 23])).
% 5.59/5.61 tff(6159,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6158])).
% 5.59/5.61 tff(6160,plain,
% 5.59/5.61 (NPX3!27 = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[510, 6159, 22])).
% 5.59/5.61 tff(6161,plain,
% 5.59/5.61 (succ(NPX3!27) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6160])).
% 5.59/5.61 tff(6162,plain,
% 5.59/5.61 (succ(NPX3!27) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6161, 42])).
% 5.59/5.61 tff(6163,plain,
% 5.59/5.61 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n0, n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6162, 6132])).
% 5.59/5.61 tff(6164,plain,
% 5.59/5.61 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6163, 40])).
% 5.59/5.61 tff(6165,plain,
% 5.59/5.61 (succ(X3!55) = succ(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6138])).
% 5.59/5.61 tff(6166,plain,
% 5.59/5.61 (succ(X3!55) = n0),
% 5.59/5.61 inference(transitivity,[status(thm)],[6165, 42])).
% 5.59/5.61 tff(6167,plain,
% 5.59/5.61 (succ(succ(X3!55)) = succ(n0)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6166])).
% 5.59/5.61 tff(6168,plain,
% 5.59/5.61 (succ(succ(X3!55)) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6167, 58])).
% 5.59/5.61 tff(6169,plain,
% 5.59/5.61 (succ(succ(succ(X3!55))) = succ(n1)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6168])).
% 5.59/5.61 tff(6170,plain,
% 5.59/5.61 (succ(succ(succ(X3!55))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6169, 36])).
% 5.59/5.61 tff(6171,plain,
% 5.59/5.61 (succ(succ(succ(succ(X3!55)))) = succ(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6170])).
% 5.59/5.61 tff(6172,plain,
% 5.59/5.61 (succ(succ(succ(succ(X3!55)))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6171, 48])).
% 5.59/5.61 tff(6173,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(X3!55))))) = succ(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6172])).
% 5.59/5.61 tff(6174,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(X3!55))))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6173, 14])).
% 5.59/5.61 tff(6175,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6174])).
% 5.59/5.61 tff(6176,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6175, 33])).
% 5.59/5.61 tff(6177,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6176])).
% 5.59/5.61 tff(6178,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6177, 30])).
% 5.59/5.61 tff(6179,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6178])).
% 5.59/5.61 tff(6180,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[6179, 39])).
% 5.59/5.61 tff(6181,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6180])).
% 5.59/5.61 tff(6182,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n8),
% 5.59/5.61 inference(transitivity,[status(thm)],[6181, 53])).
% 5.59/5.61 tff(6183,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n8)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6182])).
% 5.59/5.61 tff(6184,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6183, 45])).
% 5.59/5.61 tff(6185,plain,
% 5.59/5.61 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6184])).
% 5.59/5.61 tff(6186,plain,
% 5.59/5.61 (NSX3!25 = n10),
% 5.59/5.61 inference(transitivity,[status(thm)],[535, 6185, 28])).
% 5.59/5.61 tff(6187,plain,
% 5.59/5.61 (pred(NSX3!25) = pred(n10)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6186])).
% 5.59/5.61 tff(6188,plain,
% 5.59/5.61 (pred(NSX3!25) = n9),
% 5.59/5.61 inference(transitivity,[status(thm)],[6187, 21])).
% 5.59/5.61 tff(6189,plain,
% 5.59/5.61 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n9, n9)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6188, 6164])).
% 5.59/5.61 tff(6190,plain,
% 5.59/5.61 (Y4!52 = n7),
% 5.59/5.61 inference(transitivity,[status(thm)],[540, 6189, 54])).
% 5.59/5.61 tff(6191,plain,
% 5.59/5.61 (pred(Y4!52) = pred(n7)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6190])).
% 5.59/5.61 tff(6192,plain,
% 5.59/5.61 (pred(Y4!52) = n6),
% 5.59/5.61 inference(transitivity,[status(thm)],[6191, 18])).
% 5.59/5.61 tff(6193,plain,
% 5.59/5.61 (pred(pred(Y4!52)) = pred(n6)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6192])).
% 5.59/5.61 tff(6194,plain,
% 5.59/5.61 (pred(pred(Y4!52)) = n5),
% 5.59/5.61 inference(transitivity,[status(thm)],[6193, 17])).
% 5.59/5.61 tff(6195,plain,
% 5.59/5.61 (pred(pred(pred(Y4!52))) = pred(n5)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6194])).
% 5.59/5.61 tff(6196,plain,
% 5.59/5.61 (pred(pred(pred(Y4!52))) = n4),
% 5.59/5.61 inference(transitivity,[status(thm)],[6195, 16])).
% 5.59/5.61 tff(6197,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y4!52)))) = pred(n4)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6196])).
% 5.59/5.61 tff(6198,plain,
% 5.59/5.61 (pred(pred(pred(pred(Y4!52)))) = n3),
% 5.59/5.61 inference(transitivity,[status(thm)],[6197, 15])).
% 5.59/5.61 tff(6199,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n3)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6198])).
% 5.59/5.61 tff(6200,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(Y4!52))))) = n2),
% 5.59/5.61 inference(transitivity,[status(thm)],[6199, 25])).
% 5.59/5.61 tff(6201,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n2)),
% 5.59/5.61 inference(monotonicity,[status(thm)],[6200])).
% 5.59/5.61 tff(6202,plain,
% 5.59/5.61 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n1),
% 5.59/5.61 inference(transitivity,[status(thm)],[6201, 24])).
% 5.59/5.61 tff(6203,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6202])).
% 5.59/5.62 tff(6204,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6203, 23])).
% 5.59/5.62 tff(6205,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6204])).
% 5.59/5.62 tff(6206,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6205, 22])).
% 5.59/5.62 tff(6207,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6206])).
% 5.59/5.62 tff(6208,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6207, 21])).
% 5.59/5.62 tff(6209,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6208])).
% 5.59/5.62 tff(6210,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6209, 20])).
% 5.59/5.62 tff(6211,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6210])).
% 5.59/5.62 tff(6212,plain,
% 5.59/5.62 (NPY4!22 = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[578, 6211, 19])).
% 5.59/5.62 tff(6213,plain,
% 5.59/5.62 (succ(NPY4!22) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6212])).
% 5.59/5.62 tff(6214,plain,
% 5.59/5.62 (succ(NPY4!22) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6213, 53])).
% 5.59/5.62 tff(6215,plain,
% 5.59/5.62 (succ(Y4!52) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6190])).
% 5.59/5.62 tff(6216,plain,
% 5.59/5.62 (succ(Y4!52) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6215, 53])).
% 5.59/5.62 tff(6217,plain,
% 5.59/5.62 (succ(succ(Y4!52)) = succ(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6216])).
% 5.59/5.62 tff(6218,plain,
% 5.59/5.62 (succ(succ(Y4!52)) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6217, 45])).
% 5.59/5.62 tff(6219,plain,
% 5.59/5.62 (succ(succ(succ(Y4!52))) = succ(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6218])).
% 5.59/5.62 tff(6220,plain,
% 5.59/5.62 (succ(succ(succ(Y4!52))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6219, 28])).
% 5.59/5.62 tff(6221,plain,
% 5.59/5.62 (succ(succ(succ(succ(Y4!52)))) = succ(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6220])).
% 5.59/5.62 tff(6222,plain,
% 5.59/5.62 (succ(succ(succ(succ(Y4!52)))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6221, 42])).
% 5.59/5.62 tff(6223,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6222])).
% 5.59/5.62 tff(6224,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(Y4!52))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6223, 58])).
% 5.59/5.62 tff(6225,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6224])).
% 5.59/5.62 tff(6226,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[6225, 36])).
% 5.59/5.62 tff(6227,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6226])).
% 5.59/5.62 tff(6228,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6227, 48])).
% 5.59/5.62 tff(6229,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6228])).
% 5.59/5.62 tff(6230,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6229, 14])).
% 5.59/5.62 tff(6231,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6230])).
% 5.59/5.62 tff(6232,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6231, 33])).
% 5.59/5.62 tff(6233,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6232])).
% 5.59/5.62 tff(6234,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6233, 30])).
% 5.59/5.62 tff(6235,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6234])).
% 5.59/5.62 tff(6236,plain,
% 5.59/5.62 (NSY4!20 = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[601, 6235, 39])).
% 5.59/5.62 tff(6237,plain,
% 5.59/5.62 (pred(NSY4!20) = pred(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6236])).
% 5.59/5.62 tff(6238,plain,
% 5.59/5.62 (pred(NSY4!20) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6237, 18])).
% 5.59/5.62 tff(6239,plain,
% 5.59/5.62 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n6, n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6238, 6214])).
% 5.59/5.62 tff(6240,plain,
% 5.59/5.62 (sum(pred(NSY4!20), succ(NPY4!22)) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6239, 52])).
% 5.59/5.62 tff(6241,plain,
% 5.59/5.62 (sum(pred(Y3!54), succ(X3!55)) = sum(n9, n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6084, 6166])).
% 5.59/5.62 tff(6242,plain,
% 5.59/5.62 (sum(pred(Y3!54), succ(X3!55)) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6241, 41])).
% 5.59/5.62 tff(6243,plain,
% 5.59/5.62 (sum(pred(X3!55), succ(Y3!54)) = sum(n9, n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6140, 6108])).
% 5.59/5.62 tff(6244,plain,
% 5.59/5.62 (sum(pred(X3!55), succ(Y3!54)) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6243, 41])).
% 5.59/5.62 tff(6245,plain,
% 5.59/5.62 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n9, n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6244, 6242])).
% 5.59/5.62 tff(6246,plain,
% 5.59/5.62 (X4!53 = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[438, 6245, 54])).
% 5.59/5.62 tff(6247,plain,
% 5.59/5.62 (pred(X4!53) = pred(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6246])).
% 5.59/5.62 tff(6248,plain,
% 5.59/5.62 (pred(X4!53) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6247, 18])).
% 5.59/5.62 tff(6249,plain,
% 5.59/5.62 (pred(pred(X4!53)) = pred(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6248])).
% 5.59/5.62 tff(6250,plain,
% 5.59/5.62 (pred(pred(X4!53)) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6249, 17])).
% 5.59/5.62 tff(6251,plain,
% 5.59/5.62 (pred(pred(pred(X4!53))) = pred(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6250])).
% 5.59/5.62 tff(6252,plain,
% 5.59/5.62 (pred(pred(pred(X4!53))) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6251, 16])).
% 5.59/5.62 tff(6253,plain,
% 5.59/5.62 (pred(pred(pred(pred(X4!53)))) = pred(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6252])).
% 5.59/5.62 tff(6254,plain,
% 5.59/5.62 (pred(pred(pred(pred(X4!53)))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6253, 15])).
% 5.59/5.62 tff(6255,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(X4!53))))) = pred(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6254])).
% 5.59/5.62 tff(6256,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(X4!53))))) = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[6255, 25])).
% 5.59/5.62 tff(6257,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6256])).
% 5.59/5.62 tff(6258,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6257, 24])).
% 5.59/5.62 tff(6259,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6258])).
% 5.59/5.62 tff(6260,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6259, 23])).
% 5.59/5.62 tff(6261,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6260])).
% 5.59/5.62 tff(6262,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6261, 22])).
% 5.59/5.62 tff(6263,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6262])).
% 5.59/5.62 tff(6264,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6263, 21])).
% 5.59/5.62 tff(6265,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6264])).
% 5.59/5.62 tff(6266,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6265, 20])).
% 5.59/5.62 tff(6267,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6266])).
% 5.59/5.62 tff(6268,plain,
% 5.59/5.62 (NPX4!23 = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[626, 6267, 19])).
% 5.59/5.62 tff(6269,plain,
% 5.59/5.62 (succ(NPX4!23) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6268])).
% 5.59/5.62 tff(6270,plain,
% 5.59/5.62 (succ(NPX4!23) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6269, 53])).
% 5.59/5.62 tff(6271,plain,
% 5.59/5.62 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n8, n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6270, 6240])).
% 5.59/5.62 tff(6272,plain,
% 5.59/5.62 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6271, 64])).
% 5.59/5.62 tff(6273,plain,
% 5.59/5.62 (succ(X4!53) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6246])).
% 5.59/5.62 tff(6274,plain,
% 5.59/5.62 (succ(X4!53) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6273, 53])).
% 5.59/5.62 tff(6275,plain,
% 5.59/5.62 (succ(succ(X4!53)) = succ(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6274])).
% 5.59/5.62 tff(6276,plain,
% 5.59/5.62 (succ(succ(X4!53)) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6275, 45])).
% 5.59/5.62 tff(6277,plain,
% 5.59/5.62 (succ(succ(succ(X4!53))) = succ(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6276])).
% 5.59/5.62 tff(6278,plain,
% 5.59/5.62 (succ(succ(succ(X4!53))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6277, 28])).
% 5.59/5.62 tff(6279,plain,
% 5.59/5.62 (succ(succ(succ(succ(X4!53)))) = succ(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6278])).
% 5.59/5.62 tff(6280,plain,
% 5.59/5.62 (succ(succ(succ(succ(X4!53)))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6279, 42])).
% 5.59/5.62 tff(6281,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(X4!53))))) = succ(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6280])).
% 5.59/5.62 tff(6282,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(X4!53))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6281, 58])).
% 5.59/5.62 tff(6283,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6282])).
% 5.59/5.62 tff(6284,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[6283, 36])).
% 5.59/5.62 tff(6285,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6284])).
% 5.59/5.62 tff(6286,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6285, 48])).
% 5.59/5.62 tff(6287,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6286])).
% 5.59/5.62 tff(6288,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6287, 14])).
% 5.59/5.62 tff(6289,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6288])).
% 5.59/5.62 tff(6290,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6289, 33])).
% 5.59/5.62 tff(6291,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6290])).
% 5.59/5.62 tff(6292,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6291, 30])).
% 5.59/5.62 tff(6293,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6292])).
% 5.59/5.62 tff(6294,plain,
% 5.59/5.62 (NSX4!21 = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[651, 6293, 39])).
% 5.59/5.62 tff(6295,plain,
% 5.59/5.62 (pred(NSX4!21) = pred(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6294])).
% 5.59/5.62 tff(6296,plain,
% 5.59/5.62 (pred(NSX4!21) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6295, 18])).
% 5.59/5.62 tff(6297,plain,
% 5.59/5.62 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n6, n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6296, 6272])).
% 5.59/5.62 tff(6298,plain,
% 5.59/5.62 (Y5!50 = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[656, 6297, 788])).
% 5.59/5.62 tff(6299,plain,
% 5.59/5.62 (pred(Y5!50) = pred(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6298])).
% 5.59/5.62 tff(6300,plain,
% 5.59/5.62 (pred(Y5!50) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6299, 17])).
% 5.59/5.62 tff(6301,plain,
% 5.59/5.62 (pred(pred(Y5!50)) = pred(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6300])).
% 5.59/5.62 tff(6302,plain,
% 5.59/5.62 (pred(pred(Y5!50)) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6301, 16])).
% 5.59/5.62 tff(6303,plain,
% 5.59/5.62 (pred(pred(pred(Y5!50))) = pred(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6302])).
% 5.59/5.62 tff(6304,plain,
% 5.59/5.62 (pred(pred(pred(Y5!50))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6303, 15])).
% 5.59/5.62 tff(6305,plain,
% 5.59/5.62 (pred(pred(pred(pred(Y5!50)))) = pred(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6304])).
% 5.59/5.62 tff(6306,plain,
% 5.59/5.62 (pred(pred(pred(pred(Y5!50)))) = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[6305, 25])).
% 5.59/5.62 tff(6307,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6306])).
% 5.59/5.62 tff(6308,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(Y5!50))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6307, 24])).
% 5.59/5.62 tff(6309,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6308])).
% 5.59/5.62 tff(6310,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6309, 23])).
% 5.59/5.62 tff(6311,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6310])).
% 5.59/5.62 tff(6312,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6311, 22])).
% 5.59/5.62 tff(6313,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6312])).
% 5.59/5.62 tff(6314,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6313, 21])).
% 5.59/5.62 tff(6315,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6314])).
% 5.59/5.62 tff(6316,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6315, 20])).
% 5.59/5.62 tff(6317,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6316])).
% 5.59/5.62 tff(6318,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6317, 19])).
% 5.59/5.62 tff(6319,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6318])).
% 5.59/5.62 tff(6320,plain,
% 5.59/5.62 (NPY5!18 = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[694, 6319, 18])).
% 5.59/5.62 tff(6321,plain,
% 5.59/5.62 (succ(NPY5!18) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6320])).
% 5.59/5.62 tff(6322,plain,
% 5.59/5.62 (succ(NPY5!18) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6321, 39])).
% 5.59/5.62 tff(6323,plain,
% 5.59/5.62 (succ(Y5!50) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6298])).
% 5.59/5.62 tff(6324,plain,
% 5.59/5.62 (succ(Y5!50) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6323, 39])).
% 5.59/5.62 tff(6325,plain,
% 5.59/5.62 (succ(succ(Y5!50)) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6324])).
% 5.59/5.62 tff(6326,plain,
% 5.59/5.62 (succ(succ(Y5!50)) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6325, 53])).
% 5.59/5.62 tff(6327,plain,
% 5.59/5.62 (succ(succ(succ(Y5!50))) = succ(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6326])).
% 5.59/5.62 tff(6328,plain,
% 5.59/5.62 (succ(succ(succ(Y5!50))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6327, 45])).
% 5.59/5.62 tff(6329,plain,
% 5.59/5.62 (succ(succ(succ(succ(Y5!50)))) = succ(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6328])).
% 5.59/5.62 tff(6330,plain,
% 5.59/5.62 (succ(succ(succ(succ(Y5!50)))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6329, 28])).
% 5.59/5.62 tff(6331,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6330])).
% 5.59/5.62 tff(6332,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(Y5!50))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6331, 42])).
% 5.59/5.62 tff(6333,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6332])).
% 5.59/5.62 tff(6334,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6333, 58])).
% 5.59/5.62 tff(6335,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6334])).
% 5.59/5.62 tff(6336,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[6335, 36])).
% 5.59/5.62 tff(6337,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6336])).
% 5.59/5.62 tff(6338,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6337, 48])).
% 5.59/5.62 tff(6339,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6338])).
% 5.59/5.62 tff(6340,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6339, 14])).
% 5.59/5.62 tff(6341,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6340])).
% 5.59/5.62 tff(6342,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6341, 33])).
% 5.59/5.62 tff(6343,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6342])).
% 5.59/5.62 tff(6344,plain,
% 5.59/5.62 (NSY5!16 = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[717, 6343, 30])).
% 5.59/5.62 tff(6345,plain,
% 5.59/5.62 (pred(NSY5!16) = pred(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6344])).
% 5.59/5.62 tff(6346,plain,
% 5.59/5.62 (pred(NSY5!16) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6345, 17])).
% 5.59/5.62 tff(6347,plain,
% 5.59/5.62 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n5, n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6346, 6322])).
% 5.59/5.62 tff(6348,plain,
% 5.59/5.62 (sum(pred(NSY5!16), succ(NPY5!18)) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6347, 50])).
% 5.59/5.62 tff(6349,plain,
% 5.59/5.62 (sum(pred(Y4!52), succ(X4!53)) = sum(n6, n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6192, 6274])).
% 5.59/5.62 tff(6350,plain,
% 5.59/5.62 (sum(pred(Y4!52), succ(X4!53)) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6349, 52])).
% 5.59/5.62 tff(6351,plain,
% 5.59/5.62 (sum(pred(X4!53), succ(Y4!52)) = sum(n6, n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6248, 6216])).
% 5.59/5.62 tff(6352,plain,
% 5.59/5.62 (sum(pred(X4!53), succ(Y4!52)) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6351, 52])).
% 5.59/5.62 tff(6353,plain,
% 5.59/5.62 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n3, n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6352, 6350])).
% 5.59/5.62 tff(6354,plain,
% 5.59/5.62 (X5!51 = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[553, 6353, 51])).
% 5.59/5.62 tff(6355,plain,
% 5.59/5.62 (pred(X5!51) = pred(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6354])).
% 5.59/5.62 tff(6356,plain,
% 5.59/5.62 (pred(X5!51) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6355, 17])).
% 5.59/5.62 tff(6357,plain,
% 5.59/5.62 (pred(pred(X5!51)) = pred(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6356])).
% 5.59/5.62 tff(6358,plain,
% 5.59/5.62 (pred(pred(X5!51)) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6357, 16])).
% 5.59/5.62 tff(6359,plain,
% 5.59/5.62 (pred(pred(pred(X5!51))) = pred(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6358])).
% 5.59/5.62 tff(6360,plain,
% 5.59/5.62 (pred(pred(pred(X5!51))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6359, 15])).
% 5.59/5.62 tff(6361,plain,
% 5.59/5.62 (pred(pred(pred(pred(X5!51)))) = pred(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6360])).
% 5.59/5.62 tff(6362,plain,
% 5.59/5.62 (pred(pred(pred(pred(X5!51)))) = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[6361, 25])).
% 5.59/5.62 tff(6363,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(X5!51))))) = pred(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6362])).
% 5.59/5.62 tff(6364,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(X5!51))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6363, 24])).
% 5.59/5.62 tff(6365,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6364])).
% 5.59/5.62 tff(6366,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6365, 23])).
% 5.59/5.62 tff(6367,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6366])).
% 5.59/5.62 tff(6368,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6367, 22])).
% 5.59/5.62 tff(6369,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6368])).
% 5.59/5.62 tff(6370,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6369, 21])).
% 5.59/5.62 tff(6371,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6370])).
% 5.59/5.62 tff(6372,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6371, 20])).
% 5.59/5.62 tff(6373,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6372])).
% 5.59/5.62 tff(6374,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6373, 19])).
% 5.59/5.62 tff(6375,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6374])).
% 5.59/5.62 tff(6376,plain,
% 5.59/5.62 (NPX5!19 = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[742, 6375, 18])).
% 5.59/5.62 tff(6377,plain,
% 5.59/5.62 (succ(NPX5!19) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6376])).
% 5.59/5.62 tff(6378,plain,
% 5.59/5.62 (succ(NPX5!19) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6377, 39])).
% 5.59/5.62 tff(6379,plain,
% 5.59/5.62 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n7, n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6378, 6348])).
% 5.59/5.62 tff(6380,plain,
% 5.59/5.62 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6379, 787])).
% 5.59/5.62 tff(6381,plain,
% 5.59/5.62 (succ(X5!51) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6354])).
% 5.59/5.62 tff(6382,plain,
% 5.59/5.62 (succ(X5!51) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6381, 39])).
% 5.59/5.62 tff(6383,plain,
% 5.59/5.62 (succ(succ(X5!51)) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6382])).
% 5.59/5.62 tff(6384,plain,
% 5.59/5.62 (succ(succ(X5!51)) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6383, 53])).
% 5.59/5.62 tff(6385,plain,
% 5.59/5.62 (succ(succ(succ(X5!51))) = succ(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6384])).
% 5.59/5.62 tff(6386,plain,
% 5.59/5.62 (succ(succ(succ(X5!51))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6385, 45])).
% 5.59/5.62 tff(6387,plain,
% 5.59/5.62 (succ(succ(succ(succ(X5!51)))) = succ(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6386])).
% 5.59/5.62 tff(6388,plain,
% 5.59/5.62 (succ(succ(succ(succ(X5!51)))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6387, 28])).
% 5.59/5.62 tff(6389,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(X5!51))))) = succ(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6388])).
% 5.59/5.62 tff(6390,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(X5!51))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6389, 42])).
% 5.59/5.62 tff(6391,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6390])).
% 5.59/5.62 tff(6392,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6391, 58])).
% 5.59/5.62 tff(6393,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6392])).
% 5.59/5.62 tff(6394,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[6393, 36])).
% 5.59/5.62 tff(6395,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6394])).
% 5.59/5.62 tff(6396,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6395, 48])).
% 5.59/5.62 tff(6397,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6396])).
% 5.59/5.62 tff(6398,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6397, 14])).
% 5.59/5.62 tff(6399,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6398])).
% 5.59/5.62 tff(6400,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6399, 33])).
% 5.59/5.62 tff(6401,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6400])).
% 5.59/5.62 tff(6402,plain,
% 5.59/5.62 (NSX5!17 = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[767, 6401, 30])).
% 5.59/5.62 tff(6403,plain,
% 5.59/5.62 (pred(NSX5!17) = pred(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6402])).
% 5.59/5.62 tff(6404,plain,
% 5.59/5.62 (pred(NSX5!17) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6403, 17])).
% 5.59/5.62 tff(6405,plain,
% 5.59/5.62 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n5, n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6404, 6380])).
% 5.59/5.62 tff(6406,plain,
% 5.59/5.62 (Y6!48 = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[772, 6405, 558])).
% 5.59/5.62 tff(6407,plain,
% 5.59/5.62 (pred(Y6!48) = pred(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6406])).
% 5.59/5.62 tff(6408,plain,
% 5.59/5.62 (pred(Y6!48) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6407, 24])).
% 5.59/5.62 tff(6409,plain,
% 5.59/5.62 (pred(pred(Y6!48)) = pred(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6408])).
% 5.59/5.62 tff(6410,plain,
% 5.59/5.62 (pred(pred(Y6!48)) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6409, 23])).
% 5.59/5.62 tff(6411,plain,
% 5.59/5.62 (pred(pred(pred(Y6!48))) = pred(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6410])).
% 5.59/5.62 tff(6412,plain,
% 5.59/5.62 (pred(pred(pred(Y6!48))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6411, 22])).
% 5.59/5.62 tff(6413,plain,
% 5.59/5.62 (pred(pred(pred(pred(Y6!48)))) = pred(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6412])).
% 5.59/5.62 tff(6414,plain,
% 5.59/5.62 (pred(pred(pred(pred(Y6!48)))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6413, 21])).
% 5.59/5.62 tff(6415,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6414])).
% 5.59/5.62 tff(6416,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(Y6!48))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6415, 20])).
% 5.59/5.62 tff(6417,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6416])).
% 5.59/5.62 tff(6418,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6417, 19])).
% 5.59/5.62 tff(6419,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6418])).
% 5.59/5.62 tff(6420,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6419, 18])).
% 5.59/5.62 tff(6421,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6420])).
% 5.59/5.62 tff(6422,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6421, 17])).
% 5.59/5.62 tff(6423,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6422])).
% 5.59/5.62 tff(6424,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6423, 16])).
% 5.59/5.62 tff(6425,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6424])).
% 5.59/5.62 tff(6426,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6425, 15])).
% 5.59/5.62 tff(6427,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6426])).
% 5.59/5.62 tff(6428,plain,
% 5.59/5.62 (NPY6!14 = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[1465, 6427, 25])).
% 5.59/5.62 tff(6429,plain,
% 5.59/5.62 (succ(NPY6!14) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6428])).
% 5.59/5.62 tff(6430,plain,
% 5.59/5.62 (succ(NPY6!14) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6429, 48])).
% 5.59/5.62 tff(6431,plain,
% 5.59/5.62 (succ(Y6!48) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6406])).
% 5.59/5.62 tff(6432,plain,
% 5.59/5.62 (succ(Y6!48) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6431, 48])).
% 5.59/5.62 tff(6433,plain,
% 5.59/5.62 (succ(succ(Y6!48)) = succ(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6432])).
% 5.59/5.62 tff(6434,plain,
% 5.59/5.62 (succ(succ(Y6!48)) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6433, 14])).
% 5.59/5.62 tff(6435,plain,
% 5.59/5.62 (succ(succ(succ(Y6!48))) = succ(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6434])).
% 5.59/5.62 tff(6436,plain,
% 5.59/5.62 (succ(succ(succ(Y6!48))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6435, 33])).
% 5.59/5.62 tff(6437,plain,
% 5.59/5.62 (succ(succ(succ(succ(Y6!48)))) = succ(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6436])).
% 5.59/5.62 tff(6438,plain,
% 5.59/5.62 (succ(succ(succ(succ(Y6!48)))) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6437, 30])).
% 5.59/5.62 tff(6439,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6438])).
% 5.59/5.62 tff(6440,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(Y6!48))))) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6439, 39])).
% 5.59/5.62 tff(6441,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6440])).
% 5.59/5.62 tff(6442,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6441, 53])).
% 5.59/5.62 tff(6443,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6442])).
% 5.59/5.62 tff(6444,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6443, 45])).
% 5.59/5.62 tff(6445,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6444])).
% 5.59/5.62 tff(6446,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6445, 28])).
% 5.59/5.62 tff(6447,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6446])).
% 5.59/5.62 tff(6448,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6447, 42])).
% 5.59/5.62 tff(6449,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6448])).
% 5.59/5.62 tff(6450,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6449, 58])).
% 5.59/5.62 tff(6451,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6450])).
% 5.59/5.62 tff(6452,plain,
% 5.59/5.62 (NSY6!12 = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[1490, 6451, 36])).
% 5.59/5.62 tff(6453,plain,
% 5.59/5.62 (pred(NSY6!12) = pred(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6452])).
% 5.59/5.62 tff(6454,plain,
% 5.59/5.62 (pred(NSY6!12) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6453, 24])).
% 5.59/5.62 tff(6455,plain,
% 5.59/5.62 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n1, n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6454, 6430])).
% 5.59/5.62 tff(6456,plain,
% 5.59/5.62 (sum(pred(NSY6!12), succ(NPY6!14)) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6455, 47])).
% 5.59/5.62 tff(6457,plain,
% 5.59/5.62 (sum(pred(Y5!50), succ(X5!51)) = sum(n5, n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6300, 6382])).
% 5.59/5.62 tff(6458,plain,
% 5.59/5.62 (sum(pred(Y5!50), succ(X5!51)) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6457, 50])).
% 5.59/5.62 tff(6459,plain,
% 5.59/5.62 (sum(pred(X5!51), succ(Y5!50)) = sum(n5, n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6356, 6324])).
% 5.59/5.62 tff(6460,plain,
% 5.59/5.62 (sum(pred(X5!51), succ(Y5!50)) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6459, 50])).
% 5.59/5.62 tff(6461,plain,
% 5.59/5.62 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n1, n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6460, 6458])).
% 5.59/5.62 tff(6462,plain,
% 5.59/5.62 (X6!49 = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[669, 6461, 49])).
% 5.59/5.62 tff(6463,plain,
% 5.59/5.62 (pred(X6!49) = pred(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6462])).
% 5.59/5.62 tff(6464,plain,
% 5.59/5.62 (pred(X6!49) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6463, 24])).
% 5.59/5.62 tff(6465,plain,
% 5.59/5.62 (pred(pred(X6!49)) = pred(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6464])).
% 5.59/5.62 tff(6466,plain,
% 5.59/5.62 (pred(pred(X6!49)) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6465, 23])).
% 5.59/5.62 tff(6467,plain,
% 5.59/5.62 (pred(pred(pred(X6!49))) = pred(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6466])).
% 5.59/5.62 tff(6468,plain,
% 5.59/5.62 (pred(pred(pred(X6!49))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6467, 22])).
% 5.59/5.62 tff(6469,plain,
% 5.59/5.62 (pred(pred(pred(pred(X6!49)))) = pred(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6468])).
% 5.59/5.62 tff(6470,plain,
% 5.59/5.62 (pred(pred(pred(pred(X6!49)))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6469, 21])).
% 5.59/5.62 tff(6471,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(X6!49))))) = pred(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6470])).
% 5.59/5.62 tff(6472,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(X6!49))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6471, 20])).
% 5.59/5.62 tff(6473,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6472])).
% 5.59/5.62 tff(6474,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6473, 19])).
% 5.59/5.62 tff(6475,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6474])).
% 5.59/5.62 tff(6476,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6475, 18])).
% 5.59/5.62 tff(6477,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6476])).
% 5.59/5.62 tff(6478,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6477, 17])).
% 5.59/5.62 tff(6479,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6478])).
% 5.59/5.62 tff(6480,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6479, 16])).
% 5.59/5.62 tff(6481,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6480])).
% 5.59/5.62 tff(6482,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6481, 15])).
% 5.59/5.62 tff(6483,plain,
% 5.59/5.62 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6482])).
% 5.59/5.62 tff(6484,plain,
% 5.59/5.62 (NPX6!15 = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[1523, 6483, 25])).
% 5.59/5.62 tff(6485,plain,
% 5.59/5.62 (succ(NPX6!15) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6484])).
% 5.59/5.62 tff(6486,plain,
% 5.59/5.62 (succ(NPX6!15) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6485, 48])).
% 5.59/5.62 tff(6487,plain,
% 5.59/5.62 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n3, n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6486, 6456])).
% 5.59/5.62 tff(6488,plain,
% 5.59/5.62 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6487, 786])).
% 5.59/5.62 tff(6489,plain,
% 5.59/5.62 (succ(X6!49) = succ(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6462])).
% 5.59/5.62 tff(6490,plain,
% 5.59/5.62 (succ(X6!49) = n3),
% 5.59/5.62 inference(transitivity,[status(thm)],[6489, 48])).
% 5.59/5.62 tff(6491,plain,
% 5.59/5.62 (succ(succ(X6!49)) = succ(n3)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6490])).
% 5.59/5.62 tff(6492,plain,
% 5.59/5.62 (succ(succ(X6!49)) = n4),
% 5.59/5.62 inference(transitivity,[status(thm)],[6491, 14])).
% 5.59/5.62 tff(6493,plain,
% 5.59/5.62 (succ(succ(succ(X6!49))) = succ(n4)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6492])).
% 5.59/5.62 tff(6494,plain,
% 5.59/5.62 (succ(succ(succ(X6!49))) = n5),
% 5.59/5.62 inference(transitivity,[status(thm)],[6493, 33])).
% 5.59/5.62 tff(6495,plain,
% 5.59/5.62 (succ(succ(succ(succ(X6!49)))) = succ(n5)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6494])).
% 5.59/5.62 tff(6496,plain,
% 5.59/5.62 (succ(succ(succ(succ(X6!49)))) = n6),
% 5.59/5.62 inference(transitivity,[status(thm)],[6495, 30])).
% 5.59/5.62 tff(6497,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(X6!49))))) = succ(n6)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6496])).
% 5.59/5.62 tff(6498,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(X6!49))))) = n7),
% 5.59/5.62 inference(transitivity,[status(thm)],[6497, 39])).
% 5.59/5.62 tff(6499,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n7)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6498])).
% 5.59/5.62 tff(6500,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n8),
% 5.59/5.62 inference(transitivity,[status(thm)],[6499, 53])).
% 5.59/5.62 tff(6501,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n8)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6500])).
% 5.59/5.62 tff(6502,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n9),
% 5.59/5.62 inference(transitivity,[status(thm)],[6501, 45])).
% 5.59/5.62 tff(6503,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n9)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6502])).
% 5.59/5.62 tff(6504,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n10),
% 5.59/5.62 inference(transitivity,[status(thm)],[6503, 28])).
% 5.59/5.62 tff(6505,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n10)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6504])).
% 5.59/5.62 tff(6506,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n0),
% 5.59/5.62 inference(transitivity,[status(thm)],[6505, 42])).
% 5.59/5.62 tff(6507,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n0)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6506])).
% 5.59/5.62 tff(6508,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6507, 58])).
% 5.59/5.62 tff(6509,plain,
% 5.59/5.62 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n1)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6508])).
% 5.59/5.62 tff(6510,plain,
% 5.59/5.62 (NSX6!13 = n2),
% 5.59/5.62 inference(transitivity,[status(thm)],[1550, 6509, 36])).
% 5.59/5.62 tff(6511,plain,
% 5.59/5.62 (pred(NSX6!13) = pred(n2)),
% 5.59/5.62 inference(monotonicity,[status(thm)],[6510])).
% 5.59/5.62 tff(6512,plain,
% 5.59/5.62 (pred(NSX6!13) = n1),
% 5.59/5.62 inference(transitivity,[status(thm)],[6511, 24])).
% 5.59/5.63 tff(6513,plain,
% 5.59/5.63 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n1, n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6512, 6488])).
% 5.59/5.63 tff(6514,plain,
% 5.59/5.63 (sum(n1, n7) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.59/5.63 inference(symmetry,[status(thm)],[6513])).
% 5.59/5.63 tff(6515,plain,
% 5.59/5.63 (n8 = sum(n1, n7)),
% 5.59/5.63 inference(symmetry,[status(thm)],[791])).
% 5.59/5.63 tff(6516,plain,
% 5.59/5.63 (sum(pred(Y6!48), succ(X6!49)) = sum(n1, n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6408, 6490])).
% 5.59/5.63 tff(6517,plain,
% 5.59/5.63 (sum(pred(Y6!48), succ(X6!49)) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6516, 47])).
% 5.59/5.63 tff(6518,plain,
% 5.59/5.63 (sum(pred(X6!49), succ(Y6!48)) = sum(n1, n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6464, 6432])).
% 5.59/5.63 tff(6519,plain,
% 5.59/5.63 (sum(pred(X6!49), succ(Y6!48)) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6518, 47])).
% 5.59/5.63 tff(6520,plain,
% 5.59/5.63 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n4, n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6519, 6517])).
% 5.59/5.63 tff(6521,plain,
% 5.59/5.63 (X7!47 = Y7!46),
% 5.59/5.63 inference(transitivity,[status(thm)],[785, 6520, 46, 6515, 6514, 794])).
% 5.59/5.63 tff(6522,plain,
% 5.59/5.63 ($false),
% 5.59/5.63 inference(unit_resolution,[status(thm)],[792, 6521])).
% 5.59/5.63 tff(6523,plain,((~(X0!61 = n9)) | (X7!47 = Y7!46) | (~(Y0!60 = n3))), inference(lemma,lemma(discharge,[]))).
% 5.59/5.63 tff(6524,plain,
% 5.59/5.63 (~(X0!61 = n9)),
% 5.59/5.63 inference(unit_resolution,[status(thm)],[6523, 80, 792])).
% 5.59/5.63 tff(6525,plain,
% 5.59/5.63 (sum(n0, n6) = n6),
% 5.59/5.63 inference(and_elim,[status(thm)],[9])).
% 5.59/5.63 tff(6526,plain,
% 5.59/5.63 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n0, n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[3792, 146])).
% 5.59/5.63 tff(6527,plain,
% 5.59/5.63 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6526, 6525])).
% 5.59/5.63 tff(6528,plain,
% 5.59/5.63 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n9, n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[3818, 6527])).
% 5.59/5.63 tff(6529,plain,
% 5.59/5.63 (Y1!58 = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[196, 6528, 3874])).
% 5.59/5.63 tff(6530,plain,
% 5.59/5.63 (pred(Y1!58) = pred(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6529])).
% 5.59/5.63 tff(6531,plain,
% 5.59/5.63 (pred(Y1!58) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6530, 15])).
% 5.59/5.63 tff(6532,plain,
% 5.59/5.63 (pred(pred(Y1!58)) = pred(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6531])).
% 5.59/5.63 tff(6533,plain,
% 5.59/5.63 (pred(pred(Y1!58)) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6532, 25])).
% 5.59/5.63 tff(6534,plain,
% 5.59/5.63 (pred(pred(pred(Y1!58))) = pred(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6533])).
% 5.59/5.63 tff(6535,plain,
% 5.59/5.63 (pred(pred(pred(Y1!58))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6534, 24])).
% 5.59/5.63 tff(6536,plain,
% 5.59/5.63 (pred(pred(pred(pred(Y1!58)))) = pred(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6535])).
% 5.59/5.63 tff(6537,plain,
% 5.59/5.63 (pred(pred(pred(pred(Y1!58)))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6536, 23])).
% 5.59/5.63 tff(6538,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6537])).
% 5.59/5.63 tff(6539,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(Y1!58))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6538, 22])).
% 5.59/5.63 tff(6540,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6539])).
% 5.59/5.63 tff(6541,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6540, 21])).
% 5.59/5.63 tff(6542,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6541])).
% 5.59/5.63 tff(6543,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6542, 20])).
% 5.59/5.63 tff(6544,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6543])).
% 5.59/5.63 tff(6545,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6544, 19])).
% 5.59/5.63 tff(6546,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6545])).
% 5.59/5.63 tff(6547,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6546, 18])).
% 5.59/5.63 tff(6548,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6547])).
% 5.59/5.63 tff(6549,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6548, 17])).
% 5.59/5.63 tff(6550,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6549])).
% 5.59/5.63 tff(6551,plain,
% 5.59/5.63 (NPY1!34 = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[232, 6550, 16])).
% 5.59/5.63 tff(6552,plain,
% 5.59/5.63 (succ(NPY1!34) = succ(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6551])).
% 5.59/5.63 tff(6553,plain,
% 5.59/5.63 (succ(NPY1!34) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6552, 33])).
% 5.59/5.63 tff(6554,plain,
% 5.59/5.63 (succ(Y1!58) = succ(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6529])).
% 5.59/5.63 tff(6555,plain,
% 5.59/5.63 (succ(Y1!58) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6554, 33])).
% 5.59/5.63 tff(6556,plain,
% 5.59/5.63 (succ(succ(Y1!58)) = succ(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6555])).
% 5.59/5.63 tff(6557,plain,
% 5.59/5.63 (succ(succ(Y1!58)) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6556, 30])).
% 5.59/5.63 tff(6558,plain,
% 5.59/5.63 (succ(succ(succ(Y1!58))) = succ(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6557])).
% 5.59/5.63 tff(6559,plain,
% 5.59/5.63 (succ(succ(succ(Y1!58))) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6558, 39])).
% 5.59/5.63 tff(6560,plain,
% 5.59/5.63 (succ(succ(succ(succ(Y1!58)))) = succ(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6559])).
% 5.59/5.63 tff(6561,plain,
% 5.59/5.63 (succ(succ(succ(succ(Y1!58)))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6560, 53])).
% 5.59/5.63 tff(6562,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6561])).
% 5.59/5.63 tff(6563,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(Y1!58))))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6562, 45])).
% 5.59/5.63 tff(6564,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6563])).
% 5.59/5.63 tff(6565,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6564, 28])).
% 5.59/5.63 tff(6566,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6565])).
% 5.59/5.63 tff(6567,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6566, 42])).
% 5.59/5.63 tff(6568,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6567])).
% 5.59/5.63 tff(6569,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6568, 58])).
% 5.59/5.63 tff(6570,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6569])).
% 5.59/5.63 tff(6571,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6570, 36])).
% 5.59/5.63 tff(6572,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6571])).
% 5.59/5.63 tff(6573,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6572, 48])).
% 5.59/5.63 tff(6574,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6573])).
% 5.59/5.63 tff(6575,plain,
% 5.59/5.63 (NSY1!32 = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[255, 6574, 14])).
% 5.59/5.63 tff(6576,plain,
% 5.59/5.63 (pred(NSY1!32) = pred(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6575])).
% 5.59/5.63 tff(6577,plain,
% 5.59/5.63 (pred(NSY1!32) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6576, 15])).
% 5.59/5.63 tff(6578,plain,
% 5.59/5.63 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n3, n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6577, 6553])).
% 5.59/5.63 tff(6579,plain,
% 5.59/5.63 (sum(pred(NSY1!32), succ(NPY1!34)) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6578, 32])).
% 5.59/5.63 tff(6580,plain,
% 5.59/5.63 (sum(n2, n0) = n2),
% 5.59/5.63 inference(and_elim,[status(thm)],[9])).
% 5.59/5.63 tff(6581,plain,
% 5.59/5.63 (sum(pred(Y0!60), succ(X0!61)) = sum(n2, n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[82, 3796])).
% 5.59/5.63 tff(6582,plain,
% 5.59/5.63 (sum(pred(Y0!60), succ(X0!61)) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6581, 6580])).
% 5.59/5.63 tff(6583,plain,
% 5.59/5.63 (sum(n9, n4) = n2),
% 5.59/5.63 inference(and_elim,[status(thm)],[9])).
% 5.59/5.63 tff(6584,plain,
% 5.59/5.63 (sum(pred(X0!61), succ(Y0!60)) = sum(n9, n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[3770, 87])).
% 5.59/5.63 tff(6585,plain,
% 5.59/5.63 (sum(pred(X0!61), succ(Y0!60)) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6584, 6583])).
% 5.59/5.63 tff(6586,plain,
% 5.59/5.63 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n2, n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6585, 6582])).
% 5.59/5.63 tff(6587,plain,
% 5.59/5.63 (X1!59 = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[93, 6586, 34])).
% 5.59/5.63 tff(6588,plain,
% 5.59/5.63 (pred(X1!59) = pred(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6587])).
% 5.59/5.63 tff(6589,plain,
% 5.59/5.63 (pred(X1!59) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6588, 15])).
% 5.59/5.63 tff(6590,plain,
% 5.59/5.63 (pred(pred(X1!59)) = pred(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6589])).
% 5.59/5.63 tff(6591,plain,
% 5.59/5.63 (pred(pred(X1!59)) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6590, 25])).
% 5.59/5.63 tff(6592,plain,
% 5.59/5.63 (pred(pred(pred(X1!59))) = pred(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6591])).
% 5.59/5.63 tff(6593,plain,
% 5.59/5.63 (pred(pred(pred(X1!59))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6592, 24])).
% 5.59/5.63 tff(6594,plain,
% 5.59/5.63 (pred(pred(pred(pred(X1!59)))) = pred(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6593])).
% 5.59/5.63 tff(6595,plain,
% 5.59/5.63 (pred(pred(pred(pred(X1!59)))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6594, 23])).
% 5.59/5.63 tff(6596,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(X1!59))))) = pred(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6595])).
% 5.59/5.63 tff(6597,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(X1!59))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6596, 22])).
% 5.59/5.63 tff(6598,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6597])).
% 5.59/5.63 tff(6599,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6598, 21])).
% 5.59/5.63 tff(6600,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6599])).
% 5.59/5.63 tff(6601,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6600, 20])).
% 5.59/5.63 tff(6602,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6601])).
% 5.59/5.63 tff(6603,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6602, 19])).
% 5.59/5.63 tff(6604,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6603])).
% 5.59/5.63 tff(6605,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6604, 18])).
% 5.59/5.63 tff(6606,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6605])).
% 5.59/5.63 tff(6607,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6606, 17])).
% 5.59/5.63 tff(6608,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6607])).
% 5.59/5.63 tff(6609,plain,
% 5.59/5.63 (NPX1!35 = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[280, 6608, 16])).
% 5.59/5.63 tff(6610,plain,
% 5.59/5.63 (succ(NPX1!35) = succ(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6609])).
% 5.59/5.63 tff(6611,plain,
% 5.59/5.63 (succ(NPX1!35) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6610, 33])).
% 5.59/5.63 tff(6612,plain,
% 5.59/5.63 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n5, n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6611, 6579])).
% 5.59/5.63 tff(6613,plain,
% 5.59/5.63 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6612, 558])).
% 5.59/5.63 tff(6614,plain,
% 5.59/5.63 (succ(X1!59) = succ(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6587])).
% 5.59/5.63 tff(6615,plain,
% 5.59/5.63 (succ(X1!59) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6614, 33])).
% 5.59/5.63 tff(6616,plain,
% 5.59/5.63 (succ(succ(X1!59)) = succ(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6615])).
% 5.59/5.63 tff(6617,plain,
% 5.59/5.63 (succ(succ(X1!59)) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6616, 30])).
% 5.59/5.63 tff(6618,plain,
% 5.59/5.63 (succ(succ(succ(X1!59))) = succ(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6617])).
% 5.59/5.63 tff(6619,plain,
% 5.59/5.63 (succ(succ(succ(X1!59))) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6618, 39])).
% 5.59/5.63 tff(6620,plain,
% 5.59/5.63 (succ(succ(succ(succ(X1!59)))) = succ(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6619])).
% 5.59/5.63 tff(6621,plain,
% 5.59/5.63 (succ(succ(succ(succ(X1!59)))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6620, 53])).
% 5.59/5.63 tff(6622,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(X1!59))))) = succ(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6621])).
% 5.59/5.63 tff(6623,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(X1!59))))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6622, 45])).
% 5.59/5.63 tff(6624,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6623])).
% 5.59/5.63 tff(6625,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6624, 28])).
% 5.59/5.63 tff(6626,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6625])).
% 5.59/5.63 tff(6627,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6626, 42])).
% 5.59/5.63 tff(6628,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6627])).
% 5.59/5.63 tff(6629,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6628, 58])).
% 5.59/5.63 tff(6630,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6629])).
% 5.59/5.63 tff(6631,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6630, 36])).
% 5.59/5.63 tff(6632,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6631])).
% 5.59/5.63 tff(6633,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6632, 48])).
% 5.59/5.63 tff(6634,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6633])).
% 5.59/5.63 tff(6635,plain,
% 5.59/5.63 (NSX1!33 = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[305, 6634, 14])).
% 5.59/5.63 tff(6636,plain,
% 5.59/5.63 (pred(NSX1!33) = pred(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6635])).
% 5.59/5.63 tff(6637,plain,
% 5.59/5.63 (pred(NSX1!33) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6636, 15])).
% 5.59/5.63 tff(6638,plain,
% 5.59/5.63 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n3, n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6637, 6613])).
% 5.59/5.63 tff(6639,plain,
% 5.59/5.63 (Y2!56 = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[310, 6638, 557])).
% 5.59/5.63 tff(6640,plain,
% 5.59/5.63 (pred(Y2!56) = pred(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6639])).
% 5.59/5.63 tff(6641,plain,
% 5.59/5.63 (pred(Y2!56) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6640, 16])).
% 5.59/5.63 tff(6642,plain,
% 5.59/5.63 (pred(pred(Y2!56)) = pred(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6641])).
% 5.59/5.63 tff(6643,plain,
% 5.59/5.63 (pred(pred(Y2!56)) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6642, 15])).
% 5.59/5.63 tff(6644,plain,
% 5.59/5.63 (pred(pred(pred(Y2!56))) = pred(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6643])).
% 5.59/5.63 tff(6645,plain,
% 5.59/5.63 (pred(pred(pred(Y2!56))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6644, 25])).
% 5.59/5.63 tff(6646,plain,
% 5.59/5.63 (pred(pred(pred(pred(Y2!56)))) = pred(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6645])).
% 5.59/5.63 tff(6647,plain,
% 5.59/5.63 (pred(pred(pred(pred(Y2!56)))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6646, 24])).
% 5.59/5.63 tff(6648,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6647])).
% 5.59/5.63 tff(6649,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(Y2!56))))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6648, 23])).
% 5.59/5.63 tff(6650,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6649])).
% 5.59/5.63 tff(6651,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6650, 22])).
% 5.59/5.63 tff(6652,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6651])).
% 5.59/5.63 tff(6653,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6652, 21])).
% 5.59/5.63 tff(6654,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6653])).
% 5.59/5.63 tff(6655,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6654, 20])).
% 5.59/5.63 tff(6656,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6655])).
% 5.59/5.63 tff(6657,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6656, 19])).
% 5.59/5.63 tff(6658,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6657])).
% 5.59/5.63 tff(6659,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6658, 18])).
% 5.59/5.63 tff(6660,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6659])).
% 5.59/5.63 tff(6661,plain,
% 5.59/5.63 (NPY2!30 = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[347, 6660, 17])).
% 5.59/5.63 tff(6662,plain,
% 5.59/5.63 (succ(NPY2!30) = succ(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6661])).
% 5.59/5.63 tff(6663,plain,
% 5.59/5.63 (succ(NPY2!30) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6662, 30])).
% 5.59/5.63 tff(6664,plain,
% 5.59/5.63 (succ(Y2!56) = succ(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6639])).
% 5.59/5.63 tff(6665,plain,
% 5.59/5.63 (succ(Y2!56) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6664, 30])).
% 5.59/5.63 tff(6666,plain,
% 5.59/5.63 (succ(succ(Y2!56)) = succ(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6665])).
% 5.59/5.63 tff(6667,plain,
% 5.59/5.63 (succ(succ(Y2!56)) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6666, 39])).
% 5.59/5.63 tff(6668,plain,
% 5.59/5.63 (succ(succ(succ(Y2!56))) = succ(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6667])).
% 5.59/5.63 tff(6669,plain,
% 5.59/5.63 (succ(succ(succ(Y2!56))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6668, 53])).
% 5.59/5.63 tff(6670,plain,
% 5.59/5.63 (succ(succ(succ(succ(Y2!56)))) = succ(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6669])).
% 5.59/5.63 tff(6671,plain,
% 5.59/5.63 (succ(succ(succ(succ(Y2!56)))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6670, 45])).
% 5.59/5.63 tff(6672,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6671])).
% 5.59/5.63 tff(6673,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(Y2!56))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6672, 28])).
% 5.59/5.63 tff(6674,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6673])).
% 5.59/5.63 tff(6675,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6674, 42])).
% 5.59/5.63 tff(6676,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6675])).
% 5.59/5.63 tff(6677,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6676, 58])).
% 5.59/5.63 tff(6678,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6677])).
% 5.59/5.63 tff(6679,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6678, 36])).
% 5.59/5.63 tff(6680,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6679])).
% 5.59/5.63 tff(6681,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6680, 48])).
% 5.59/5.63 tff(6682,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6681])).
% 5.59/5.63 tff(6683,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6682, 14])).
% 5.59/5.63 tff(6684,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6683])).
% 5.59/5.63 tff(6685,plain,
% 5.59/5.63 (NSY2!28 = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[370, 6684, 33])).
% 5.59/5.63 tff(6686,plain,
% 5.59/5.63 (pred(NSY2!28) = pred(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6685])).
% 5.59/5.63 tff(6687,plain,
% 5.59/5.63 (pred(NSY2!28) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6686, 16])).
% 5.59/5.63 tff(6688,plain,
% 5.59/5.63 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n4, n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6687, 6663])).
% 5.59/5.63 tff(6689,plain,
% 5.59/5.63 (sum(pred(NSY2!28), succ(NPY2!30)) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6688, 12])).
% 5.59/5.63 tff(6690,plain,
% 5.59/5.63 (sum(pred(Y1!58), succ(X1!59)) = sum(n3, n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6531, 6615])).
% 5.59/5.63 tff(6691,plain,
% 5.59/5.63 (sum(pred(Y1!58), succ(X1!59)) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6690, 32])).
% 5.59/5.63 tff(6692,plain,
% 5.59/5.63 (sum(pred(X1!59), succ(Y1!58)) = sum(n3, n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6589, 6555])).
% 5.59/5.63 tff(6693,plain,
% 5.59/5.63 (sum(pred(X1!59), succ(Y1!58)) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6692, 32])).
% 5.59/5.63 tff(6694,plain,
% 5.59/5.63 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n8, n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6693, 6691])).
% 5.59/5.63 tff(6695,plain,
% 5.59/5.63 (X2!57 = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[209, 6694, 31])).
% 5.59/5.63 tff(6696,plain,
% 5.59/5.63 (pred(X2!57) = pred(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6695])).
% 5.59/5.63 tff(6697,plain,
% 5.59/5.63 (pred(X2!57) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6696, 16])).
% 5.59/5.63 tff(6698,plain,
% 5.59/5.63 (pred(pred(X2!57)) = pred(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6697])).
% 5.59/5.63 tff(6699,plain,
% 5.59/5.63 (pred(pred(X2!57)) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6698, 15])).
% 5.59/5.63 tff(6700,plain,
% 5.59/5.63 (pred(pred(pred(X2!57))) = pred(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6699])).
% 5.59/5.63 tff(6701,plain,
% 5.59/5.63 (pred(pred(pred(X2!57))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6700, 25])).
% 5.59/5.63 tff(6702,plain,
% 5.59/5.63 (pred(pred(pred(pred(X2!57)))) = pred(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6701])).
% 5.59/5.63 tff(6703,plain,
% 5.59/5.63 (pred(pred(pred(pred(X2!57)))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6702, 24])).
% 5.59/5.63 tff(6704,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(X2!57))))) = pred(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6703])).
% 5.59/5.63 tff(6705,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(X2!57))))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6704, 23])).
% 5.59/5.63 tff(6706,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6705])).
% 5.59/5.63 tff(6707,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6706, 22])).
% 5.59/5.63 tff(6708,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6707])).
% 5.59/5.63 tff(6709,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6708, 21])).
% 5.59/5.63 tff(6710,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6709])).
% 5.59/5.63 tff(6711,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6710, 20])).
% 5.59/5.63 tff(6712,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6711])).
% 5.59/5.63 tff(6713,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6712, 19])).
% 5.59/5.63 tff(6714,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6713])).
% 5.59/5.63 tff(6715,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6714, 18])).
% 5.59/5.63 tff(6716,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6715])).
% 5.59/5.63 tff(6717,plain,
% 5.59/5.63 (NPX2!31 = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[395, 6716, 17])).
% 5.59/5.63 tff(6718,plain,
% 5.59/5.63 (succ(NPX2!31) = succ(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6717])).
% 5.59/5.63 tff(6719,plain,
% 5.59/5.63 (succ(NPX2!31) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6718, 30])).
% 5.59/5.63 tff(6720,plain,
% 5.59/5.63 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n6, n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6719, 6689])).
% 5.59/5.63 tff(6721,plain,
% 5.59/5.63 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6720, 674])).
% 5.59/5.63 tff(6722,plain,
% 5.59/5.63 (succ(X2!57) = succ(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6695])).
% 5.59/5.63 tff(6723,plain,
% 5.59/5.63 (succ(X2!57) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6722, 30])).
% 5.59/5.63 tff(6724,plain,
% 5.59/5.63 (succ(succ(X2!57)) = succ(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6723])).
% 5.59/5.63 tff(6725,plain,
% 5.59/5.63 (succ(succ(X2!57)) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6724, 39])).
% 5.59/5.63 tff(6726,plain,
% 5.59/5.63 (succ(succ(succ(X2!57))) = succ(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6725])).
% 5.59/5.63 tff(6727,plain,
% 5.59/5.63 (succ(succ(succ(X2!57))) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6726, 53])).
% 5.59/5.63 tff(6728,plain,
% 5.59/5.63 (succ(succ(succ(succ(X2!57)))) = succ(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6727])).
% 5.59/5.63 tff(6729,plain,
% 5.59/5.63 (succ(succ(succ(succ(X2!57)))) = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[6728, 45])).
% 5.59/5.63 tff(6730,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(X2!57))))) = succ(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6729])).
% 5.59/5.63 tff(6731,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(X2!57))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6730, 28])).
% 5.59/5.63 tff(6732,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6731])).
% 5.59/5.63 tff(6733,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6732, 42])).
% 5.59/5.63 tff(6734,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6733])).
% 5.59/5.63 tff(6735,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6734, 58])).
% 5.59/5.63 tff(6736,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6735])).
% 5.59/5.63 tff(6737,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6736, 36])).
% 5.59/5.63 tff(6738,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6737])).
% 5.59/5.63 tff(6739,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6738, 48])).
% 5.59/5.63 tff(6740,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6739])).
% 5.59/5.63 tff(6741,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6740, 14])).
% 5.59/5.63 tff(6742,plain,
% 5.59/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6741])).
% 5.59/5.63 tff(6743,plain,
% 5.59/5.63 (NSX2!29 = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[420, 6742, 33])).
% 5.59/5.63 tff(6744,plain,
% 5.59/5.63 (pred(NSX2!29) = pred(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6743])).
% 5.59/5.63 tff(6745,plain,
% 5.59/5.63 (pred(NSX2!29) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6744, 16])).
% 5.59/5.63 tff(6746,plain,
% 5.59/5.63 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n4, n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6745, 6721])).
% 5.59/5.63 tff(6747,plain,
% 5.59/5.63 (Y3!54 = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[425, 6746, 673])).
% 5.59/5.63 tff(6748,plain,
% 5.59/5.63 (pred(Y3!54) = pred(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6747])).
% 5.59/5.63 tff(6749,plain,
% 5.59/5.63 (pred(Y3!54) = n8),
% 5.59/5.63 inference(transitivity,[status(thm)],[6748, 20])).
% 5.59/5.63 tff(6750,plain,
% 5.59/5.63 (pred(pred(Y3!54)) = pred(n8)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6749])).
% 5.59/5.63 tff(6751,plain,
% 5.59/5.63 (pred(pred(Y3!54)) = n7),
% 5.59/5.63 inference(transitivity,[status(thm)],[6750, 19])).
% 5.59/5.63 tff(6752,plain,
% 5.59/5.63 (pred(pred(pred(Y3!54))) = pred(n7)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6751])).
% 5.59/5.63 tff(6753,plain,
% 5.59/5.63 (pred(pred(pred(Y3!54))) = n6),
% 5.59/5.63 inference(transitivity,[status(thm)],[6752, 18])).
% 5.59/5.63 tff(6754,plain,
% 5.59/5.63 (pred(pred(pred(pred(Y3!54)))) = pred(n6)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6753])).
% 5.59/5.63 tff(6755,plain,
% 5.59/5.63 (pred(pred(pred(pred(Y3!54)))) = n5),
% 5.59/5.63 inference(transitivity,[status(thm)],[6754, 17])).
% 5.59/5.63 tff(6756,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n5)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6755])).
% 5.59/5.63 tff(6757,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(Y3!54))))) = n4),
% 5.59/5.63 inference(transitivity,[status(thm)],[6756, 16])).
% 5.59/5.63 tff(6758,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n4)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6757])).
% 5.59/5.63 tff(6759,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n3),
% 5.59/5.63 inference(transitivity,[status(thm)],[6758, 15])).
% 5.59/5.63 tff(6760,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n3)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6759])).
% 5.59/5.63 tff(6761,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n2),
% 5.59/5.63 inference(transitivity,[status(thm)],[6760, 25])).
% 5.59/5.63 tff(6762,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n2)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6761])).
% 5.59/5.63 tff(6763,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n1),
% 5.59/5.63 inference(transitivity,[status(thm)],[6762, 24])).
% 5.59/5.63 tff(6764,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n1)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6763])).
% 5.59/5.63 tff(6765,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n0),
% 5.59/5.63 inference(transitivity,[status(thm)],[6764, 23])).
% 5.59/5.63 tff(6766,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n0)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6765])).
% 5.59/5.63 tff(6767,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6766, 22])).
% 5.59/5.63 tff(6768,plain,
% 5.59/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n10)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6767])).
% 5.59/5.63 tff(6769,plain,
% 5.59/5.63 (NPY3!26 = n9),
% 5.59/5.63 inference(transitivity,[status(thm)],[462, 6768, 21])).
% 5.59/5.63 tff(6770,plain,
% 5.59/5.63 (succ(NPY3!26) = succ(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6769])).
% 5.59/5.63 tff(6771,plain,
% 5.59/5.63 (succ(NPY3!26) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6770, 28])).
% 5.59/5.63 tff(6772,plain,
% 5.59/5.63 (succ(Y3!54) = succ(n9)),
% 5.59/5.63 inference(monotonicity,[status(thm)],[6747])).
% 5.59/5.63 tff(6773,plain,
% 5.59/5.63 (succ(Y3!54) = n10),
% 5.59/5.63 inference(transitivity,[status(thm)],[6772, 28])).
% 5.59/5.63 tff(6774,plain,
% 5.59/5.63 (succ(succ(Y3!54)) = succ(n10)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6773])).
% 5.70/5.63 tff(6775,plain,
% 5.70/5.63 (succ(succ(Y3!54)) = n0),
% 5.70/5.63 inference(transitivity,[status(thm)],[6774, 42])).
% 5.70/5.63 tff(6776,plain,
% 5.70/5.63 (succ(succ(succ(Y3!54))) = succ(n0)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6775])).
% 5.70/5.63 tff(6777,plain,
% 5.70/5.63 (succ(succ(succ(Y3!54))) = n1),
% 5.70/5.63 inference(transitivity,[status(thm)],[6776, 58])).
% 5.70/5.63 tff(6778,plain,
% 5.70/5.63 (succ(succ(succ(succ(Y3!54)))) = succ(n1)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6777])).
% 5.70/5.63 tff(6779,plain,
% 5.70/5.63 (succ(succ(succ(succ(Y3!54)))) = n2),
% 5.70/5.63 inference(transitivity,[status(thm)],[6778, 36])).
% 5.70/5.63 tff(6780,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n2)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6779])).
% 5.70/5.63 tff(6781,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(Y3!54))))) = n3),
% 5.70/5.63 inference(transitivity,[status(thm)],[6780, 48])).
% 5.70/5.63 tff(6782,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n3)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6781])).
% 5.70/5.63 tff(6783,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n4),
% 5.70/5.63 inference(transitivity,[status(thm)],[6782, 14])).
% 5.70/5.63 tff(6784,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n4)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6783])).
% 5.70/5.63 tff(6785,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n5),
% 5.70/5.63 inference(transitivity,[status(thm)],[6784, 33])).
% 5.70/5.63 tff(6786,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n5)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6785])).
% 5.70/5.63 tff(6787,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n6),
% 5.70/5.63 inference(transitivity,[status(thm)],[6786, 30])).
% 5.70/5.63 tff(6788,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n6)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6787])).
% 5.70/5.63 tff(6789,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n7),
% 5.70/5.63 inference(transitivity,[status(thm)],[6788, 39])).
% 5.70/5.63 tff(6790,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n7)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6789])).
% 5.70/5.63 tff(6791,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n8),
% 5.70/5.63 inference(transitivity,[status(thm)],[6790, 53])).
% 5.70/5.63 tff(6792,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n8)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6791])).
% 5.70/5.63 tff(6793,plain,
% 5.70/5.63 (NSY3!24 = n9),
% 5.70/5.63 inference(transitivity,[status(thm)],[485, 6792, 45])).
% 5.70/5.63 tff(6794,plain,
% 5.70/5.63 (pred(NSY3!24) = pred(n9)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6793])).
% 5.70/5.63 tff(6795,plain,
% 5.70/5.63 (pred(NSY3!24) = n8),
% 5.70/5.63 inference(transitivity,[status(thm)],[6794, 20])).
% 5.70/5.63 tff(6796,plain,
% 5.70/5.63 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n8, n10)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6795, 6771])).
% 5.70/5.63 tff(6797,plain,
% 5.70/5.63 (sum(pred(NSY3!24), succ(NPY3!26)) = n7),
% 5.70/5.63 inference(transitivity,[status(thm)],[6796, 27])).
% 5.70/5.63 tff(6798,plain,
% 5.70/5.63 (sum(pred(Y2!56), succ(X2!57)) = sum(n4, n6)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6641, 6723])).
% 5.70/5.63 tff(6799,plain,
% 5.70/5.63 (sum(pred(Y2!56), succ(X2!57)) = n10),
% 5.70/5.63 inference(transitivity,[status(thm)],[6798, 12])).
% 5.70/5.63 tff(6800,plain,
% 5.70/5.63 (sum(pred(X2!57), succ(Y2!56)) = sum(n4, n6)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6697, 6665])).
% 5.70/5.63 tff(6801,plain,
% 5.70/5.63 (sum(pred(X2!57), succ(Y2!56)) = n10),
% 5.70/5.63 inference(transitivity,[status(thm)],[6800, 12])).
% 5.70/5.63 tff(6802,plain,
% 5.70/5.63 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n10, n10)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6801, 6799])).
% 5.70/5.63 tff(6803,plain,
% 5.70/5.63 (X3!55 = n9),
% 5.70/5.63 inference(transitivity,[status(thm)],[323, 6802, 29])).
% 5.70/5.63 tff(6804,plain,
% 5.70/5.63 (pred(X3!55) = pred(n9)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6803])).
% 5.70/5.63 tff(6805,plain,
% 5.70/5.63 (pred(X3!55) = n8),
% 5.70/5.63 inference(transitivity,[status(thm)],[6804, 20])).
% 5.70/5.63 tff(6806,plain,
% 5.70/5.63 (pred(pred(X3!55)) = pred(n8)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6805])).
% 5.70/5.63 tff(6807,plain,
% 5.70/5.63 (pred(pred(X3!55)) = n7),
% 5.70/5.63 inference(transitivity,[status(thm)],[6806, 19])).
% 5.70/5.63 tff(6808,plain,
% 5.70/5.63 (pred(pred(pred(X3!55))) = pred(n7)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6807])).
% 5.70/5.63 tff(6809,plain,
% 5.70/5.63 (pred(pred(pred(X3!55))) = n6),
% 5.70/5.63 inference(transitivity,[status(thm)],[6808, 18])).
% 5.70/5.63 tff(6810,plain,
% 5.70/5.63 (pred(pred(pred(pred(X3!55)))) = pred(n6)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6809])).
% 5.70/5.63 tff(6811,plain,
% 5.70/5.63 (pred(pred(pred(pred(X3!55)))) = n5),
% 5.70/5.63 inference(transitivity,[status(thm)],[6810, 17])).
% 5.70/5.63 tff(6812,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(X3!55))))) = pred(n5)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6811])).
% 5.70/5.63 tff(6813,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(X3!55))))) = n4),
% 5.70/5.63 inference(transitivity,[status(thm)],[6812, 16])).
% 5.70/5.63 tff(6814,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n4)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6813])).
% 5.70/5.63 tff(6815,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n3),
% 5.70/5.63 inference(transitivity,[status(thm)],[6814, 15])).
% 5.70/5.63 tff(6816,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n3)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6815])).
% 5.70/5.63 tff(6817,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n2),
% 5.70/5.63 inference(transitivity,[status(thm)],[6816, 25])).
% 5.70/5.63 tff(6818,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n2)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6817])).
% 5.70/5.63 tff(6819,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n1),
% 5.70/5.63 inference(transitivity,[status(thm)],[6818, 24])).
% 5.70/5.63 tff(6820,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n1)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6819])).
% 5.70/5.63 tff(6821,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n0),
% 5.70/5.63 inference(transitivity,[status(thm)],[6820, 23])).
% 5.70/5.63 tff(6822,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n0)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6821])).
% 5.70/5.63 tff(6823,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n10),
% 5.70/5.63 inference(transitivity,[status(thm)],[6822, 22])).
% 5.70/5.63 tff(6824,plain,
% 5.70/5.63 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n10)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6823])).
% 5.70/5.63 tff(6825,plain,
% 5.70/5.63 (NPX3!27 = n9),
% 5.70/5.63 inference(transitivity,[status(thm)],[510, 6824, 21])).
% 5.70/5.63 tff(6826,plain,
% 5.70/5.63 (succ(NPX3!27) = succ(n9)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6825])).
% 5.70/5.63 tff(6827,plain,
% 5.70/5.63 (succ(NPX3!27) = n10),
% 5.70/5.63 inference(transitivity,[status(thm)],[6826, 28])).
% 5.70/5.63 tff(6828,plain,
% 5.70/5.63 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n10, n7)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6827, 6797])).
% 5.70/5.63 tff(6829,plain,
% 5.70/5.63 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n6),
% 5.70/5.63 inference(transitivity,[status(thm)],[6828, 69])).
% 5.70/5.63 tff(6830,plain,
% 5.70/5.63 (succ(X3!55) = succ(n9)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6803])).
% 5.70/5.63 tff(6831,plain,
% 5.70/5.63 (succ(X3!55) = n10),
% 5.70/5.63 inference(transitivity,[status(thm)],[6830, 28])).
% 5.70/5.63 tff(6832,plain,
% 5.70/5.63 (succ(succ(X3!55)) = succ(n10)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6831])).
% 5.70/5.63 tff(6833,plain,
% 5.70/5.63 (succ(succ(X3!55)) = n0),
% 5.70/5.63 inference(transitivity,[status(thm)],[6832, 42])).
% 5.70/5.63 tff(6834,plain,
% 5.70/5.63 (succ(succ(succ(X3!55))) = succ(n0)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6833])).
% 5.70/5.63 tff(6835,plain,
% 5.70/5.63 (succ(succ(succ(X3!55))) = n1),
% 5.70/5.63 inference(transitivity,[status(thm)],[6834, 58])).
% 5.70/5.63 tff(6836,plain,
% 5.70/5.63 (succ(succ(succ(succ(X3!55)))) = succ(n1)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6835])).
% 5.70/5.63 tff(6837,plain,
% 5.70/5.63 (succ(succ(succ(succ(X3!55)))) = n2),
% 5.70/5.63 inference(transitivity,[status(thm)],[6836, 36])).
% 5.70/5.63 tff(6838,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(X3!55))))) = succ(n2)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6837])).
% 5.70/5.63 tff(6839,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(X3!55))))) = n3),
% 5.70/5.63 inference(transitivity,[status(thm)],[6838, 48])).
% 5.70/5.63 tff(6840,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n3)),
% 5.70/5.63 inference(monotonicity,[status(thm)],[6839])).
% 5.70/5.63 tff(6841,plain,
% 5.70/5.63 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n4),
% 5.70/5.63 inference(transitivity,[status(thm)],[6840, 14])).
% 5.70/5.64 tff(6842,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6841])).
% 5.70/5.64 tff(6843,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[6842, 33])).
% 5.70/5.64 tff(6844,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6843])).
% 5.70/5.64 tff(6845,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6844, 30])).
% 5.70/5.64 tff(6846,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6845])).
% 5.70/5.64 tff(6847,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6846, 39])).
% 5.70/5.64 tff(6848,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6847])).
% 5.70/5.64 tff(6849,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[6848, 53])).
% 5.70/5.64 tff(6850,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6849])).
% 5.70/5.64 tff(6851,plain,
% 5.70/5.64 (NSX3!25 = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[535, 6850, 45])).
% 5.70/5.64 tff(6852,plain,
% 5.70/5.64 (pred(NSX3!25) = pred(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6851])).
% 5.70/5.64 tff(6853,plain,
% 5.70/5.64 (pred(NSX3!25) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[6852, 20])).
% 5.70/5.64 tff(6854,plain,
% 5.70/5.64 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n8, n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6853, 6829])).
% 5.70/5.64 tff(6855,plain,
% 5.70/5.64 (Y4!52 = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[540, 6854, 98])).
% 5.70/5.64 tff(6856,plain,
% 5.70/5.64 (pred(Y4!52) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6855])).
% 5.70/5.64 tff(6857,plain,
% 5.70/5.64 (pred(Y4!52) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6856, 25])).
% 5.70/5.64 tff(6858,plain,
% 5.70/5.64 (pred(pred(Y4!52)) = pred(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6857])).
% 5.70/5.64 tff(6859,plain,
% 5.70/5.64 (pred(pred(Y4!52)) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[6858, 24])).
% 5.70/5.64 tff(6860,plain,
% 5.70/5.64 (pred(pred(pred(Y4!52))) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6859])).
% 5.70/5.64 tff(6861,plain,
% 5.70/5.64 (pred(pred(pred(Y4!52))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[6860, 23])).
% 5.70/5.64 tff(6862,plain,
% 5.70/5.64 (pred(pred(pred(pred(Y4!52)))) = pred(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6861])).
% 5.70/5.64 tff(6863,plain,
% 5.70/5.64 (pred(pred(pred(pred(Y4!52)))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[6862, 22])).
% 5.70/5.64 tff(6864,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6863])).
% 5.70/5.64 tff(6865,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(Y4!52))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[6864, 21])).
% 5.70/5.64 tff(6866,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6865])).
% 5.70/5.64 tff(6867,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[6866, 20])).
% 5.70/5.64 tff(6868,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6867])).
% 5.70/5.64 tff(6869,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6868, 19])).
% 5.70/5.64 tff(6870,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6869])).
% 5.70/5.64 tff(6871,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6870, 18])).
% 5.70/5.64 tff(6872,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6871])).
% 5.70/5.64 tff(6873,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[6872, 17])).
% 5.70/5.64 tff(6874,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6873])).
% 5.70/5.64 tff(6875,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6874, 16])).
% 5.70/5.64 tff(6876,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6875])).
% 5.70/5.64 tff(6877,plain,
% 5.70/5.64 (NPY4!22 = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[578, 6876, 15])).
% 5.70/5.64 tff(6878,plain,
% 5.70/5.64 (succ(NPY4!22) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6877])).
% 5.70/5.64 tff(6879,plain,
% 5.70/5.64 (succ(NPY4!22) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6878, 14])).
% 5.70/5.64 tff(6880,plain,
% 5.70/5.64 (succ(Y4!52) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6855])).
% 5.70/5.64 tff(6881,plain,
% 5.70/5.64 (succ(Y4!52) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6880, 14])).
% 5.70/5.64 tff(6882,plain,
% 5.70/5.64 (succ(succ(Y4!52)) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6881])).
% 5.70/5.64 tff(6883,plain,
% 5.70/5.64 (succ(succ(Y4!52)) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[6882, 33])).
% 5.70/5.64 tff(6884,plain,
% 5.70/5.64 (succ(succ(succ(Y4!52))) = succ(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6883])).
% 5.70/5.64 tff(6885,plain,
% 5.70/5.64 (succ(succ(succ(Y4!52))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6884, 30])).
% 5.70/5.64 tff(6886,plain,
% 5.70/5.64 (succ(succ(succ(succ(Y4!52)))) = succ(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6885])).
% 5.70/5.64 tff(6887,plain,
% 5.70/5.64 (succ(succ(succ(succ(Y4!52)))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6886, 39])).
% 5.70/5.64 tff(6888,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6887])).
% 5.70/5.64 tff(6889,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(Y4!52))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[6888, 53])).
% 5.70/5.64 tff(6890,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6889])).
% 5.70/5.64 tff(6891,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[6890, 45])).
% 5.70/5.64 tff(6892,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6891])).
% 5.70/5.64 tff(6893,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[6892, 28])).
% 5.70/5.64 tff(6894,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6893])).
% 5.70/5.64 tff(6895,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[6894, 42])).
% 5.70/5.64 tff(6896,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6895])).
% 5.70/5.64 tff(6897,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[6896, 58])).
% 5.70/5.64 tff(6898,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6897])).
% 5.70/5.64 tff(6899,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6898, 36])).
% 5.70/5.64 tff(6900,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6899])).
% 5.70/5.64 tff(6901,plain,
% 5.70/5.64 (NSY4!20 = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[601, 6900, 48])).
% 5.70/5.64 tff(6902,plain,
% 5.70/5.64 (pred(NSY4!20) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6901])).
% 5.70/5.64 tff(6903,plain,
% 5.70/5.64 (pred(NSY4!20) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6902, 25])).
% 5.70/5.64 tff(6904,plain,
% 5.70/5.64 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n2, n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6903, 6879])).
% 5.70/5.64 tff(6905,plain,
% 5.70/5.64 (sum(pred(NSY4!20), succ(NPY4!22)) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6904, 13])).
% 5.70/5.64 tff(6906,plain,
% 5.70/5.64 (sum(pred(Y3!54), succ(X3!55)) = sum(n8, n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6749, 6831])).
% 5.70/5.64 tff(6907,plain,
% 5.70/5.64 (sum(pred(Y3!54), succ(X3!55)) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6906, 27])).
% 5.70/5.64 tff(6908,plain,
% 5.70/5.64 (sum(pred(X3!55), succ(Y3!54)) = sum(n8, n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6805, 6773])).
% 5.70/5.64 tff(6909,plain,
% 5.70/5.64 (sum(pred(X3!55), succ(Y3!54)) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6908, 27])).
% 5.70/5.64 tff(6910,plain,
% 5.70/5.64 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n7, n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6909, 6907])).
% 5.70/5.64 tff(6911,plain,
% 5.70/5.64 (X4!53 = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[438, 6910, 26])).
% 5.70/5.64 tff(6912,plain,
% 5.70/5.64 (pred(X4!53) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6911])).
% 5.70/5.64 tff(6913,plain,
% 5.70/5.64 (pred(X4!53) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6912, 25])).
% 5.70/5.64 tff(6914,plain,
% 5.70/5.64 (pred(pred(X4!53)) = pred(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6913])).
% 5.70/5.64 tff(6915,plain,
% 5.70/5.64 (pred(pred(X4!53)) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[6914, 24])).
% 5.70/5.64 tff(6916,plain,
% 5.70/5.64 (pred(pred(pred(X4!53))) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6915])).
% 5.70/5.64 tff(6917,plain,
% 5.70/5.64 (pred(pred(pred(X4!53))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[6916, 23])).
% 5.70/5.64 tff(6918,plain,
% 5.70/5.64 (pred(pred(pred(pred(X4!53)))) = pred(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6917])).
% 5.70/5.64 tff(6919,plain,
% 5.70/5.64 (pred(pred(pred(pred(X4!53)))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[6918, 22])).
% 5.70/5.64 tff(6920,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(X4!53))))) = pred(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6919])).
% 5.70/5.64 tff(6921,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(X4!53))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[6920, 21])).
% 5.70/5.64 tff(6922,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6921])).
% 5.70/5.64 tff(6923,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[6922, 20])).
% 5.70/5.64 tff(6924,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6923])).
% 5.70/5.64 tff(6925,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6924, 19])).
% 5.70/5.64 tff(6926,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6925])).
% 5.70/5.64 tff(6927,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6926, 18])).
% 5.70/5.64 tff(6928,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6927])).
% 5.70/5.64 tff(6929,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[6928, 17])).
% 5.70/5.64 tff(6930,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6929])).
% 5.70/5.64 tff(6931,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6930, 16])).
% 5.70/5.64 tff(6932,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6931])).
% 5.70/5.64 tff(6933,plain,
% 5.70/5.64 (NPX4!23 = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[626, 6932, 15])).
% 5.70/5.64 tff(6934,plain,
% 5.70/5.64 (succ(NPX4!23) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6933])).
% 5.70/5.64 tff(6935,plain,
% 5.70/5.64 (succ(NPX4!23) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6934, 14])).
% 5.70/5.64 tff(6936,plain,
% 5.70/5.64 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n4, n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6935, 6905])).
% 5.70/5.64 tff(6937,plain,
% 5.70/5.64 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[6936, 12])).
% 5.70/5.64 tff(6938,plain,
% 5.70/5.64 (succ(X4!53) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6911])).
% 5.70/5.64 tff(6939,plain,
% 5.70/5.64 (succ(X4!53) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6938, 14])).
% 5.70/5.64 tff(6940,plain,
% 5.70/5.64 (succ(succ(X4!53)) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6939])).
% 5.70/5.64 tff(6941,plain,
% 5.70/5.64 (succ(succ(X4!53)) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[6940, 33])).
% 5.70/5.64 tff(6942,plain,
% 5.70/5.64 (succ(succ(succ(X4!53))) = succ(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6941])).
% 5.70/5.64 tff(6943,plain,
% 5.70/5.64 (succ(succ(succ(X4!53))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6942, 30])).
% 5.70/5.64 tff(6944,plain,
% 5.70/5.64 (succ(succ(succ(succ(X4!53)))) = succ(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6943])).
% 5.70/5.64 tff(6945,plain,
% 5.70/5.64 (succ(succ(succ(succ(X4!53)))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6944, 39])).
% 5.70/5.64 tff(6946,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(X4!53))))) = succ(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6945])).
% 5.70/5.64 tff(6947,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(X4!53))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[6946, 53])).
% 5.70/5.64 tff(6948,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6947])).
% 5.70/5.64 tff(6949,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[6948, 45])).
% 5.70/5.64 tff(6950,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6949])).
% 5.70/5.64 tff(6951,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[6950, 28])).
% 5.70/5.64 tff(6952,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6951])).
% 5.70/5.64 tff(6953,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[6952, 42])).
% 5.70/5.64 tff(6954,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6953])).
% 5.70/5.64 tff(6955,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[6954, 58])).
% 5.70/5.64 tff(6956,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6955])).
% 5.70/5.64 tff(6957,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6956, 36])).
% 5.70/5.64 tff(6958,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6957])).
% 5.70/5.64 tff(6959,plain,
% 5.70/5.64 (NSX4!21 = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[651, 6958, 48])).
% 5.70/5.64 tff(6960,plain,
% 5.70/5.64 (pred(NSX4!21) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6959])).
% 5.70/5.64 tff(6961,plain,
% 5.70/5.64 (pred(NSX4!21) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6960, 25])).
% 5.70/5.64 tff(6962,plain,
% 5.70/5.64 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n2, n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6961, 6937])).
% 5.70/5.64 tff(6963,plain,
% 5.70/5.64 (Y5!50 = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[656, 6962, 327])).
% 5.70/5.64 tff(6964,plain,
% 5.70/5.64 (pred(Y5!50) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6963])).
% 5.70/5.64 tff(6965,plain,
% 5.70/5.64 (pred(Y5!50) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[6964, 23])).
% 5.70/5.64 tff(6966,plain,
% 5.70/5.64 (pred(pred(Y5!50)) = pred(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6965])).
% 5.70/5.64 tff(6967,plain,
% 5.70/5.64 (pred(pred(Y5!50)) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[6966, 22])).
% 5.70/5.64 tff(6968,plain,
% 5.70/5.64 (pred(pred(pred(Y5!50))) = pred(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6967])).
% 5.70/5.64 tff(6969,plain,
% 5.70/5.64 (pred(pred(pred(Y5!50))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[6968, 21])).
% 5.70/5.64 tff(6970,plain,
% 5.70/5.64 (pred(pred(pred(pred(Y5!50)))) = pred(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6969])).
% 5.70/5.64 tff(6971,plain,
% 5.70/5.64 (pred(pred(pred(pred(Y5!50)))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[6970, 20])).
% 5.70/5.64 tff(6972,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6971])).
% 5.70/5.64 tff(6973,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(Y5!50))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6972, 19])).
% 5.70/5.64 tff(6974,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6973])).
% 5.70/5.64 tff(6975,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6974, 18])).
% 5.70/5.64 tff(6976,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6975])).
% 5.70/5.64 tff(6977,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[6976, 17])).
% 5.70/5.64 tff(6978,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6977])).
% 5.70/5.64 tff(6979,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6978, 16])).
% 5.70/5.64 tff(6980,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6979])).
% 5.70/5.64 tff(6981,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[6980, 15])).
% 5.70/5.64 tff(6982,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6981])).
% 5.70/5.64 tff(6983,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6982, 25])).
% 5.70/5.64 tff(6984,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6983])).
% 5.70/5.64 tff(6985,plain,
% 5.70/5.64 (NPY5!18 = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[694, 6984, 24])).
% 5.70/5.64 tff(6986,plain,
% 5.70/5.64 (succ(NPY5!18) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6985])).
% 5.70/5.64 tff(6987,plain,
% 5.70/5.64 (succ(NPY5!18) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6986, 36])).
% 5.70/5.64 tff(6988,plain,
% 5.70/5.64 (succ(Y5!50) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6963])).
% 5.70/5.64 tff(6989,plain,
% 5.70/5.64 (succ(Y5!50) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[6988, 36])).
% 5.70/5.64 tff(6990,plain,
% 5.70/5.64 (succ(succ(Y5!50)) = succ(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6989])).
% 5.70/5.64 tff(6991,plain,
% 5.70/5.64 (succ(succ(Y5!50)) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[6990, 48])).
% 5.70/5.64 tff(6992,plain,
% 5.70/5.64 (succ(succ(succ(Y5!50))) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6991])).
% 5.70/5.64 tff(6993,plain,
% 5.70/5.64 (succ(succ(succ(Y5!50))) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[6992, 14])).
% 5.70/5.64 tff(6994,plain,
% 5.70/5.64 (succ(succ(succ(succ(Y5!50)))) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6993])).
% 5.70/5.64 tff(6995,plain,
% 5.70/5.64 (succ(succ(succ(succ(Y5!50)))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[6994, 33])).
% 5.70/5.64 tff(6996,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6995])).
% 5.70/5.64 tff(6997,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(Y5!50))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[6996, 30])).
% 5.70/5.64 tff(6998,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6997])).
% 5.70/5.64 tff(6999,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[6998, 39])).
% 5.70/5.64 tff(7000,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6999])).
% 5.70/5.64 tff(7001,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7000, 53])).
% 5.70/5.64 tff(7002,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7001])).
% 5.70/5.64 tff(7003,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[7002, 45])).
% 5.70/5.64 tff(7004,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7003])).
% 5.70/5.64 tff(7005,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[7004, 28])).
% 5.70/5.64 tff(7006,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7005])).
% 5.70/5.64 tff(7007,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7006, 42])).
% 5.70/5.64 tff(7008,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7007])).
% 5.70/5.64 tff(7009,plain,
% 5.70/5.64 (NSY5!16 = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[717, 7008, 58])).
% 5.70/5.64 tff(7010,plain,
% 5.70/5.64 (pred(NSY5!16) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7009])).
% 5.70/5.64 tff(7011,plain,
% 5.70/5.64 (pred(NSY5!16) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7010, 23])).
% 5.70/5.64 tff(7012,plain,
% 5.70/5.64 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n0, n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7011, 6987])).
% 5.70/5.64 tff(7013,plain,
% 5.70/5.64 (sum(pred(NSY5!16), succ(NPY5!18)) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7012, 35])).
% 5.70/5.64 tff(7014,plain,
% 5.70/5.64 (sum(pred(Y4!52), succ(X4!53)) = sum(n2, n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6857, 6939])).
% 5.70/5.64 tff(7015,plain,
% 5.70/5.64 (sum(pred(Y4!52), succ(X4!53)) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7014, 13])).
% 5.70/5.64 tff(7016,plain,
% 5.70/5.64 (sum(pred(X4!53), succ(Y4!52)) = sum(n2, n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6913, 6881])).
% 5.70/5.64 tff(7017,plain,
% 5.70/5.64 (sum(pred(X4!53), succ(Y4!52)) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7016, 13])).
% 5.70/5.64 tff(7018,plain,
% 5.70/5.64 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n6, n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7017, 7015])).
% 5.70/5.64 tff(7019,plain,
% 5.70/5.64 (X5!51 = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[553, 7018, 37])).
% 5.70/5.64 tff(7020,plain,
% 5.70/5.64 (pred(X5!51) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7019])).
% 5.70/5.64 tff(7021,plain,
% 5.70/5.64 (pred(X5!51) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7020, 23])).
% 5.70/5.64 tff(7022,plain,
% 5.70/5.64 (pred(pred(X5!51)) = pred(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7021])).
% 5.70/5.64 tff(7023,plain,
% 5.70/5.64 (pred(pred(X5!51)) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[7022, 22])).
% 5.70/5.64 tff(7024,plain,
% 5.70/5.64 (pred(pred(pred(X5!51))) = pred(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7023])).
% 5.70/5.64 tff(7025,plain,
% 5.70/5.64 (pred(pred(pred(X5!51))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[7024, 21])).
% 5.70/5.64 tff(7026,plain,
% 5.70/5.64 (pred(pred(pred(pred(X5!51)))) = pred(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7025])).
% 5.70/5.64 tff(7027,plain,
% 5.70/5.64 (pred(pred(pred(pred(X5!51)))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7026, 20])).
% 5.70/5.64 tff(7028,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(X5!51))))) = pred(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7027])).
% 5.70/5.64 tff(7029,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(X5!51))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[7028, 19])).
% 5.70/5.64 tff(7030,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7029])).
% 5.70/5.64 tff(7031,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7030, 18])).
% 5.70/5.64 tff(7032,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7031])).
% 5.70/5.64 tff(7033,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7032, 17])).
% 5.70/5.64 tff(7034,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7033])).
% 5.70/5.64 tff(7035,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[7034, 16])).
% 5.70/5.64 tff(7036,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7035])).
% 5.70/5.64 tff(7037,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[7036, 15])).
% 5.70/5.64 tff(7038,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7037])).
% 5.70/5.64 tff(7039,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7038, 25])).
% 5.70/5.64 tff(7040,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7039])).
% 5.70/5.64 tff(7041,plain,
% 5.70/5.64 (NPX5!19 = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[742, 7040, 24])).
% 5.70/5.64 tff(7042,plain,
% 5.70/5.64 (succ(NPX5!19) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7041])).
% 5.70/5.64 tff(7043,plain,
% 5.70/5.64 (succ(NPX5!19) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7042, 36])).
% 5.70/5.64 tff(7044,plain,
% 5.70/5.64 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n2, n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7043, 7013])).
% 5.70/5.64 tff(7045,plain,
% 5.70/5.64 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[7044, 34])).
% 5.70/5.64 tff(7046,plain,
% 5.70/5.64 (succ(X5!51) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7019])).
% 5.70/5.64 tff(7047,plain,
% 5.70/5.64 (succ(X5!51) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7046, 36])).
% 5.70/5.64 tff(7048,plain,
% 5.70/5.64 (succ(succ(X5!51)) = succ(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7047])).
% 5.70/5.64 tff(7049,plain,
% 5.70/5.64 (succ(succ(X5!51)) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[7048, 48])).
% 5.70/5.64 tff(7050,plain,
% 5.70/5.64 (succ(succ(succ(X5!51))) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7049])).
% 5.70/5.64 tff(7051,plain,
% 5.70/5.64 (succ(succ(succ(X5!51))) = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[7050, 14])).
% 5.70/5.64 tff(7052,plain,
% 5.70/5.64 (succ(succ(succ(succ(X5!51)))) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7051])).
% 5.70/5.64 tff(7053,plain,
% 5.70/5.64 (succ(succ(succ(succ(X5!51)))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7052, 33])).
% 5.70/5.64 tff(7054,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(X5!51))))) = succ(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7053])).
% 5.70/5.64 tff(7055,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(X5!51))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7054, 30])).
% 5.70/5.64 tff(7056,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7055])).
% 5.70/5.64 tff(7057,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[7056, 39])).
% 5.70/5.64 tff(7058,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7057])).
% 5.70/5.64 tff(7059,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7058, 53])).
% 5.70/5.64 tff(7060,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7059])).
% 5.70/5.64 tff(7061,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[7060, 45])).
% 5.70/5.64 tff(7062,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7061])).
% 5.70/5.64 tff(7063,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[7062, 28])).
% 5.70/5.64 tff(7064,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7063])).
% 5.70/5.64 tff(7065,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7064, 42])).
% 5.70/5.64 tff(7066,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7065])).
% 5.70/5.64 tff(7067,plain,
% 5.70/5.64 (NSX5!17 = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[767, 7066, 58])).
% 5.70/5.64 tff(7068,plain,
% 5.70/5.64 (pred(NSX5!17) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7067])).
% 5.70/5.64 tff(7069,plain,
% 5.70/5.64 (pred(NSX5!17) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7068, 23])).
% 5.70/5.64 tff(7070,plain,
% 5.70/5.64 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n0, n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7069, 7045])).
% 5.70/5.64 tff(7071,plain,
% 5.70/5.64 (Y6!48 = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[772, 7070, 442])).
% 5.70/5.64 tff(7072,plain,
% 5.70/5.64 (pred(Y6!48) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7071])).
% 5.70/5.64 tff(7073,plain,
% 5.70/5.64 (pred(Y6!48) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[7072, 15])).
% 5.70/5.64 tff(7074,plain,
% 5.70/5.64 (pred(pred(Y6!48)) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7073])).
% 5.70/5.64 tff(7075,plain,
% 5.70/5.64 (pred(pred(Y6!48)) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7074, 25])).
% 5.70/5.64 tff(7076,plain,
% 5.70/5.64 (pred(pred(pred(Y6!48))) = pred(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7075])).
% 5.70/5.64 tff(7077,plain,
% 5.70/5.64 (pred(pred(pred(Y6!48))) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[7076, 24])).
% 5.70/5.64 tff(7078,plain,
% 5.70/5.64 (pred(pred(pred(pred(Y6!48)))) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7077])).
% 5.70/5.64 tff(7079,plain,
% 5.70/5.64 (pred(pred(pred(pred(Y6!48)))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7078, 23])).
% 5.70/5.64 tff(7080,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7079])).
% 5.70/5.64 tff(7081,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(Y6!48))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[7080, 22])).
% 5.70/5.64 tff(7082,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7081])).
% 5.70/5.64 tff(7083,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[7082, 21])).
% 5.70/5.64 tff(7084,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7083])).
% 5.70/5.64 tff(7085,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7084, 20])).
% 5.70/5.64 tff(7086,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7085])).
% 5.70/5.64 tff(7087,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[7086, 19])).
% 5.70/5.64 tff(7088,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7087])).
% 5.70/5.64 tff(7089,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7088, 18])).
% 5.70/5.64 tff(7090,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7089])).
% 5.70/5.64 tff(7091,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7090, 17])).
% 5.70/5.64 tff(7092,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7091])).
% 5.70/5.64 tff(7093,plain,
% 5.70/5.64 (NPY6!14 = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[1465, 7092, 16])).
% 5.70/5.64 tff(7094,plain,
% 5.70/5.64 (succ(NPY6!14) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7093])).
% 5.70/5.64 tff(7095,plain,
% 5.70/5.64 (succ(NPY6!14) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7094, 33])).
% 5.70/5.64 tff(7096,plain,
% 5.70/5.64 (succ(Y6!48) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7071])).
% 5.70/5.64 tff(7097,plain,
% 5.70/5.64 (succ(Y6!48) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7096, 33])).
% 5.70/5.64 tff(7098,plain,
% 5.70/5.64 (succ(succ(Y6!48)) = succ(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7097])).
% 5.70/5.64 tff(7099,plain,
% 5.70/5.64 (succ(succ(Y6!48)) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7098, 30])).
% 5.70/5.64 tff(7100,plain,
% 5.70/5.64 (succ(succ(succ(Y6!48))) = succ(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7099])).
% 5.70/5.64 tff(7101,plain,
% 5.70/5.64 (succ(succ(succ(Y6!48))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[7100, 39])).
% 5.70/5.64 tff(7102,plain,
% 5.70/5.64 (succ(succ(succ(succ(Y6!48)))) = succ(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7101])).
% 5.70/5.64 tff(7103,plain,
% 5.70/5.64 (succ(succ(succ(succ(Y6!48)))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7102, 53])).
% 5.70/5.64 tff(7104,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7103])).
% 5.70/5.64 tff(7105,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(Y6!48))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[7104, 45])).
% 5.70/5.64 tff(7106,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7105])).
% 5.70/5.64 tff(7107,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[7106, 28])).
% 5.70/5.64 tff(7108,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7107])).
% 5.70/5.64 tff(7109,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7108, 42])).
% 5.70/5.64 tff(7110,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7109])).
% 5.70/5.64 tff(7111,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[7110, 58])).
% 5.70/5.64 tff(7112,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7111])).
% 5.70/5.64 tff(7113,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7112, 36])).
% 5.70/5.64 tff(7114,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7113])).
% 5.70/5.64 tff(7115,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[7114, 48])).
% 5.70/5.64 tff(7116,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7115])).
% 5.70/5.64 tff(7117,plain,
% 5.70/5.64 (NSY6!12 = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[1490, 7116, 14])).
% 5.70/5.64 tff(7118,plain,
% 5.70/5.64 (pred(NSY6!12) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7117])).
% 5.70/5.64 tff(7119,plain,
% 5.70/5.64 (pred(NSY6!12) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[7118, 15])).
% 5.70/5.64 tff(7120,plain,
% 5.70/5.64 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n3, n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7119, 7095])).
% 5.70/5.64 tff(7121,plain,
% 5.70/5.64 (sum(pred(NSY6!12), succ(NPY6!14)) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7120, 32])).
% 5.70/5.64 tff(7122,plain,
% 5.70/5.64 (sum(pred(Y5!50), succ(X5!51)) = sum(n0, n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[6965, 7047])).
% 5.70/5.64 tff(7123,plain,
% 5.70/5.64 (sum(pred(Y5!50), succ(X5!51)) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7122, 35])).
% 5.70/5.64 tff(7124,plain,
% 5.70/5.64 (sum(pred(X5!51), succ(Y5!50)) = sum(n0, n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7021, 6989])).
% 5.70/5.64 tff(7125,plain,
% 5.70/5.64 (sum(pred(X5!51), succ(Y5!50)) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7124, 35])).
% 5.70/5.64 tff(7126,plain,
% 5.70/5.64 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n2, n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7125, 7123])).
% 5.70/5.64 tff(7127,plain,
% 5.70/5.64 (X6!49 = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[669, 7126, 34])).
% 5.70/5.64 tff(7128,plain,
% 5.70/5.64 (pred(X6!49) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7127])).
% 5.70/5.64 tff(7129,plain,
% 5.70/5.64 (pred(X6!49) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[7128, 15])).
% 5.70/5.64 tff(7130,plain,
% 5.70/5.64 (pred(pred(X6!49)) = pred(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7129])).
% 5.70/5.64 tff(7131,plain,
% 5.70/5.64 (pred(pred(X6!49)) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7130, 25])).
% 5.70/5.64 tff(7132,plain,
% 5.70/5.64 (pred(pred(pred(X6!49))) = pred(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7131])).
% 5.70/5.64 tff(7133,plain,
% 5.70/5.64 (pred(pred(pred(X6!49))) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[7132, 24])).
% 5.70/5.64 tff(7134,plain,
% 5.70/5.64 (pred(pred(pred(pred(X6!49)))) = pred(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7133])).
% 5.70/5.64 tff(7135,plain,
% 5.70/5.64 (pred(pred(pred(pred(X6!49)))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7134, 23])).
% 5.70/5.64 tff(7136,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(X6!49))))) = pred(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7135])).
% 5.70/5.64 tff(7137,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(X6!49))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[7136, 22])).
% 5.70/5.64 tff(7138,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7137])).
% 5.70/5.64 tff(7139,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[7138, 21])).
% 5.70/5.64 tff(7140,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7139])).
% 5.70/5.64 tff(7141,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7140, 20])).
% 5.70/5.64 tff(7142,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7141])).
% 5.70/5.64 tff(7143,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[7142, 19])).
% 5.70/5.64 tff(7144,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7143])).
% 5.70/5.64 tff(7145,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7144, 18])).
% 5.70/5.64 tff(7146,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7145])).
% 5.70/5.64 tff(7147,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7146, 17])).
% 5.70/5.64 tff(7148,plain,
% 5.70/5.64 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7147])).
% 5.70/5.64 tff(7149,plain,
% 5.70/5.64 (NPX6!15 = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[1523, 7148, 16])).
% 5.70/5.64 tff(7150,plain,
% 5.70/5.64 (succ(NPX6!15) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7149])).
% 5.70/5.64 tff(7151,plain,
% 5.70/5.64 (succ(NPX6!15) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7150, 33])).
% 5.70/5.64 tff(7152,plain,
% 5.70/5.64 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n5, n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7151, 7121])).
% 5.70/5.64 tff(7153,plain,
% 5.70/5.64 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7152, 558])).
% 5.70/5.64 tff(7154,plain,
% 5.70/5.64 (succ(X6!49) = succ(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7127])).
% 5.70/5.64 tff(7155,plain,
% 5.70/5.64 (succ(X6!49) = n5),
% 5.70/5.64 inference(transitivity,[status(thm)],[7154, 33])).
% 5.70/5.64 tff(7156,plain,
% 5.70/5.64 (succ(succ(X6!49)) = succ(n5)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7155])).
% 5.70/5.64 tff(7157,plain,
% 5.70/5.64 (succ(succ(X6!49)) = n6),
% 5.70/5.64 inference(transitivity,[status(thm)],[7156, 30])).
% 5.70/5.64 tff(7158,plain,
% 5.70/5.64 (succ(succ(succ(X6!49))) = succ(n6)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7157])).
% 5.70/5.64 tff(7159,plain,
% 5.70/5.64 (succ(succ(succ(X6!49))) = n7),
% 5.70/5.64 inference(transitivity,[status(thm)],[7158, 39])).
% 5.70/5.64 tff(7160,plain,
% 5.70/5.64 (succ(succ(succ(succ(X6!49)))) = succ(n7)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7159])).
% 5.70/5.64 tff(7161,plain,
% 5.70/5.64 (succ(succ(succ(succ(X6!49)))) = n8),
% 5.70/5.64 inference(transitivity,[status(thm)],[7160, 53])).
% 5.70/5.64 tff(7162,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(X6!49))))) = succ(n8)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7161])).
% 5.70/5.64 tff(7163,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(X6!49))))) = n9),
% 5.70/5.64 inference(transitivity,[status(thm)],[7162, 45])).
% 5.70/5.64 tff(7164,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n9)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7163])).
% 5.70/5.64 tff(7165,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n10),
% 5.70/5.64 inference(transitivity,[status(thm)],[7164, 28])).
% 5.70/5.64 tff(7166,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n10)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7165])).
% 5.70/5.64 tff(7167,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n0),
% 5.70/5.64 inference(transitivity,[status(thm)],[7166, 42])).
% 5.70/5.64 tff(7168,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n0)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7167])).
% 5.70/5.64 tff(7169,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n1),
% 5.70/5.64 inference(transitivity,[status(thm)],[7168, 58])).
% 5.70/5.64 tff(7170,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n1)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7169])).
% 5.70/5.64 tff(7171,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n2),
% 5.70/5.64 inference(transitivity,[status(thm)],[7170, 36])).
% 5.70/5.64 tff(7172,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n2)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7171])).
% 5.70/5.64 tff(7173,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n3),
% 5.70/5.64 inference(transitivity,[status(thm)],[7172, 48])).
% 5.70/5.64 tff(7174,plain,
% 5.70/5.64 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n3)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7173])).
% 5.70/5.64 tff(7175,plain,
% 5.70/5.64 (NSX6!13 = n4),
% 5.70/5.64 inference(transitivity,[status(thm)],[1550, 7174, 14])).
% 5.70/5.64 tff(7176,plain,
% 5.70/5.64 (pred(NSX6!13) = pred(n4)),
% 5.70/5.64 inference(monotonicity,[status(thm)],[7175])).
% 5.70/5.65 tff(7177,plain,
% 5.70/5.65 (pred(NSX6!13) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7176, 15])).
% 5.70/5.65 tff(7178,plain,
% 5.70/5.65 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n3, n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7177, 7153])).
% 5.70/5.65 tff(7179,plain,
% 5.70/5.65 (sum(n3, n2) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.70/5.65 inference(symmetry,[status(thm)],[7178])).
% 5.70/5.65 tff(7180,plain,
% 5.70/5.65 (sum(pred(Y6!48), succ(X6!49)) = sum(n3, n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7073, 7155])).
% 5.70/5.65 tff(7181,plain,
% 5.70/5.65 (sum(pred(Y6!48), succ(X6!49)) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7180, 32])).
% 5.70/5.65 tff(7182,plain,
% 5.70/5.65 (sum(pred(X6!49), succ(Y6!48)) = sum(n3, n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7129, 7097])).
% 5.70/5.65 tff(7183,plain,
% 5.70/5.65 (sum(pred(X6!49), succ(Y6!48)) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7182, 32])).
% 5.70/5.65 tff(7184,plain,
% 5.70/5.65 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n8, n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7183, 7181])).
% 5.70/5.65 tff(7185,plain,
% 5.70/5.65 (X7!47 = Y7!46),
% 5.70/5.65 inference(transitivity,[status(thm)],[785, 7184, 31, 2275, 7179, 794])).
% 5.70/5.65 tff(7186,plain,
% 5.70/5.65 ($false),
% 5.70/5.65 inference(unit_resolution,[status(thm)],[792, 7185])).
% 5.70/5.65 tff(7187,plain,((~(X0!61 = n10)) | (X7!47 = Y7!46) | (~(Y0!60 = n3))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.65 tff(7188,plain,
% 5.70/5.65 (~(X0!61 = n10)),
% 5.70/5.65 inference(unit_resolution,[status(thm)],[7187, 80, 792])).
% 5.70/5.65 tff(7189,plain,
% 5.70/5.65 (sum(n4, n1) = n5),
% 5.70/5.65 inference(and_elim,[status(thm)],[9])).
% 5.70/5.65 tff(7190,assumption,(X0!61 = n5), introduced(assumption)).
% 5.70/5.65 tff(7191,plain,
% 5.70/5.65 (pred(X0!61) = pred(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7190])).
% 5.70/5.65 tff(7192,plain,
% 5.70/5.65 (pred(X0!61) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7191, 16])).
% 5.70/5.65 tff(7193,plain,
% 5.70/5.65 (pred(pred(X0!61)) = pred(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7192])).
% 5.70/5.65 tff(7194,plain,
% 5.70/5.65 (pred(pred(X0!61)) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7193, 15])).
% 5.70/5.65 tff(7195,plain,
% 5.70/5.65 (pred(pred(pred(X0!61))) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7194])).
% 5.70/5.65 tff(7196,plain,
% 5.70/5.65 (pred(pred(pred(X0!61))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7195, 25])).
% 5.70/5.65 tff(7197,plain,
% 5.70/5.65 (pred(pred(pred(pred(X0!61)))) = pred(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7196])).
% 5.70/5.65 tff(7198,plain,
% 5.70/5.65 (pred(pred(pred(pred(X0!61)))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7197, 24])).
% 5.70/5.65 tff(7199,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(X0!61))))) = pred(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7198])).
% 5.70/5.65 tff(7200,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(X0!61))))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7199, 23])).
% 5.70/5.65 tff(7201,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7200])).
% 5.70/5.65 tff(7202,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7201, 22])).
% 5.70/5.65 tff(7203,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7202])).
% 5.70/5.65 tff(7204,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7203, 21])).
% 5.70/5.65 tff(7205,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7204])).
% 5.70/5.65 tff(7206,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7205, 20])).
% 5.70/5.65 tff(7207,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7206])).
% 5.70/5.65 tff(7208,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7207, 19])).
% 5.70/5.65 tff(7209,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7208])).
% 5.70/5.65 tff(7210,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7209, 18])).
% 5.70/5.65 tff(7211,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7210])).
% 5.70/5.65 tff(7212,plain,
% 5.70/5.65 (NPX0!39 = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[166, 7211, 17])).
% 5.70/5.65 tff(7213,plain,
% 5.70/5.65 (succ(NPX0!39) = succ(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7212])).
% 5.70/5.65 tff(7214,plain,
% 5.70/5.65 (succ(NPX0!39) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7213, 30])).
% 5.70/5.65 tff(7215,plain,
% 5.70/5.65 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n6, n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7214, 3768])).
% 5.70/5.65 tff(7216,plain,
% 5.70/5.65 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7215, 674])).
% 5.70/5.65 tff(7217,plain,
% 5.70/5.65 (succ(X0!61) = succ(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7190])).
% 5.70/5.65 tff(7218,plain,
% 5.70/5.65 (succ(X0!61) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7217, 30])).
% 5.70/5.65 tff(7219,plain,
% 5.70/5.65 (succ(succ(X0!61)) = succ(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7218])).
% 5.70/5.65 tff(7220,plain,
% 5.70/5.65 (succ(succ(X0!61)) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7219, 39])).
% 5.70/5.65 tff(7221,plain,
% 5.70/5.65 (succ(succ(succ(X0!61))) = succ(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7220])).
% 5.70/5.65 tff(7222,plain,
% 5.70/5.65 (succ(succ(succ(X0!61))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7221, 53])).
% 5.70/5.65 tff(7223,plain,
% 5.70/5.65 (succ(succ(succ(succ(X0!61)))) = succ(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7222])).
% 5.70/5.65 tff(7224,plain,
% 5.70/5.65 (succ(succ(succ(succ(X0!61)))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7223, 45])).
% 5.70/5.65 tff(7225,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(X0!61))))) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7224])).
% 5.70/5.65 tff(7226,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(X0!61))))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7225, 28])).
% 5.70/5.65 tff(7227,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7226])).
% 5.70/5.65 tff(7228,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7227, 42])).
% 5.70/5.65 tff(7229,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7228])).
% 5.70/5.65 tff(7230,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7229, 58])).
% 5.70/5.65 tff(7231,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7230])).
% 5.70/5.65 tff(7232,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7231, 36])).
% 5.70/5.65 tff(7233,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7232])).
% 5.70/5.65 tff(7234,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7233, 48])).
% 5.70/5.65 tff(7235,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7234])).
% 5.70/5.65 tff(7236,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7235, 14])).
% 5.70/5.65 tff(7237,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7236])).
% 5.70/5.65 tff(7238,plain,
% 5.70/5.65 (NSX0!37 = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[191, 7237, 33])).
% 5.70/5.65 tff(7239,plain,
% 5.70/5.65 (pred(NSX0!37) = pred(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7238])).
% 5.70/5.65 tff(7240,plain,
% 5.70/5.65 (pred(NSX0!37) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7239, 16])).
% 5.70/5.65 tff(7241,plain,
% 5.70/5.65 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n4, n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7240, 7216])).
% 5.70/5.65 tff(7242,plain,
% 5.70/5.65 (Y1!58 = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[196, 7241, 673])).
% 5.70/5.65 tff(7243,plain,
% 5.70/5.65 (pred(Y1!58) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7242])).
% 5.70/5.65 tff(7244,plain,
% 5.70/5.65 (pred(Y1!58) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7243, 20])).
% 5.70/5.65 tff(7245,plain,
% 5.70/5.65 (pred(pred(Y1!58)) = pred(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7244])).
% 5.70/5.65 tff(7246,plain,
% 5.70/5.65 (pred(pred(Y1!58)) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7245, 19])).
% 5.70/5.65 tff(7247,plain,
% 5.70/5.65 (pred(pred(pred(Y1!58))) = pred(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7246])).
% 5.70/5.65 tff(7248,plain,
% 5.70/5.65 (pred(pred(pred(Y1!58))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7247, 18])).
% 5.70/5.65 tff(7249,plain,
% 5.70/5.65 (pred(pred(pred(pred(Y1!58)))) = pred(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7248])).
% 5.70/5.65 tff(7250,plain,
% 5.70/5.65 (pred(pred(pred(pred(Y1!58)))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7249, 17])).
% 5.70/5.65 tff(7251,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7250])).
% 5.70/5.65 tff(7252,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(Y1!58))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7251, 16])).
% 5.70/5.65 tff(7253,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7252])).
% 5.70/5.65 tff(7254,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7253, 15])).
% 5.70/5.65 tff(7255,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7254])).
% 5.70/5.65 tff(7256,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7255, 25])).
% 5.70/5.65 tff(7257,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7256])).
% 5.70/5.65 tff(7258,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7257, 24])).
% 5.70/5.65 tff(7259,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7258])).
% 5.70/5.65 tff(7260,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7259, 23])).
% 5.70/5.65 tff(7261,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7260])).
% 5.70/5.65 tff(7262,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7261, 22])).
% 5.70/5.65 tff(7263,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7262])).
% 5.70/5.65 tff(7264,plain,
% 5.70/5.65 (NPY1!34 = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[232, 7263, 21])).
% 5.70/5.65 tff(7265,plain,
% 5.70/5.65 (succ(NPY1!34) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7264])).
% 5.70/5.65 tff(7266,plain,
% 5.70/5.65 (succ(NPY1!34) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7265, 28])).
% 5.70/5.65 tff(7267,plain,
% 5.70/5.65 (succ(Y1!58) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7242])).
% 5.70/5.65 tff(7268,plain,
% 5.70/5.65 (succ(Y1!58) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7267, 28])).
% 5.70/5.65 tff(7269,plain,
% 5.70/5.65 (succ(succ(Y1!58)) = succ(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7268])).
% 5.70/5.65 tff(7270,plain,
% 5.70/5.65 (succ(succ(Y1!58)) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7269, 42])).
% 5.70/5.65 tff(7271,plain,
% 5.70/5.65 (succ(succ(succ(Y1!58))) = succ(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7270])).
% 5.70/5.65 tff(7272,plain,
% 5.70/5.65 (succ(succ(succ(Y1!58))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7271, 58])).
% 5.70/5.65 tff(7273,plain,
% 5.70/5.65 (succ(succ(succ(succ(Y1!58)))) = succ(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7272])).
% 5.70/5.65 tff(7274,plain,
% 5.70/5.65 (succ(succ(succ(succ(Y1!58)))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7273, 36])).
% 5.70/5.65 tff(7275,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7274])).
% 5.70/5.65 tff(7276,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(Y1!58))))) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7275, 48])).
% 5.70/5.65 tff(7277,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7276])).
% 5.70/5.65 tff(7278,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7277, 14])).
% 5.70/5.65 tff(7279,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7278])).
% 5.70/5.65 tff(7280,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7279, 33])).
% 5.70/5.65 tff(7281,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7280])).
% 5.70/5.65 tff(7282,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7281, 30])).
% 5.70/5.65 tff(7283,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7282])).
% 5.70/5.65 tff(7284,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7283, 39])).
% 5.70/5.65 tff(7285,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7284])).
% 5.70/5.65 tff(7286,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7285, 53])).
% 5.70/5.65 tff(7287,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7286])).
% 5.70/5.65 tff(7288,plain,
% 5.70/5.65 (NSY1!32 = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[255, 7287, 45])).
% 5.70/5.65 tff(7289,plain,
% 5.70/5.65 (pred(NSY1!32) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7288])).
% 5.70/5.65 tff(7290,plain,
% 5.70/5.65 (pred(NSY1!32) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7289, 20])).
% 5.70/5.65 tff(7291,plain,
% 5.70/5.65 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n8, n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7290, 7266])).
% 5.70/5.65 tff(7292,plain,
% 5.70/5.65 (sum(pred(NSY1!32), succ(NPY1!34)) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7291, 27])).
% 5.70/5.65 tff(7293,plain,
% 5.70/5.65 (sum(pred(Y0!60), succ(X0!61)) = sum(n4, n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[3720, 7218])).
% 5.70/5.65 tff(7294,plain,
% 5.70/5.65 (sum(pred(Y0!60), succ(X0!61)) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7293, 12])).
% 5.70/5.65 tff(7295,plain,
% 5.70/5.65 (sum(pred(X0!61), succ(Y0!60)) = sum(n4, n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7192, 3744])).
% 5.70/5.65 tff(7296,plain,
% 5.70/5.65 (sum(pred(X0!61), succ(Y0!60)) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7295, 12])).
% 5.70/5.65 tff(7297,plain,
% 5.70/5.65 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n10, n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7296, 7294])).
% 5.70/5.65 tff(7298,plain,
% 5.70/5.65 (X1!59 = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[93, 7297, 29])).
% 5.70/5.65 tff(7299,plain,
% 5.70/5.65 (pred(X1!59) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7298])).
% 5.70/5.65 tff(7300,plain,
% 5.70/5.65 (pred(X1!59) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7299, 20])).
% 5.70/5.65 tff(7301,plain,
% 5.70/5.65 (pred(pred(X1!59)) = pred(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7300])).
% 5.70/5.65 tff(7302,plain,
% 5.70/5.65 (pred(pred(X1!59)) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7301, 19])).
% 5.70/5.65 tff(7303,plain,
% 5.70/5.65 (pred(pred(pred(X1!59))) = pred(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7302])).
% 5.70/5.65 tff(7304,plain,
% 5.70/5.65 (pred(pred(pred(X1!59))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7303, 18])).
% 5.70/5.65 tff(7305,plain,
% 5.70/5.65 (pred(pred(pred(pred(X1!59)))) = pred(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7304])).
% 5.70/5.65 tff(7306,plain,
% 5.70/5.65 (pred(pred(pred(pred(X1!59)))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7305, 17])).
% 5.70/5.65 tff(7307,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(X1!59))))) = pred(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7306])).
% 5.70/5.65 tff(7308,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(X1!59))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7307, 16])).
% 5.70/5.65 tff(7309,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7308])).
% 5.70/5.65 tff(7310,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7309, 15])).
% 5.70/5.65 tff(7311,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7310])).
% 5.70/5.65 tff(7312,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7311, 25])).
% 5.70/5.65 tff(7313,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7312])).
% 5.70/5.65 tff(7314,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7313, 24])).
% 5.70/5.65 tff(7315,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7314])).
% 5.70/5.65 tff(7316,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7315, 23])).
% 5.70/5.65 tff(7317,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7316])).
% 5.70/5.65 tff(7318,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7317, 22])).
% 5.70/5.65 tff(7319,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7318])).
% 5.70/5.65 tff(7320,plain,
% 5.70/5.65 (NPX1!35 = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[280, 7319, 21])).
% 5.70/5.65 tff(7321,plain,
% 5.70/5.65 (succ(NPX1!35) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7320])).
% 5.70/5.65 tff(7322,plain,
% 5.70/5.65 (succ(NPX1!35) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7321, 28])).
% 5.70/5.65 tff(7323,plain,
% 5.70/5.65 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n10, n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7322, 7292])).
% 5.70/5.65 tff(7324,plain,
% 5.70/5.65 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7323, 69])).
% 5.70/5.65 tff(7325,plain,
% 5.70/5.65 (succ(X1!59) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7298])).
% 5.70/5.65 tff(7326,plain,
% 5.70/5.65 (succ(X1!59) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7325, 28])).
% 5.70/5.65 tff(7327,plain,
% 5.70/5.65 (succ(succ(X1!59)) = succ(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7326])).
% 5.70/5.65 tff(7328,plain,
% 5.70/5.65 (succ(succ(X1!59)) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7327, 42])).
% 5.70/5.65 tff(7329,plain,
% 5.70/5.65 (succ(succ(succ(X1!59))) = succ(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7328])).
% 5.70/5.65 tff(7330,plain,
% 5.70/5.65 (succ(succ(succ(X1!59))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7329, 58])).
% 5.70/5.65 tff(7331,plain,
% 5.70/5.65 (succ(succ(succ(succ(X1!59)))) = succ(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7330])).
% 5.70/5.65 tff(7332,plain,
% 5.70/5.65 (succ(succ(succ(succ(X1!59)))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7331, 36])).
% 5.70/5.65 tff(7333,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(X1!59))))) = succ(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7332])).
% 5.70/5.65 tff(7334,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(X1!59))))) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7333, 48])).
% 5.70/5.65 tff(7335,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7334])).
% 5.70/5.65 tff(7336,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7335, 14])).
% 5.70/5.65 tff(7337,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7336])).
% 5.70/5.65 tff(7338,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7337, 33])).
% 5.70/5.65 tff(7339,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7338])).
% 5.70/5.65 tff(7340,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7339, 30])).
% 5.70/5.65 tff(7341,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7340])).
% 5.70/5.65 tff(7342,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7341, 39])).
% 5.70/5.65 tff(7343,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7342])).
% 5.70/5.65 tff(7344,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7343, 53])).
% 5.70/5.65 tff(7345,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7344])).
% 5.70/5.65 tff(7346,plain,
% 5.70/5.65 (NSX1!33 = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[305, 7345, 45])).
% 5.70/5.65 tff(7347,plain,
% 5.70/5.65 (pred(NSX1!33) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7346])).
% 5.70/5.65 tff(7348,plain,
% 5.70/5.65 (pred(NSX1!33) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7347, 20])).
% 5.70/5.65 tff(7349,plain,
% 5.70/5.65 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n8, n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7348, 7324])).
% 5.70/5.65 tff(7350,plain,
% 5.70/5.65 (Y2!56 = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[310, 7349, 98])).
% 5.70/5.65 tff(7351,plain,
% 5.70/5.65 (pred(Y2!56) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7350])).
% 5.70/5.65 tff(7352,plain,
% 5.70/5.65 (pred(Y2!56) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7351, 25])).
% 5.70/5.65 tff(7353,plain,
% 5.70/5.65 (pred(pred(Y2!56)) = pred(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7352])).
% 5.70/5.65 tff(7354,plain,
% 5.70/5.65 (pred(pred(Y2!56)) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7353, 24])).
% 5.70/5.65 tff(7355,plain,
% 5.70/5.65 (pred(pred(pred(Y2!56))) = pred(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7354])).
% 5.70/5.65 tff(7356,plain,
% 5.70/5.65 (pred(pred(pred(Y2!56))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7355, 23])).
% 5.70/5.65 tff(7357,plain,
% 5.70/5.65 (pred(pred(pred(pred(Y2!56)))) = pred(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7356])).
% 5.70/5.65 tff(7358,plain,
% 5.70/5.65 (pred(pred(pred(pred(Y2!56)))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7357, 22])).
% 5.70/5.65 tff(7359,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7358])).
% 5.70/5.65 tff(7360,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(Y2!56))))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7359, 21])).
% 5.70/5.65 tff(7361,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7360])).
% 5.70/5.65 tff(7362,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7361, 20])).
% 5.70/5.65 tff(7363,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7362])).
% 5.70/5.65 tff(7364,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7363, 19])).
% 5.70/5.65 tff(7365,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7364])).
% 5.70/5.65 tff(7366,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7365, 18])).
% 5.70/5.65 tff(7367,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7366])).
% 5.70/5.65 tff(7368,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7367, 17])).
% 5.70/5.65 tff(7369,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7368])).
% 5.70/5.65 tff(7370,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7369, 16])).
% 5.70/5.65 tff(7371,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7370])).
% 5.70/5.65 tff(7372,plain,
% 5.70/5.65 (NPY2!30 = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[347, 7371, 15])).
% 5.70/5.65 tff(7373,plain,
% 5.70/5.65 (succ(NPY2!30) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7372])).
% 5.70/5.65 tff(7374,plain,
% 5.70/5.65 (succ(NPY2!30) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7373, 14])).
% 5.70/5.65 tff(7375,plain,
% 5.70/5.65 (succ(Y2!56) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7350])).
% 5.70/5.65 tff(7376,plain,
% 5.70/5.65 (succ(Y2!56) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7375, 14])).
% 5.70/5.65 tff(7377,plain,
% 5.70/5.65 (succ(succ(Y2!56)) = succ(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7376])).
% 5.70/5.65 tff(7378,plain,
% 5.70/5.65 (succ(succ(Y2!56)) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7377, 33])).
% 5.70/5.65 tff(7379,plain,
% 5.70/5.65 (succ(succ(succ(Y2!56))) = succ(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7378])).
% 5.70/5.65 tff(7380,plain,
% 5.70/5.65 (succ(succ(succ(Y2!56))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7379, 30])).
% 5.70/5.65 tff(7381,plain,
% 5.70/5.65 (succ(succ(succ(succ(Y2!56)))) = succ(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7380])).
% 5.70/5.65 tff(7382,plain,
% 5.70/5.65 (succ(succ(succ(succ(Y2!56)))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7381, 39])).
% 5.70/5.65 tff(7383,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7382])).
% 5.70/5.65 tff(7384,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(Y2!56))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7383, 53])).
% 5.70/5.65 tff(7385,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7384])).
% 5.70/5.65 tff(7386,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7385, 45])).
% 5.70/5.65 tff(7387,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7386])).
% 5.70/5.65 tff(7388,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7387, 28])).
% 5.70/5.65 tff(7389,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7388])).
% 5.70/5.65 tff(7390,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7389, 42])).
% 5.70/5.65 tff(7391,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7390])).
% 5.70/5.65 tff(7392,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7391, 58])).
% 5.70/5.65 tff(7393,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7392])).
% 5.70/5.65 tff(7394,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7393, 36])).
% 5.70/5.65 tff(7395,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7394])).
% 5.70/5.65 tff(7396,plain,
% 5.70/5.65 (NSY2!28 = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[370, 7395, 48])).
% 5.70/5.65 tff(7397,plain,
% 5.70/5.65 (pred(NSY2!28) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7396])).
% 5.70/5.65 tff(7398,plain,
% 5.70/5.65 (pred(NSY2!28) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7397, 25])).
% 5.70/5.65 tff(7399,plain,
% 5.70/5.65 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n2, n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7398, 7374])).
% 5.70/5.65 tff(7400,plain,
% 5.70/5.65 (sum(pred(NSY2!28), succ(NPY2!30)) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7399, 13])).
% 5.70/5.65 tff(7401,plain,
% 5.70/5.65 (sum(pred(Y1!58), succ(X1!59)) = sum(n8, n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7244, 7326])).
% 5.70/5.65 tff(7402,plain,
% 5.70/5.65 (sum(pred(Y1!58), succ(X1!59)) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7401, 27])).
% 5.70/5.65 tff(7403,plain,
% 5.70/5.65 (sum(pred(X1!59), succ(Y1!58)) = sum(n8, n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7300, 7268])).
% 5.70/5.65 tff(7404,plain,
% 5.70/5.65 (sum(pred(X1!59), succ(Y1!58)) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7403, 27])).
% 5.70/5.65 tff(7405,plain,
% 5.70/5.65 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n7, n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7404, 7402])).
% 5.70/5.65 tff(7406,plain,
% 5.70/5.65 (X2!57 = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[209, 7405, 26])).
% 5.70/5.65 tff(7407,plain,
% 5.70/5.65 (pred(X2!57) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7406])).
% 5.70/5.65 tff(7408,plain,
% 5.70/5.65 (pred(X2!57) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7407, 25])).
% 5.70/5.65 tff(7409,plain,
% 5.70/5.65 (pred(pred(X2!57)) = pred(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7408])).
% 5.70/5.65 tff(7410,plain,
% 5.70/5.65 (pred(pred(X2!57)) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7409, 24])).
% 5.70/5.65 tff(7411,plain,
% 5.70/5.65 (pred(pred(pred(X2!57))) = pred(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7410])).
% 5.70/5.65 tff(7412,plain,
% 5.70/5.65 (pred(pred(pred(X2!57))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7411, 23])).
% 5.70/5.65 tff(7413,plain,
% 5.70/5.65 (pred(pred(pred(pred(X2!57)))) = pred(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7412])).
% 5.70/5.65 tff(7414,plain,
% 5.70/5.65 (pred(pred(pred(pred(X2!57)))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7413, 22])).
% 5.70/5.65 tff(7415,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(X2!57))))) = pred(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7414])).
% 5.70/5.65 tff(7416,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(X2!57))))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7415, 21])).
% 5.70/5.65 tff(7417,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7416])).
% 5.70/5.65 tff(7418,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7417, 20])).
% 5.70/5.65 tff(7419,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7418])).
% 5.70/5.65 tff(7420,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7419, 19])).
% 5.70/5.65 tff(7421,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7420])).
% 5.70/5.65 tff(7422,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7421, 18])).
% 5.70/5.65 tff(7423,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7422])).
% 5.70/5.65 tff(7424,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7423, 17])).
% 5.70/5.65 tff(7425,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7424])).
% 5.70/5.65 tff(7426,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7425, 16])).
% 5.70/5.65 tff(7427,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7426])).
% 5.70/5.65 tff(7428,plain,
% 5.70/5.65 (NPX2!31 = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[395, 7427, 15])).
% 5.70/5.65 tff(7429,plain,
% 5.70/5.65 (succ(NPX2!31) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7428])).
% 5.70/5.65 tff(7430,plain,
% 5.70/5.65 (succ(NPX2!31) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7429, 14])).
% 5.70/5.65 tff(7431,plain,
% 5.70/5.65 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n4, n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7430, 7400])).
% 5.70/5.65 tff(7432,plain,
% 5.70/5.65 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7431, 12])).
% 5.70/5.65 tff(7433,plain,
% 5.70/5.65 (succ(X2!57) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7406])).
% 5.70/5.65 tff(7434,plain,
% 5.70/5.65 (succ(X2!57) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7433, 14])).
% 5.70/5.65 tff(7435,plain,
% 5.70/5.65 (succ(succ(X2!57)) = succ(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7434])).
% 5.70/5.65 tff(7436,plain,
% 5.70/5.65 (succ(succ(X2!57)) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7435, 33])).
% 5.70/5.65 tff(7437,plain,
% 5.70/5.65 (succ(succ(succ(X2!57))) = succ(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7436])).
% 5.70/5.65 tff(7438,plain,
% 5.70/5.65 (succ(succ(succ(X2!57))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7437, 30])).
% 5.70/5.65 tff(7439,plain,
% 5.70/5.65 (succ(succ(succ(succ(X2!57)))) = succ(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7438])).
% 5.70/5.65 tff(7440,plain,
% 5.70/5.65 (succ(succ(succ(succ(X2!57)))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7439, 39])).
% 5.70/5.65 tff(7441,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(X2!57))))) = succ(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7440])).
% 5.70/5.65 tff(7442,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(X2!57))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7441, 53])).
% 5.70/5.65 tff(7443,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7442])).
% 5.70/5.65 tff(7444,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7443, 45])).
% 5.70/5.65 tff(7445,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7444])).
% 5.70/5.65 tff(7446,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7445, 28])).
% 5.70/5.65 tff(7447,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7446])).
% 5.70/5.65 tff(7448,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7447, 42])).
% 5.70/5.65 tff(7449,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7448])).
% 5.70/5.65 tff(7450,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[7449, 58])).
% 5.70/5.65 tff(7451,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7450])).
% 5.70/5.65 tff(7452,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7451, 36])).
% 5.70/5.65 tff(7453,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7452])).
% 5.70/5.65 tff(7454,plain,
% 5.70/5.65 (NSX2!29 = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[420, 7453, 48])).
% 5.70/5.65 tff(7455,plain,
% 5.70/5.65 (pred(NSX2!29) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7454])).
% 5.70/5.65 tff(7456,plain,
% 5.70/5.65 (pred(NSX2!29) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7455, 25])).
% 5.70/5.65 tff(7457,plain,
% 5.70/5.65 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n2, n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7456, 7432])).
% 5.70/5.65 tff(7458,plain,
% 5.70/5.65 (Y3!54 = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[425, 7457, 327])).
% 5.70/5.65 tff(7459,plain,
% 5.70/5.65 (pred(Y3!54) = pred(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7458])).
% 5.70/5.65 tff(7460,plain,
% 5.70/5.65 (pred(Y3!54) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7459, 23])).
% 5.70/5.65 tff(7461,plain,
% 5.70/5.65 (pred(pred(Y3!54)) = pred(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7460])).
% 5.70/5.65 tff(7462,plain,
% 5.70/5.65 (pred(pred(Y3!54)) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7461, 22])).
% 5.70/5.65 tff(7463,plain,
% 5.70/5.65 (pred(pred(pred(Y3!54))) = pred(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7462])).
% 5.70/5.65 tff(7464,plain,
% 5.70/5.65 (pred(pred(pred(Y3!54))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7463, 21])).
% 5.70/5.65 tff(7465,plain,
% 5.70/5.65 (pred(pred(pred(pred(Y3!54)))) = pred(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7464])).
% 5.70/5.65 tff(7466,plain,
% 5.70/5.65 (pred(pred(pred(pred(Y3!54)))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7465, 20])).
% 5.70/5.65 tff(7467,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7466])).
% 5.70/5.65 tff(7468,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(Y3!54))))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7467, 19])).
% 5.70/5.65 tff(7469,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7468])).
% 5.70/5.65 tff(7470,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7469, 18])).
% 5.70/5.65 tff(7471,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7470])).
% 5.70/5.65 tff(7472,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7471, 17])).
% 5.70/5.65 tff(7473,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7472])).
% 5.70/5.65 tff(7474,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7473, 16])).
% 5.70/5.65 tff(7475,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7474])).
% 5.70/5.65 tff(7476,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7475, 15])).
% 5.70/5.65 tff(7477,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7476])).
% 5.70/5.65 tff(7478,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7477, 25])).
% 5.70/5.65 tff(7479,plain,
% 5.70/5.65 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7478])).
% 5.70/5.65 tff(7480,plain,
% 5.70/5.65 (NPY3!26 = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[462, 7479, 24])).
% 5.70/5.65 tff(7481,plain,
% 5.70/5.65 (succ(NPY3!26) = succ(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7480])).
% 5.70/5.65 tff(7482,plain,
% 5.70/5.65 (succ(NPY3!26) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7481, 36])).
% 5.70/5.65 tff(7483,plain,
% 5.70/5.65 (succ(Y3!54) = succ(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7458])).
% 5.70/5.65 tff(7484,plain,
% 5.70/5.65 (succ(Y3!54) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7483, 36])).
% 5.70/5.65 tff(7485,plain,
% 5.70/5.65 (succ(succ(Y3!54)) = succ(n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7484])).
% 5.70/5.65 tff(7486,plain,
% 5.70/5.65 (succ(succ(Y3!54)) = n3),
% 5.70/5.65 inference(transitivity,[status(thm)],[7485, 48])).
% 5.70/5.65 tff(7487,plain,
% 5.70/5.65 (succ(succ(succ(Y3!54))) = succ(n3)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7486])).
% 5.70/5.65 tff(7488,plain,
% 5.70/5.65 (succ(succ(succ(Y3!54))) = n4),
% 5.70/5.65 inference(transitivity,[status(thm)],[7487, 14])).
% 5.70/5.65 tff(7489,plain,
% 5.70/5.65 (succ(succ(succ(succ(Y3!54)))) = succ(n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7488])).
% 5.70/5.65 tff(7490,plain,
% 5.70/5.65 (succ(succ(succ(succ(Y3!54)))) = n5),
% 5.70/5.65 inference(transitivity,[status(thm)],[7489, 33])).
% 5.70/5.65 tff(7491,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n5)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7490])).
% 5.70/5.65 tff(7492,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(Y3!54))))) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7491, 30])).
% 5.70/5.65 tff(7493,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n6)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7492])).
% 5.70/5.65 tff(7494,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n7),
% 5.70/5.65 inference(transitivity,[status(thm)],[7493, 39])).
% 5.70/5.65 tff(7495,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n7)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7494])).
% 5.70/5.65 tff(7496,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n8),
% 5.70/5.65 inference(transitivity,[status(thm)],[7495, 53])).
% 5.70/5.65 tff(7497,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n8)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7496])).
% 5.70/5.65 tff(7498,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n9),
% 5.70/5.65 inference(transitivity,[status(thm)],[7497, 45])).
% 5.70/5.65 tff(7499,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n9)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7498])).
% 5.70/5.65 tff(7500,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n10),
% 5.70/5.65 inference(transitivity,[status(thm)],[7499, 28])).
% 5.70/5.65 tff(7501,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n10)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7500])).
% 5.70/5.65 tff(7502,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7501, 42])).
% 5.70/5.65 tff(7503,plain,
% 5.70/5.65 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n0)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7502])).
% 5.70/5.65 tff(7504,plain,
% 5.70/5.65 (NSY3!24 = n1),
% 5.70/5.65 inference(transitivity,[status(thm)],[485, 7503, 58])).
% 5.70/5.65 tff(7505,plain,
% 5.70/5.65 (pred(NSY3!24) = pred(n1)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7504])).
% 5.70/5.65 tff(7506,plain,
% 5.70/5.65 (pred(NSY3!24) = n0),
% 5.70/5.65 inference(transitivity,[status(thm)],[7505, 23])).
% 5.70/5.65 tff(7507,plain,
% 5.70/5.65 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n0, n2)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7506, 7482])).
% 5.70/5.65 tff(7508,plain,
% 5.70/5.65 (sum(pred(NSY3!24), succ(NPY3!26)) = n2),
% 5.70/5.65 inference(transitivity,[status(thm)],[7507, 35])).
% 5.70/5.65 tff(7509,plain,
% 5.70/5.65 (sum(pred(Y2!56), succ(X2!57)) = sum(n2, n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7352, 7434])).
% 5.70/5.65 tff(7510,plain,
% 5.70/5.65 (sum(pred(Y2!56), succ(X2!57)) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7509, 13])).
% 5.70/5.65 tff(7511,plain,
% 5.70/5.65 (sum(pred(X2!57), succ(Y2!56)) = sum(n2, n4)),
% 5.70/5.65 inference(monotonicity,[status(thm)],[7408, 7376])).
% 5.70/5.65 tff(7512,plain,
% 5.70/5.65 (sum(pred(X2!57), succ(Y2!56)) = n6),
% 5.70/5.65 inference(transitivity,[status(thm)],[7511, 13])).
% 5.70/5.65 tff(7513,plain,
% 5.70/5.65 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n6, n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7512, 7510])).
% 5.70/5.66 tff(7514,plain,
% 5.70/5.66 (X3!55 = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[323, 7513, 37])).
% 5.70/5.66 tff(7515,plain,
% 5.70/5.66 (pred(X3!55) = pred(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7514])).
% 5.70/5.66 tff(7516,plain,
% 5.70/5.66 (pred(X3!55) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7515, 23])).
% 5.70/5.66 tff(7517,plain,
% 5.70/5.66 (pred(pred(X3!55)) = pred(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7516])).
% 5.70/5.66 tff(7518,plain,
% 5.70/5.66 (pred(pred(X3!55)) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7517, 22])).
% 5.70/5.66 tff(7519,plain,
% 5.70/5.66 (pred(pred(pred(X3!55))) = pred(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7518])).
% 5.70/5.66 tff(7520,plain,
% 5.70/5.66 (pred(pred(pred(X3!55))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7519, 21])).
% 5.70/5.66 tff(7521,plain,
% 5.70/5.66 (pred(pred(pred(pred(X3!55)))) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7520])).
% 5.70/5.66 tff(7522,plain,
% 5.70/5.66 (pred(pred(pred(pred(X3!55)))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7521, 20])).
% 5.70/5.66 tff(7523,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X3!55))))) = pred(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7522])).
% 5.70/5.66 tff(7524,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X3!55))))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7523, 19])).
% 5.70/5.66 tff(7525,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7524])).
% 5.70/5.66 tff(7526,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7525, 18])).
% 5.70/5.66 tff(7527,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7526])).
% 5.70/5.66 tff(7528,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7527, 17])).
% 5.70/5.66 tff(7529,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7528])).
% 5.70/5.66 tff(7530,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7529, 16])).
% 5.70/5.66 tff(7531,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7530])).
% 5.70/5.66 tff(7532,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7531, 15])).
% 5.70/5.66 tff(7533,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7532])).
% 5.70/5.66 tff(7534,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7533, 25])).
% 5.70/5.66 tff(7535,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7534])).
% 5.70/5.66 tff(7536,plain,
% 5.70/5.66 (NPX3!27 = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[510, 7535, 24])).
% 5.70/5.66 tff(7537,plain,
% 5.70/5.66 (succ(NPX3!27) = succ(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7536])).
% 5.70/5.66 tff(7538,plain,
% 5.70/5.66 (succ(NPX3!27) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7537, 36])).
% 5.70/5.66 tff(7539,plain,
% 5.70/5.66 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n2, n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7538, 7508])).
% 5.70/5.66 tff(7540,plain,
% 5.70/5.66 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7539, 34])).
% 5.70/5.66 tff(7541,plain,
% 5.70/5.66 (succ(X3!55) = succ(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7514])).
% 5.70/5.66 tff(7542,plain,
% 5.70/5.66 (succ(X3!55) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7541, 36])).
% 5.70/5.66 tff(7543,plain,
% 5.70/5.66 (succ(succ(X3!55)) = succ(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7542])).
% 5.70/5.66 tff(7544,plain,
% 5.70/5.66 (succ(succ(X3!55)) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7543, 48])).
% 5.70/5.66 tff(7545,plain,
% 5.70/5.66 (succ(succ(succ(X3!55))) = succ(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7544])).
% 5.70/5.66 tff(7546,plain,
% 5.70/5.66 (succ(succ(succ(X3!55))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7545, 14])).
% 5.70/5.66 tff(7547,plain,
% 5.70/5.66 (succ(succ(succ(succ(X3!55)))) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7546])).
% 5.70/5.66 tff(7548,plain,
% 5.70/5.66 (succ(succ(succ(succ(X3!55)))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7547, 33])).
% 5.70/5.66 tff(7549,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(X3!55))))) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7548])).
% 5.70/5.66 tff(7550,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(X3!55))))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7549, 30])).
% 5.70/5.66 tff(7551,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7550])).
% 5.70/5.66 tff(7552,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7551, 39])).
% 5.70/5.66 tff(7553,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7552])).
% 5.70/5.66 tff(7554,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7553, 53])).
% 5.70/5.66 tff(7555,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7554])).
% 5.70/5.66 tff(7556,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7555, 45])).
% 5.70/5.66 tff(7557,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7556])).
% 5.70/5.66 tff(7558,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7557, 28])).
% 5.70/5.66 tff(7559,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7558])).
% 5.70/5.66 tff(7560,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7559, 42])).
% 5.70/5.66 tff(7561,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7560])).
% 5.70/5.66 tff(7562,plain,
% 5.70/5.66 (NSX3!25 = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[535, 7561, 58])).
% 5.70/5.66 tff(7563,plain,
% 5.70/5.66 (pred(NSX3!25) = pred(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7562])).
% 5.70/5.66 tff(7564,plain,
% 5.70/5.66 (pred(NSX3!25) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7563, 23])).
% 5.70/5.66 tff(7565,plain,
% 5.70/5.66 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n0, n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7564, 7540])).
% 5.70/5.66 tff(7566,plain,
% 5.70/5.66 (Y4!52 = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[540, 7565, 442])).
% 5.70/5.66 tff(7567,plain,
% 5.70/5.66 (pred(Y4!52) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7566])).
% 5.70/5.66 tff(7568,plain,
% 5.70/5.66 (pred(Y4!52) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7567, 15])).
% 5.70/5.66 tff(7569,plain,
% 5.70/5.66 (pred(pred(Y4!52)) = pred(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7568])).
% 5.70/5.66 tff(7570,plain,
% 5.70/5.66 (pred(pred(Y4!52)) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7569, 25])).
% 5.70/5.66 tff(7571,plain,
% 5.70/5.66 (pred(pred(pred(Y4!52))) = pred(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7570])).
% 5.70/5.66 tff(7572,plain,
% 5.70/5.66 (pred(pred(pred(Y4!52))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7571, 24])).
% 5.70/5.66 tff(7573,plain,
% 5.70/5.66 (pred(pred(pred(pred(Y4!52)))) = pred(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7572])).
% 5.70/5.66 tff(7574,plain,
% 5.70/5.66 (pred(pred(pred(pred(Y4!52)))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7573, 23])).
% 5.70/5.66 tff(7575,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7574])).
% 5.70/5.66 tff(7576,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(Y4!52))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7575, 22])).
% 5.70/5.66 tff(7577,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7576])).
% 5.70/5.66 tff(7578,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7577, 21])).
% 5.70/5.66 tff(7579,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7578])).
% 5.70/5.66 tff(7580,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7579, 20])).
% 5.70/5.66 tff(7581,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7580])).
% 5.70/5.66 tff(7582,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7581, 19])).
% 5.70/5.66 tff(7583,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7582])).
% 5.70/5.66 tff(7584,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7583, 18])).
% 5.70/5.66 tff(7585,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7584])).
% 5.70/5.66 tff(7586,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7585, 17])).
% 5.70/5.66 tff(7587,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7586])).
% 5.70/5.66 tff(7588,plain,
% 5.70/5.66 (NPY4!22 = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[578, 7587, 16])).
% 5.70/5.66 tff(7589,plain,
% 5.70/5.66 (succ(NPY4!22) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7588])).
% 5.70/5.66 tff(7590,plain,
% 5.70/5.66 (succ(NPY4!22) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7589, 33])).
% 5.70/5.66 tff(7591,plain,
% 5.70/5.66 (succ(Y4!52) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7566])).
% 5.70/5.66 tff(7592,plain,
% 5.70/5.66 (succ(Y4!52) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7591, 33])).
% 5.70/5.66 tff(7593,plain,
% 5.70/5.66 (succ(succ(Y4!52)) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7592])).
% 5.70/5.66 tff(7594,plain,
% 5.70/5.66 (succ(succ(Y4!52)) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7593, 30])).
% 5.70/5.66 tff(7595,plain,
% 5.70/5.66 (succ(succ(succ(Y4!52))) = succ(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7594])).
% 5.70/5.66 tff(7596,plain,
% 5.70/5.66 (succ(succ(succ(Y4!52))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7595, 39])).
% 5.70/5.66 tff(7597,plain,
% 5.70/5.66 (succ(succ(succ(succ(Y4!52)))) = succ(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7596])).
% 5.70/5.66 tff(7598,plain,
% 5.70/5.66 (succ(succ(succ(succ(Y4!52)))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7597, 53])).
% 5.70/5.66 tff(7599,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7598])).
% 5.70/5.66 tff(7600,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(Y4!52))))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7599, 45])).
% 5.70/5.66 tff(7601,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7600])).
% 5.70/5.66 tff(7602,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7601, 28])).
% 5.70/5.66 tff(7603,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7602])).
% 5.70/5.66 tff(7604,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7603, 42])).
% 5.70/5.66 tff(7605,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7604])).
% 5.70/5.66 tff(7606,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7605, 58])).
% 5.70/5.66 tff(7607,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7606])).
% 5.70/5.66 tff(7608,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7607, 36])).
% 5.70/5.66 tff(7609,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7608])).
% 5.70/5.66 tff(7610,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7609, 48])).
% 5.70/5.66 tff(7611,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7610])).
% 5.70/5.66 tff(7612,plain,
% 5.70/5.66 (NSY4!20 = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[601, 7611, 14])).
% 5.70/5.66 tff(7613,plain,
% 5.70/5.66 (pred(NSY4!20) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7612])).
% 5.70/5.66 tff(7614,plain,
% 5.70/5.66 (pred(NSY4!20) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7613, 15])).
% 5.70/5.66 tff(7615,plain,
% 5.70/5.66 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n3, n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7614, 7590])).
% 5.70/5.66 tff(7616,plain,
% 5.70/5.66 (sum(pred(NSY4!20), succ(NPY4!22)) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7615, 32])).
% 5.70/5.66 tff(7617,plain,
% 5.70/5.66 (sum(pred(Y3!54), succ(X3!55)) = sum(n0, n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7460, 7542])).
% 5.70/5.66 tff(7618,plain,
% 5.70/5.66 (sum(pred(Y3!54), succ(X3!55)) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7617, 35])).
% 5.70/5.66 tff(7619,plain,
% 5.70/5.66 (sum(pred(X3!55), succ(Y3!54)) = sum(n0, n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7516, 7484])).
% 5.70/5.66 tff(7620,plain,
% 5.70/5.66 (sum(pred(X3!55), succ(Y3!54)) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7619, 35])).
% 5.70/5.66 tff(7621,plain,
% 5.70/5.66 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n2, n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7620, 7618])).
% 5.70/5.66 tff(7622,plain,
% 5.70/5.66 (X4!53 = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[438, 7621, 34])).
% 5.70/5.66 tff(7623,plain,
% 5.70/5.66 (pred(X4!53) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7622])).
% 5.70/5.66 tff(7624,plain,
% 5.70/5.66 (pred(X4!53) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7623, 15])).
% 5.70/5.66 tff(7625,plain,
% 5.70/5.66 (pred(pred(X4!53)) = pred(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7624])).
% 5.70/5.66 tff(7626,plain,
% 5.70/5.66 (pred(pred(X4!53)) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7625, 25])).
% 5.70/5.66 tff(7627,plain,
% 5.70/5.66 (pred(pred(pred(X4!53))) = pred(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7626])).
% 5.70/5.66 tff(7628,plain,
% 5.70/5.66 (pred(pred(pred(X4!53))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7627, 24])).
% 5.70/5.66 tff(7629,plain,
% 5.70/5.66 (pred(pred(pred(pred(X4!53)))) = pred(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7628])).
% 5.70/5.66 tff(7630,plain,
% 5.70/5.66 (pred(pred(pred(pred(X4!53)))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7629, 23])).
% 5.70/5.66 tff(7631,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X4!53))))) = pred(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7630])).
% 5.70/5.66 tff(7632,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X4!53))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7631, 22])).
% 5.70/5.66 tff(7633,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7632])).
% 5.70/5.66 tff(7634,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7633, 21])).
% 5.70/5.66 tff(7635,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7634])).
% 5.70/5.66 tff(7636,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7635, 20])).
% 5.70/5.66 tff(7637,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7636])).
% 5.70/5.66 tff(7638,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7637, 19])).
% 5.70/5.66 tff(7639,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7638])).
% 5.70/5.66 tff(7640,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7639, 18])).
% 5.70/5.66 tff(7641,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7640])).
% 5.70/5.66 tff(7642,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7641, 17])).
% 5.70/5.66 tff(7643,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7642])).
% 5.70/5.66 tff(7644,plain,
% 5.70/5.66 (NPX4!23 = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[626, 7643, 16])).
% 5.70/5.66 tff(7645,plain,
% 5.70/5.66 (succ(NPX4!23) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7644])).
% 5.70/5.66 tff(7646,plain,
% 5.70/5.66 (succ(NPX4!23) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7645, 33])).
% 5.70/5.66 tff(7647,plain,
% 5.70/5.66 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n5, n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7646, 7616])).
% 5.70/5.66 tff(7648,plain,
% 5.70/5.66 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7647, 558])).
% 5.70/5.66 tff(7649,plain,
% 5.70/5.66 (succ(X4!53) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7622])).
% 5.70/5.66 tff(7650,plain,
% 5.70/5.66 (succ(X4!53) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7649, 33])).
% 5.70/5.66 tff(7651,plain,
% 5.70/5.66 (succ(succ(X4!53)) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7650])).
% 5.70/5.66 tff(7652,plain,
% 5.70/5.66 (succ(succ(X4!53)) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7651, 30])).
% 5.70/5.66 tff(7653,plain,
% 5.70/5.66 (succ(succ(succ(X4!53))) = succ(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7652])).
% 5.70/5.66 tff(7654,plain,
% 5.70/5.66 (succ(succ(succ(X4!53))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7653, 39])).
% 5.70/5.66 tff(7655,plain,
% 5.70/5.66 (succ(succ(succ(succ(X4!53)))) = succ(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7654])).
% 5.70/5.66 tff(7656,plain,
% 5.70/5.66 (succ(succ(succ(succ(X4!53)))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7655, 53])).
% 5.70/5.66 tff(7657,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(X4!53))))) = succ(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7656])).
% 5.70/5.66 tff(7658,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(X4!53))))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7657, 45])).
% 5.70/5.66 tff(7659,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7658])).
% 5.70/5.66 tff(7660,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7659, 28])).
% 5.70/5.66 tff(7661,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7660])).
% 5.70/5.66 tff(7662,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7661, 42])).
% 5.70/5.66 tff(7663,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7662])).
% 5.70/5.66 tff(7664,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7663, 58])).
% 5.70/5.66 tff(7665,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7664])).
% 5.70/5.66 tff(7666,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7665, 36])).
% 5.70/5.66 tff(7667,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7666])).
% 5.70/5.66 tff(7668,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7667, 48])).
% 5.70/5.66 tff(7669,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7668])).
% 5.70/5.66 tff(7670,plain,
% 5.70/5.66 (NSX4!21 = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[651, 7669, 14])).
% 5.70/5.66 tff(7671,plain,
% 5.70/5.66 (pred(NSX4!21) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7670])).
% 5.70/5.66 tff(7672,plain,
% 5.70/5.66 (pred(NSX4!21) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7671, 15])).
% 5.70/5.66 tff(7673,plain,
% 5.70/5.66 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n3, n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7672, 7648])).
% 5.70/5.66 tff(7674,plain,
% 5.70/5.66 (Y5!50 = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[656, 7673, 557])).
% 5.70/5.66 tff(7675,plain,
% 5.70/5.66 (pred(Y5!50) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7674])).
% 5.70/5.66 tff(7676,plain,
% 5.70/5.66 (pred(Y5!50) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7675, 16])).
% 5.70/5.66 tff(7677,plain,
% 5.70/5.66 (pred(pred(Y5!50)) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7676])).
% 5.70/5.66 tff(7678,plain,
% 5.70/5.66 (pred(pred(Y5!50)) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7677, 15])).
% 5.70/5.66 tff(7679,plain,
% 5.70/5.66 (pred(pred(pred(Y5!50))) = pred(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7678])).
% 5.70/5.66 tff(7680,plain,
% 5.70/5.66 (pred(pred(pred(Y5!50))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7679, 25])).
% 5.70/5.66 tff(7681,plain,
% 5.70/5.66 (pred(pred(pred(pred(Y5!50)))) = pred(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7680])).
% 5.70/5.66 tff(7682,plain,
% 5.70/5.66 (pred(pred(pred(pred(Y5!50)))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7681, 24])).
% 5.70/5.66 tff(7683,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7682])).
% 5.70/5.66 tff(7684,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(Y5!50))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7683, 23])).
% 5.70/5.66 tff(7685,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7684])).
% 5.70/5.66 tff(7686,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7685, 22])).
% 5.70/5.66 tff(7687,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7686])).
% 5.70/5.66 tff(7688,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7687, 21])).
% 5.70/5.66 tff(7689,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7688])).
% 5.70/5.66 tff(7690,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7689, 20])).
% 5.70/5.66 tff(7691,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7690])).
% 5.70/5.66 tff(7692,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7691, 19])).
% 5.70/5.66 tff(7693,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7692])).
% 5.70/5.66 tff(7694,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7693, 18])).
% 5.70/5.66 tff(7695,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7694])).
% 5.70/5.66 tff(7696,plain,
% 5.70/5.66 (NPY5!18 = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[694, 7695, 17])).
% 5.70/5.66 tff(7697,plain,
% 5.70/5.66 (succ(NPY5!18) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7696])).
% 5.70/5.66 tff(7698,plain,
% 5.70/5.66 (succ(NPY5!18) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7697, 30])).
% 5.70/5.66 tff(7699,plain,
% 5.70/5.66 (succ(Y5!50) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7674])).
% 5.70/5.66 tff(7700,plain,
% 5.70/5.66 (succ(Y5!50) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7699, 30])).
% 5.70/5.66 tff(7701,plain,
% 5.70/5.66 (succ(succ(Y5!50)) = succ(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7700])).
% 5.70/5.66 tff(7702,plain,
% 5.70/5.66 (succ(succ(Y5!50)) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7701, 39])).
% 5.70/5.66 tff(7703,plain,
% 5.70/5.66 (succ(succ(succ(Y5!50))) = succ(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7702])).
% 5.70/5.66 tff(7704,plain,
% 5.70/5.66 (succ(succ(succ(Y5!50))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7703, 53])).
% 5.70/5.66 tff(7705,plain,
% 5.70/5.66 (succ(succ(succ(succ(Y5!50)))) = succ(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7704])).
% 5.70/5.66 tff(7706,plain,
% 5.70/5.66 (succ(succ(succ(succ(Y5!50)))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7705, 45])).
% 5.70/5.66 tff(7707,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7706])).
% 5.70/5.66 tff(7708,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(Y5!50))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7707, 28])).
% 5.70/5.66 tff(7709,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7708])).
% 5.70/5.66 tff(7710,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7709, 42])).
% 5.70/5.66 tff(7711,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7710])).
% 5.70/5.66 tff(7712,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7711, 58])).
% 5.70/5.66 tff(7713,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7712])).
% 5.70/5.66 tff(7714,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7713, 36])).
% 5.70/5.66 tff(7715,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7714])).
% 5.70/5.66 tff(7716,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7715, 48])).
% 5.70/5.66 tff(7717,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7716])).
% 5.70/5.66 tff(7718,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7717, 14])).
% 5.70/5.66 tff(7719,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7718])).
% 5.70/5.66 tff(7720,plain,
% 5.70/5.66 (NSY5!16 = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[717, 7719, 33])).
% 5.70/5.66 tff(7721,plain,
% 5.70/5.66 (pred(NSY5!16) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7720])).
% 5.70/5.66 tff(7722,plain,
% 5.70/5.66 (pred(NSY5!16) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7721, 16])).
% 5.70/5.66 tff(7723,plain,
% 5.70/5.66 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n4, n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7722, 7698])).
% 5.70/5.66 tff(7724,plain,
% 5.70/5.66 (sum(pred(NSY5!16), succ(NPY5!18)) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7723, 12])).
% 5.70/5.66 tff(7725,plain,
% 5.70/5.66 (sum(pred(Y4!52), succ(X4!53)) = sum(n3, n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7568, 7650])).
% 5.70/5.66 tff(7726,plain,
% 5.70/5.66 (sum(pred(Y4!52), succ(X4!53)) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7725, 32])).
% 5.70/5.66 tff(7727,plain,
% 5.70/5.66 (sum(pred(X4!53), succ(Y4!52)) = sum(n3, n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7624, 7592])).
% 5.70/5.66 tff(7728,plain,
% 5.70/5.66 (sum(pred(X4!53), succ(Y4!52)) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7727, 32])).
% 5.70/5.66 tff(7729,plain,
% 5.70/5.66 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n8, n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7728, 7726])).
% 5.70/5.66 tff(7730,plain,
% 5.70/5.66 (X5!51 = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[553, 7729, 31])).
% 5.70/5.66 tff(7731,plain,
% 5.70/5.66 (pred(X5!51) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7730])).
% 5.70/5.66 tff(7732,plain,
% 5.70/5.66 (pred(X5!51) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7731, 16])).
% 5.70/5.66 tff(7733,plain,
% 5.70/5.66 (pred(pred(X5!51)) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7732])).
% 5.70/5.66 tff(7734,plain,
% 5.70/5.66 (pred(pred(X5!51)) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7733, 15])).
% 5.70/5.66 tff(7735,plain,
% 5.70/5.66 (pred(pred(pred(X5!51))) = pred(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7734])).
% 5.70/5.66 tff(7736,plain,
% 5.70/5.66 (pred(pred(pred(X5!51))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7735, 25])).
% 5.70/5.66 tff(7737,plain,
% 5.70/5.66 (pred(pred(pred(pred(X5!51)))) = pred(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7736])).
% 5.70/5.66 tff(7738,plain,
% 5.70/5.66 (pred(pred(pred(pred(X5!51)))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7737, 24])).
% 5.70/5.66 tff(7739,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X5!51))))) = pred(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7738])).
% 5.70/5.66 tff(7740,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X5!51))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7739, 23])).
% 5.70/5.66 tff(7741,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7740])).
% 5.70/5.66 tff(7742,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7741, 22])).
% 5.70/5.66 tff(7743,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7742])).
% 5.70/5.66 tff(7744,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7743, 21])).
% 5.70/5.66 tff(7745,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7744])).
% 5.70/5.66 tff(7746,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7745, 20])).
% 5.70/5.66 tff(7747,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7746])).
% 5.70/5.66 tff(7748,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7747, 19])).
% 5.70/5.66 tff(7749,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7748])).
% 5.70/5.66 tff(7750,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7749, 18])).
% 5.70/5.66 tff(7751,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7750])).
% 5.70/5.66 tff(7752,plain,
% 5.70/5.66 (NPX5!19 = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[742, 7751, 17])).
% 5.70/5.66 tff(7753,plain,
% 5.70/5.66 (succ(NPX5!19) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7752])).
% 5.70/5.66 tff(7754,plain,
% 5.70/5.66 (succ(NPX5!19) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7753, 30])).
% 5.70/5.66 tff(7755,plain,
% 5.70/5.66 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n6, n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7754, 7724])).
% 5.70/5.66 tff(7756,plain,
% 5.70/5.66 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7755, 674])).
% 5.70/5.66 tff(7757,plain,
% 5.70/5.66 (succ(X5!51) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7730])).
% 5.70/5.66 tff(7758,plain,
% 5.70/5.66 (succ(X5!51) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7757, 30])).
% 5.70/5.66 tff(7759,plain,
% 5.70/5.66 (succ(succ(X5!51)) = succ(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7758])).
% 5.70/5.66 tff(7760,plain,
% 5.70/5.66 (succ(succ(X5!51)) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7759, 39])).
% 5.70/5.66 tff(7761,plain,
% 5.70/5.66 (succ(succ(succ(X5!51))) = succ(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7760])).
% 5.70/5.66 tff(7762,plain,
% 5.70/5.66 (succ(succ(succ(X5!51))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7761, 53])).
% 5.70/5.66 tff(7763,plain,
% 5.70/5.66 (succ(succ(succ(succ(X5!51)))) = succ(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7762])).
% 5.70/5.66 tff(7764,plain,
% 5.70/5.66 (succ(succ(succ(succ(X5!51)))) = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[7763, 45])).
% 5.70/5.66 tff(7765,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(X5!51))))) = succ(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7764])).
% 5.70/5.66 tff(7766,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(X5!51))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7765, 28])).
% 5.70/5.66 tff(7767,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7766])).
% 5.70/5.66 tff(7768,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7767, 42])).
% 5.70/5.66 tff(7769,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7768])).
% 5.70/5.66 tff(7770,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7769, 58])).
% 5.70/5.66 tff(7771,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7770])).
% 5.70/5.66 tff(7772,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7771, 36])).
% 5.70/5.66 tff(7773,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7772])).
% 5.70/5.66 tff(7774,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7773, 48])).
% 5.70/5.66 tff(7775,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7774])).
% 5.70/5.66 tff(7776,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7775, 14])).
% 5.70/5.66 tff(7777,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7776])).
% 5.70/5.66 tff(7778,plain,
% 5.70/5.66 (NSX5!17 = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[767, 7777, 33])).
% 5.70/5.66 tff(7779,plain,
% 5.70/5.66 (pred(NSX5!17) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7778])).
% 5.70/5.66 tff(7780,plain,
% 5.70/5.66 (pred(NSX5!17) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7779, 16])).
% 5.70/5.66 tff(7781,plain,
% 5.70/5.66 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n4, n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7780, 7756])).
% 5.70/5.66 tff(7782,plain,
% 5.70/5.66 (Y6!48 = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[772, 7781, 673])).
% 5.70/5.66 tff(7783,plain,
% 5.70/5.66 (pred(Y6!48) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7782])).
% 5.70/5.66 tff(7784,plain,
% 5.70/5.66 (pred(Y6!48) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7783, 20])).
% 5.70/5.66 tff(7785,plain,
% 5.70/5.66 (pred(pred(Y6!48)) = pred(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7784])).
% 5.70/5.66 tff(7786,plain,
% 5.70/5.66 (pred(pred(Y6!48)) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7785, 19])).
% 5.70/5.66 tff(7787,plain,
% 5.70/5.66 (pred(pred(pred(Y6!48))) = pred(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7786])).
% 5.70/5.66 tff(7788,plain,
% 5.70/5.66 (pred(pred(pred(Y6!48))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7787, 18])).
% 5.70/5.66 tff(7789,plain,
% 5.70/5.66 (pred(pred(pred(pred(Y6!48)))) = pred(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7788])).
% 5.70/5.66 tff(7790,plain,
% 5.70/5.66 (pred(pred(pred(pred(Y6!48)))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7789, 17])).
% 5.70/5.66 tff(7791,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7790])).
% 5.70/5.66 tff(7792,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(Y6!48))))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7791, 16])).
% 5.70/5.66 tff(7793,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7792])).
% 5.70/5.66 tff(7794,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7793, 15])).
% 5.70/5.66 tff(7795,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7794])).
% 5.70/5.66 tff(7796,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7795, 25])).
% 5.70/5.66 tff(7797,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7796])).
% 5.70/5.66 tff(7798,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7797, 24])).
% 5.70/5.66 tff(7799,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7798])).
% 5.70/5.66 tff(7800,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7799, 23])).
% 5.70/5.66 tff(7801,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7800])).
% 5.70/5.66 tff(7802,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7801, 22])).
% 5.70/5.66 tff(7803,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7802])).
% 5.70/5.66 tff(7804,plain,
% 5.70/5.66 (NPY6!14 = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[1465, 7803, 21])).
% 5.70/5.66 tff(7805,plain,
% 5.70/5.66 (succ(NPY6!14) = succ(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7804])).
% 5.70/5.66 tff(7806,plain,
% 5.70/5.66 (succ(NPY6!14) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7805, 28])).
% 5.70/5.66 tff(7807,plain,
% 5.70/5.66 (succ(Y6!48) = succ(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7782])).
% 5.70/5.66 tff(7808,plain,
% 5.70/5.66 (succ(Y6!48) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7807, 28])).
% 5.70/5.66 tff(7809,plain,
% 5.70/5.66 (succ(succ(Y6!48)) = succ(n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7808])).
% 5.70/5.66 tff(7810,plain,
% 5.70/5.66 (succ(succ(Y6!48)) = n0),
% 5.70/5.66 inference(transitivity,[status(thm)],[7809, 42])).
% 5.70/5.66 tff(7811,plain,
% 5.70/5.66 (succ(succ(succ(Y6!48))) = succ(n0)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7810])).
% 5.70/5.66 tff(7812,plain,
% 5.70/5.66 (succ(succ(succ(Y6!48))) = n1),
% 5.70/5.66 inference(transitivity,[status(thm)],[7811, 58])).
% 5.70/5.66 tff(7813,plain,
% 5.70/5.66 (succ(succ(succ(succ(Y6!48)))) = succ(n1)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7812])).
% 5.70/5.66 tff(7814,plain,
% 5.70/5.66 (succ(succ(succ(succ(Y6!48)))) = n2),
% 5.70/5.66 inference(transitivity,[status(thm)],[7813, 36])).
% 5.70/5.66 tff(7815,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n2)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7814])).
% 5.70/5.66 tff(7816,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(Y6!48))))) = n3),
% 5.70/5.66 inference(transitivity,[status(thm)],[7815, 48])).
% 5.70/5.66 tff(7817,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n3)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7816])).
% 5.70/5.66 tff(7818,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7817, 14])).
% 5.70/5.66 tff(7819,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7818])).
% 5.70/5.66 tff(7820,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7819, 33])).
% 5.70/5.66 tff(7821,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7820])).
% 5.70/5.66 tff(7822,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7821, 30])).
% 5.70/5.66 tff(7823,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7822])).
% 5.70/5.66 tff(7824,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7823, 39])).
% 5.70/5.66 tff(7825,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7824])).
% 5.70/5.66 tff(7826,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7825, 53])).
% 5.70/5.66 tff(7827,plain,
% 5.70/5.66 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7826])).
% 5.70/5.66 tff(7828,plain,
% 5.70/5.66 (NSY6!12 = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[1490, 7827, 45])).
% 5.70/5.66 tff(7829,plain,
% 5.70/5.66 (pred(NSY6!12) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7828])).
% 5.70/5.66 tff(7830,plain,
% 5.70/5.66 (pred(NSY6!12) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7829, 20])).
% 5.70/5.66 tff(7831,plain,
% 5.70/5.66 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n8, n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7830, 7806])).
% 5.70/5.66 tff(7832,plain,
% 5.70/5.66 (sum(pred(NSY6!12), succ(NPY6!14)) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7831, 27])).
% 5.70/5.66 tff(7833,plain,
% 5.70/5.66 (sum(pred(Y5!50), succ(X5!51)) = sum(n4, n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7676, 7758])).
% 5.70/5.66 tff(7834,plain,
% 5.70/5.66 (sum(pred(Y5!50), succ(X5!51)) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7833, 12])).
% 5.70/5.66 tff(7835,plain,
% 5.70/5.66 (sum(pred(X5!51), succ(Y5!50)) = sum(n4, n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7732, 7700])).
% 5.70/5.66 tff(7836,plain,
% 5.70/5.66 (sum(pred(X5!51), succ(Y5!50)) = n10),
% 5.70/5.66 inference(transitivity,[status(thm)],[7835, 12])).
% 5.70/5.66 tff(7837,plain,
% 5.70/5.66 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n10, n10)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7836, 7834])).
% 5.70/5.66 tff(7838,plain,
% 5.70/5.66 (X6!49 = n9),
% 5.70/5.66 inference(transitivity,[status(thm)],[669, 7837, 29])).
% 5.70/5.66 tff(7839,plain,
% 5.70/5.66 (pred(X6!49) = pred(n9)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7838])).
% 5.70/5.66 tff(7840,plain,
% 5.70/5.66 (pred(X6!49) = n8),
% 5.70/5.66 inference(transitivity,[status(thm)],[7839, 20])).
% 5.70/5.66 tff(7841,plain,
% 5.70/5.66 (pred(pred(X6!49)) = pred(n8)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7840])).
% 5.70/5.66 tff(7842,plain,
% 5.70/5.66 (pred(pred(X6!49)) = n7),
% 5.70/5.66 inference(transitivity,[status(thm)],[7841, 19])).
% 5.70/5.66 tff(7843,plain,
% 5.70/5.66 (pred(pred(pred(X6!49))) = pred(n7)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7842])).
% 5.70/5.66 tff(7844,plain,
% 5.70/5.66 (pred(pred(pred(X6!49))) = n6),
% 5.70/5.66 inference(transitivity,[status(thm)],[7843, 18])).
% 5.70/5.66 tff(7845,plain,
% 5.70/5.66 (pred(pred(pred(pred(X6!49)))) = pred(n6)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7844])).
% 5.70/5.66 tff(7846,plain,
% 5.70/5.66 (pred(pred(pred(pred(X6!49)))) = n5),
% 5.70/5.66 inference(transitivity,[status(thm)],[7845, 17])).
% 5.70/5.66 tff(7847,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X6!49))))) = pred(n5)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7846])).
% 5.70/5.66 tff(7848,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(X6!49))))) = n4),
% 5.70/5.66 inference(transitivity,[status(thm)],[7847, 16])).
% 5.70/5.66 tff(7849,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n4)),
% 5.70/5.66 inference(monotonicity,[status(thm)],[7848])).
% 5.70/5.66 tff(7850,plain,
% 5.70/5.66 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[7849, 15])).
% 5.70/5.67 tff(7851,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7850])).
% 5.70/5.67 tff(7852,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[7851, 25])).
% 5.70/5.67 tff(7853,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7852])).
% 5.70/5.67 tff(7854,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7853, 24])).
% 5.70/5.67 tff(7855,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7854])).
% 5.70/5.67 tff(7856,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[7855, 23])).
% 5.70/5.67 tff(7857,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7856])).
% 5.70/5.67 tff(7858,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[7857, 22])).
% 5.70/5.67 tff(7859,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7858])).
% 5.70/5.67 tff(7860,plain,
% 5.70/5.67 (NPX6!15 = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[1523, 7859, 21])).
% 5.70/5.67 tff(7861,plain,
% 5.70/5.67 (succ(NPX6!15) = succ(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7860])).
% 5.70/5.67 tff(7862,plain,
% 5.70/5.67 (succ(NPX6!15) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[7861, 28])).
% 5.70/5.67 tff(7863,plain,
% 5.70/5.67 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n10, n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7862, 7832])).
% 5.70/5.67 tff(7864,plain,
% 5.70/5.67 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[7863, 69])).
% 5.70/5.67 tff(7865,plain,
% 5.70/5.67 (succ(X6!49) = succ(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7838])).
% 5.70/5.67 tff(7866,plain,
% 5.70/5.67 (succ(X6!49) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[7865, 28])).
% 5.70/5.67 tff(7867,plain,
% 5.70/5.67 (succ(succ(X6!49)) = succ(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7866])).
% 5.70/5.67 tff(7868,plain,
% 5.70/5.67 (succ(succ(X6!49)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[7867, 42])).
% 5.70/5.67 tff(7869,plain,
% 5.70/5.67 (succ(succ(succ(X6!49))) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7868])).
% 5.70/5.67 tff(7870,plain,
% 5.70/5.67 (succ(succ(succ(X6!49))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7869, 58])).
% 5.70/5.67 tff(7871,plain,
% 5.70/5.67 (succ(succ(succ(succ(X6!49)))) = succ(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7870])).
% 5.70/5.67 tff(7872,plain,
% 5.70/5.67 (succ(succ(succ(succ(X6!49)))) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[7871, 36])).
% 5.70/5.67 tff(7873,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(X6!49))))) = succ(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7872])).
% 5.70/5.67 tff(7874,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(X6!49))))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[7873, 48])).
% 5.70/5.67 tff(7875,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7874])).
% 5.70/5.67 tff(7876,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[7875, 14])).
% 5.70/5.67 tff(7877,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7876])).
% 5.70/5.67 tff(7878,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[7877, 33])).
% 5.70/5.67 tff(7879,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7878])).
% 5.70/5.67 tff(7880,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[7879, 30])).
% 5.70/5.67 tff(7881,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7880])).
% 5.70/5.67 tff(7882,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[7881, 39])).
% 5.70/5.67 tff(7883,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7882])).
% 5.70/5.67 tff(7884,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[7883, 53])).
% 5.70/5.67 tff(7885,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7884])).
% 5.70/5.67 tff(7886,plain,
% 5.70/5.67 (NSX6!13 = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[1550, 7885, 45])).
% 5.70/5.67 tff(7887,plain,
% 5.70/5.67 (pred(NSX6!13) = pred(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7886])).
% 5.70/5.67 tff(7888,plain,
% 5.70/5.67 (pred(NSX6!13) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[7887, 20])).
% 5.70/5.67 tff(7889,plain,
% 5.70/5.67 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n8, n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7888, 7864])).
% 5.70/5.67 tff(7890,plain,
% 5.70/5.67 (sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.70/5.67 inference(symmetry,[status(thm)],[7889])).
% 5.70/5.67 tff(7891,plain,
% 5.70/5.67 (sum(pred(Y6!48), succ(X6!49)) = sum(n8, n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7784, 7866])).
% 5.70/5.67 tff(7892,plain,
% 5.70/5.67 (sum(pred(Y6!48), succ(X6!49)) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[7891, 27])).
% 5.70/5.67 tff(7893,plain,
% 5.70/5.67 (sum(pred(X6!49), succ(Y6!48)) = sum(n8, n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7840, 7808])).
% 5.70/5.67 tff(7894,plain,
% 5.70/5.67 (sum(pred(X6!49), succ(Y6!48)) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[7893, 27])).
% 5.70/5.67 tff(7895,plain,
% 5.70/5.67 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n7, n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7894, 7892])).
% 5.70/5.67 tff(7896,plain,
% 5.70/5.67 (X7!47 = Y7!46),
% 5.70/5.67 inference(transitivity,[status(thm)],[785, 7895, 26, 1556, 7890, 794])).
% 5.70/5.67 tff(7897,plain,
% 5.70/5.67 ($false),
% 5.70/5.67 inference(unit_resolution,[status(thm)],[792, 7896])).
% 5.70/5.67 tff(7898,plain,((~(Y0!60 = n5)) | (X7!47 = Y7!46) | (~(X0!61 = n5))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.67 tff(7899,plain,
% 5.70/5.67 (~(Y0!60 = n5)),
% 5.70/5.67 inference(unit_resolution,[status(thm)],[7898, 7190, 792])).
% 5.70/5.67 tff(7900,plain,
% 5.70/5.67 (sum(n4, n7) = n0),
% 5.70/5.67 inference(and_elim,[status(thm)],[9])).
% 5.70/5.67 tff(7901,plain,
% 5.70/5.67 (sum(n6, n1) = n7),
% 5.70/5.67 inference(and_elim,[status(thm)],[9])).
% 5.70/5.67 tff(7902,plain,
% 5.70/5.67 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n6, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7214, 1622])).
% 5.70/5.67 tff(7903,plain,
% 5.70/5.67 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[7902, 7901])).
% 5.70/5.67 tff(7904,plain,
% 5.70/5.67 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n4, n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7240, 7903])).
% 5.70/5.67 tff(7905,plain,
% 5.70/5.67 (Y1!58 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[196, 7904, 7900])).
% 5.70/5.67 tff(7906,plain,
% 5.70/5.67 (pred(Y1!58) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7905])).
% 5.70/5.67 tff(7907,plain,
% 5.70/5.67 (pred(Y1!58) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[7906, 22])).
% 5.70/5.67 tff(7908,plain,
% 5.70/5.67 (pred(pred(Y1!58)) = pred(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7907])).
% 5.70/5.67 tff(7909,plain,
% 5.70/5.67 (pred(pred(Y1!58)) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[7908, 21])).
% 5.70/5.67 tff(7910,plain,
% 5.70/5.67 (pred(pred(pred(Y1!58))) = pred(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7909])).
% 5.70/5.67 tff(7911,plain,
% 5.70/5.67 (pred(pred(pred(Y1!58))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[7910, 20])).
% 5.70/5.67 tff(7912,plain,
% 5.70/5.67 (pred(pred(pred(pred(Y1!58)))) = pred(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7911])).
% 5.70/5.67 tff(7913,plain,
% 5.70/5.67 (pred(pred(pred(pred(Y1!58)))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[7912, 19])).
% 5.70/5.67 tff(7914,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7913])).
% 5.70/5.67 tff(7915,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(Y1!58))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[7914, 18])).
% 5.70/5.67 tff(7916,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7915])).
% 5.70/5.67 tff(7917,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[7916, 17])).
% 5.70/5.67 tff(7918,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7917])).
% 5.70/5.67 tff(7919,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[7918, 16])).
% 5.70/5.67 tff(7920,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7919])).
% 5.70/5.67 tff(7921,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[7920, 15])).
% 5.70/5.67 tff(7922,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7921])).
% 5.70/5.67 tff(7923,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[7922, 25])).
% 5.70/5.67 tff(7924,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7923])).
% 5.70/5.67 tff(7925,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7924, 24])).
% 5.70/5.67 tff(7926,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7925])).
% 5.70/5.67 tff(7927,plain,
% 5.70/5.67 (NPY1!34 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[232, 7926, 23])).
% 5.70/5.67 tff(7928,plain,
% 5.70/5.67 (succ(NPY1!34) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7927])).
% 5.70/5.67 tff(7929,plain,
% 5.70/5.67 (succ(NPY1!34) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7928, 58])).
% 5.70/5.67 tff(7930,plain,
% 5.70/5.67 (succ(Y1!58) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7905])).
% 5.70/5.67 tff(7931,plain,
% 5.70/5.67 (succ(Y1!58) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7930, 58])).
% 5.70/5.67 tff(7932,plain,
% 5.70/5.67 (succ(succ(Y1!58)) = succ(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7931])).
% 5.70/5.67 tff(7933,plain,
% 5.70/5.67 (succ(succ(Y1!58)) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[7932, 36])).
% 5.70/5.67 tff(7934,plain,
% 5.70/5.67 (succ(succ(succ(Y1!58))) = succ(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7933])).
% 5.70/5.67 tff(7935,plain,
% 5.70/5.67 (succ(succ(succ(Y1!58))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[7934, 48])).
% 5.70/5.67 tff(7936,plain,
% 5.70/5.67 (succ(succ(succ(succ(Y1!58)))) = succ(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7935])).
% 5.70/5.67 tff(7937,plain,
% 5.70/5.67 (succ(succ(succ(succ(Y1!58)))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[7936, 14])).
% 5.70/5.67 tff(7938,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7937])).
% 5.70/5.67 tff(7939,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(Y1!58))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[7938, 33])).
% 5.70/5.67 tff(7940,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7939])).
% 5.70/5.67 tff(7941,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[7940, 30])).
% 5.70/5.67 tff(7942,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7941])).
% 5.70/5.67 tff(7943,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[7942, 39])).
% 5.70/5.67 tff(7944,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7943])).
% 5.70/5.67 tff(7945,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[7944, 53])).
% 5.70/5.67 tff(7946,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7945])).
% 5.70/5.67 tff(7947,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[7946, 45])).
% 5.70/5.67 tff(7948,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7947])).
% 5.70/5.67 tff(7949,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[7948, 28])).
% 5.70/5.67 tff(7950,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7949])).
% 5.70/5.67 tff(7951,plain,
% 5.70/5.67 (NSY1!32 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[255, 7950, 42])).
% 5.70/5.67 tff(7952,plain,
% 5.70/5.67 (pred(NSY1!32) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7951])).
% 5.70/5.67 tff(7953,plain,
% 5.70/5.67 (pred(NSY1!32) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[7952, 22])).
% 5.70/5.67 tff(7954,plain,
% 5.70/5.67 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7953, 7929])).
% 5.70/5.67 tff(7955,plain,
% 5.70/5.67 (sum(pred(NSY1!32), succ(NPY1!34)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[7954, 57])).
% 5.70/5.67 tff(7956,plain,
% 5.70/5.67 (sum(pred(Y0!60), succ(X0!61)) = sum(n5, n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[1574, 7218])).
% 5.70/5.67 tff(7957,plain,
% 5.70/5.67 (sum(pred(Y0!60), succ(X0!61)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[7956, 60])).
% 5.70/5.67 tff(7958,plain,
% 5.70/5.67 (sum(pred(X0!61), succ(Y0!60)) = sum(n4, n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7192, 1598])).
% 5.70/5.67 tff(7959,plain,
% 5.70/5.67 (sum(pred(X0!61), succ(Y0!60)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[7958, 7900])).
% 5.70/5.67 tff(7960,plain,
% 5.70/5.67 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n0, n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7959, 7957])).
% 5.70/5.67 tff(7961,plain,
% 5.70/5.67 (X1!59 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[93, 7960, 59])).
% 5.70/5.67 tff(7962,plain,
% 5.70/5.67 (pred(X1!59) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7961])).
% 5.70/5.67 tff(7963,plain,
% 5.70/5.67 (pred(X1!59) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[7962, 22])).
% 5.70/5.67 tff(7964,plain,
% 5.70/5.67 (pred(pred(X1!59)) = pred(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7963])).
% 5.70/5.67 tff(7965,plain,
% 5.70/5.67 (pred(pred(X1!59)) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[7964, 21])).
% 5.70/5.67 tff(7966,plain,
% 5.70/5.67 (pred(pred(pred(X1!59))) = pred(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7965])).
% 5.70/5.67 tff(7967,plain,
% 5.70/5.67 (pred(pred(pred(X1!59))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[7966, 20])).
% 5.70/5.67 tff(7968,plain,
% 5.70/5.67 (pred(pred(pred(pred(X1!59)))) = pred(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7967])).
% 5.70/5.67 tff(7969,plain,
% 5.70/5.67 (pred(pred(pred(pred(X1!59)))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[7968, 19])).
% 5.70/5.67 tff(7970,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(X1!59))))) = pred(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7969])).
% 5.70/5.67 tff(7971,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(X1!59))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[7970, 18])).
% 5.70/5.67 tff(7972,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7971])).
% 5.70/5.67 tff(7973,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[7972, 17])).
% 5.70/5.67 tff(7974,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7973])).
% 5.70/5.67 tff(7975,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[7974, 16])).
% 5.70/5.67 tff(7976,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7975])).
% 5.70/5.67 tff(7977,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[7976, 15])).
% 5.70/5.67 tff(7978,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7977])).
% 5.70/5.67 tff(7979,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[7978, 25])).
% 5.70/5.67 tff(7980,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7979])).
% 5.70/5.67 tff(7981,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7980, 24])).
% 5.70/5.67 tff(7982,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7981])).
% 5.70/5.67 tff(7983,plain,
% 5.70/5.67 (NPX1!35 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[280, 7982, 23])).
% 5.70/5.67 tff(7984,plain,
% 5.70/5.67 (succ(NPX1!35) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7983])).
% 5.70/5.67 tff(7985,plain,
% 5.70/5.67 (succ(NPX1!35) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7984, 58])).
% 5.70/5.67 tff(7986,plain,
% 5.70/5.67 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n1, n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7985, 7955])).
% 5.70/5.67 tff(7987,plain,
% 5.70/5.67 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7986, 56])).
% 5.70/5.67 tff(7988,plain,
% 5.70/5.67 (succ(X1!59) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7961])).
% 5.70/5.67 tff(7989,plain,
% 5.70/5.67 (succ(X1!59) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[7988, 58])).
% 5.70/5.67 tff(7990,plain,
% 5.70/5.67 (succ(succ(X1!59)) = succ(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7989])).
% 5.70/5.67 tff(7991,plain,
% 5.70/5.67 (succ(succ(X1!59)) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[7990, 36])).
% 5.70/5.67 tff(7992,plain,
% 5.70/5.67 (succ(succ(succ(X1!59))) = succ(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7991])).
% 5.70/5.67 tff(7993,plain,
% 5.70/5.67 (succ(succ(succ(X1!59))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[7992, 48])).
% 5.70/5.67 tff(7994,plain,
% 5.70/5.67 (succ(succ(succ(succ(X1!59)))) = succ(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7993])).
% 5.70/5.67 tff(7995,plain,
% 5.70/5.67 (succ(succ(succ(succ(X1!59)))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[7994, 14])).
% 5.70/5.67 tff(7996,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(X1!59))))) = succ(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7995])).
% 5.70/5.67 tff(7997,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(X1!59))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[7996, 33])).
% 5.70/5.67 tff(7998,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7997])).
% 5.70/5.67 tff(7999,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[7998, 30])).
% 5.70/5.67 tff(8000,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7999])).
% 5.70/5.67 tff(8001,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8000, 39])).
% 5.70/5.67 tff(8002,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8001])).
% 5.70/5.67 tff(8003,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8002, 53])).
% 5.70/5.67 tff(8004,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8003])).
% 5.70/5.67 tff(8005,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8004, 45])).
% 5.70/5.67 tff(8006,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8005])).
% 5.70/5.67 tff(8007,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8006, 28])).
% 5.70/5.67 tff(8008,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8007])).
% 5.70/5.67 tff(8009,plain,
% 5.70/5.67 (NSX1!33 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[305, 8008, 42])).
% 5.70/5.67 tff(8010,plain,
% 5.70/5.67 (pred(NSX1!33) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8009])).
% 5.70/5.67 tff(8011,plain,
% 5.70/5.67 (pred(NSX1!33) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8010, 22])).
% 5.70/5.67 tff(8012,plain,
% 5.70/5.67 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8011, 7987])).
% 5.70/5.67 tff(8013,plain,
% 5.70/5.67 (Y2!56 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[310, 8012, 57])).
% 5.70/5.67 tff(8014,plain,
% 5.70/5.67 (pred(Y2!56) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8013])).
% 5.70/5.67 tff(8015,plain,
% 5.70/5.67 (pred(Y2!56) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8014, 22])).
% 5.70/5.67 tff(8016,plain,
% 5.70/5.67 (pred(pred(Y2!56)) = pred(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8015])).
% 5.70/5.67 tff(8017,plain,
% 5.70/5.67 (pred(pred(Y2!56)) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8016, 21])).
% 5.70/5.67 tff(8018,plain,
% 5.70/5.67 (pred(pred(pred(Y2!56))) = pred(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8017])).
% 5.70/5.67 tff(8019,plain,
% 5.70/5.67 (pred(pred(pred(Y2!56))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8018, 20])).
% 5.70/5.67 tff(8020,plain,
% 5.70/5.67 (pred(pred(pred(pred(Y2!56)))) = pred(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8019])).
% 5.70/5.67 tff(8021,plain,
% 5.70/5.67 (pred(pred(pred(pred(Y2!56)))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8020, 19])).
% 5.70/5.67 tff(8022,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8021])).
% 5.70/5.67 tff(8023,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(Y2!56))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[8022, 18])).
% 5.70/5.67 tff(8024,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8023])).
% 5.70/5.67 tff(8025,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[8024, 17])).
% 5.70/5.67 tff(8026,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8025])).
% 5.70/5.67 tff(8027,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[8026, 16])).
% 5.70/5.67 tff(8028,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8027])).
% 5.70/5.67 tff(8029,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[8028, 15])).
% 5.70/5.67 tff(8030,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8029])).
% 5.70/5.67 tff(8031,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[8030, 25])).
% 5.70/5.67 tff(8032,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8031])).
% 5.70/5.67 tff(8033,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8032, 24])).
% 5.70/5.67 tff(8034,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8033])).
% 5.70/5.67 tff(8035,plain,
% 5.70/5.67 (NPY2!30 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[347, 8034, 23])).
% 5.70/5.67 tff(8036,plain,
% 5.70/5.67 (succ(NPY2!30) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8035])).
% 5.70/5.67 tff(8037,plain,
% 5.70/5.67 (succ(NPY2!30) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8036, 58])).
% 5.70/5.67 tff(8038,plain,
% 5.70/5.67 (succ(Y2!56) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8013])).
% 5.70/5.67 tff(8039,plain,
% 5.70/5.67 (succ(Y2!56) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8038, 58])).
% 5.70/5.67 tff(8040,plain,
% 5.70/5.67 (succ(succ(Y2!56)) = succ(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8039])).
% 5.70/5.67 tff(8041,plain,
% 5.70/5.67 (succ(succ(Y2!56)) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[8040, 36])).
% 5.70/5.67 tff(8042,plain,
% 5.70/5.67 (succ(succ(succ(Y2!56))) = succ(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8041])).
% 5.70/5.67 tff(8043,plain,
% 5.70/5.67 (succ(succ(succ(Y2!56))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[8042, 48])).
% 5.70/5.67 tff(8044,plain,
% 5.70/5.67 (succ(succ(succ(succ(Y2!56)))) = succ(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8043])).
% 5.70/5.67 tff(8045,plain,
% 5.70/5.67 (succ(succ(succ(succ(Y2!56)))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[8044, 14])).
% 5.70/5.67 tff(8046,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8045])).
% 5.70/5.67 tff(8047,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(Y2!56))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[8046, 33])).
% 5.70/5.67 tff(8048,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8047])).
% 5.70/5.67 tff(8049,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[8048, 30])).
% 5.70/5.67 tff(8050,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8049])).
% 5.70/5.67 tff(8051,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8050, 39])).
% 5.70/5.67 tff(8052,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8051])).
% 5.70/5.67 tff(8053,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8052, 53])).
% 5.70/5.67 tff(8054,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8053])).
% 5.70/5.67 tff(8055,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8054, 45])).
% 5.70/5.67 tff(8056,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8055])).
% 5.70/5.67 tff(8057,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8056, 28])).
% 5.70/5.67 tff(8058,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8057])).
% 5.70/5.67 tff(8059,plain,
% 5.70/5.67 (NSY2!28 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[370, 8058, 42])).
% 5.70/5.67 tff(8060,plain,
% 5.70/5.67 (pred(NSY2!28) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8059])).
% 5.70/5.67 tff(8061,plain,
% 5.70/5.67 (pred(NSY2!28) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8060, 22])).
% 5.70/5.67 tff(8062,plain,
% 5.70/5.67 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8061, 8037])).
% 5.70/5.67 tff(8063,plain,
% 5.70/5.67 (sum(pred(NSY2!28), succ(NPY2!30)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[8062, 57])).
% 5.70/5.67 tff(8064,plain,
% 5.70/5.67 (sum(pred(Y1!58), succ(X1!59)) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7907, 7989])).
% 5.70/5.67 tff(8065,plain,
% 5.70/5.67 (sum(pred(Y1!58), succ(X1!59)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[8064, 57])).
% 5.70/5.67 tff(8066,plain,
% 5.70/5.67 (sum(pred(X1!59), succ(Y1!58)) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[7963, 7931])).
% 5.70/5.67 tff(8067,plain,
% 5.70/5.67 (sum(pred(X1!59), succ(Y1!58)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[8066, 57])).
% 5.70/5.67 tff(8068,plain,
% 5.70/5.67 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n0, n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8067, 8065])).
% 5.70/5.67 tff(8069,plain,
% 5.70/5.67 (X2!57 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[209, 8068, 59])).
% 5.70/5.67 tff(8070,plain,
% 5.70/5.67 (pred(X2!57) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8069])).
% 5.70/5.67 tff(8071,plain,
% 5.70/5.67 (pred(X2!57) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8070, 22])).
% 5.70/5.67 tff(8072,plain,
% 5.70/5.67 (pred(pred(X2!57)) = pred(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8071])).
% 5.70/5.67 tff(8073,plain,
% 5.70/5.67 (pred(pred(X2!57)) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8072, 21])).
% 5.70/5.67 tff(8074,plain,
% 5.70/5.67 (pred(pred(pred(X2!57))) = pred(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8073])).
% 5.70/5.67 tff(8075,plain,
% 5.70/5.67 (pred(pred(pred(X2!57))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8074, 20])).
% 5.70/5.67 tff(8076,plain,
% 5.70/5.67 (pred(pred(pred(pred(X2!57)))) = pred(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8075])).
% 5.70/5.67 tff(8077,plain,
% 5.70/5.67 (pred(pred(pred(pred(X2!57)))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8076, 19])).
% 5.70/5.67 tff(8078,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(X2!57))))) = pred(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8077])).
% 5.70/5.67 tff(8079,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(X2!57))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[8078, 18])).
% 5.70/5.67 tff(8080,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8079])).
% 5.70/5.67 tff(8081,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[8080, 17])).
% 5.70/5.67 tff(8082,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8081])).
% 5.70/5.67 tff(8083,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[8082, 16])).
% 5.70/5.67 tff(8084,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8083])).
% 5.70/5.67 tff(8085,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[8084, 15])).
% 5.70/5.67 tff(8086,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8085])).
% 5.70/5.67 tff(8087,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[8086, 25])).
% 5.70/5.67 tff(8088,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8087])).
% 5.70/5.67 tff(8089,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8088, 24])).
% 5.70/5.67 tff(8090,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8089])).
% 5.70/5.67 tff(8091,plain,
% 5.70/5.67 (NPX2!31 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[395, 8090, 23])).
% 5.70/5.67 tff(8092,plain,
% 5.70/5.67 (succ(NPX2!31) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8091])).
% 5.70/5.67 tff(8093,plain,
% 5.70/5.67 (succ(NPX2!31) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8092, 58])).
% 5.70/5.67 tff(8094,plain,
% 5.70/5.67 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n1, n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8093, 8063])).
% 5.70/5.67 tff(8095,plain,
% 5.70/5.67 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8094, 56])).
% 5.70/5.67 tff(8096,plain,
% 5.70/5.67 (succ(X2!57) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8069])).
% 5.70/5.67 tff(8097,plain,
% 5.70/5.67 (succ(X2!57) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8096, 58])).
% 5.70/5.67 tff(8098,plain,
% 5.70/5.67 (succ(succ(X2!57)) = succ(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8097])).
% 5.70/5.67 tff(8099,plain,
% 5.70/5.67 (succ(succ(X2!57)) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[8098, 36])).
% 5.70/5.67 tff(8100,plain,
% 5.70/5.67 (succ(succ(succ(X2!57))) = succ(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8099])).
% 5.70/5.67 tff(8101,plain,
% 5.70/5.67 (succ(succ(succ(X2!57))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[8100, 48])).
% 5.70/5.67 tff(8102,plain,
% 5.70/5.67 (succ(succ(succ(succ(X2!57)))) = succ(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8101])).
% 5.70/5.67 tff(8103,plain,
% 5.70/5.67 (succ(succ(succ(succ(X2!57)))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[8102, 14])).
% 5.70/5.67 tff(8104,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(X2!57))))) = succ(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8103])).
% 5.70/5.67 tff(8105,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(X2!57))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[8104, 33])).
% 5.70/5.67 tff(8106,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8105])).
% 5.70/5.67 tff(8107,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[8106, 30])).
% 5.70/5.67 tff(8108,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8107])).
% 5.70/5.67 tff(8109,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8108, 39])).
% 5.70/5.67 tff(8110,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8109])).
% 5.70/5.67 tff(8111,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8110, 53])).
% 5.70/5.67 tff(8112,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8111])).
% 5.70/5.67 tff(8113,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8112, 45])).
% 5.70/5.67 tff(8114,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8113])).
% 5.70/5.67 tff(8115,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8114, 28])).
% 5.70/5.67 tff(8116,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8115])).
% 5.70/5.67 tff(8117,plain,
% 5.70/5.67 (NSX2!29 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[420, 8116, 42])).
% 5.70/5.67 tff(8118,plain,
% 5.70/5.67 (pred(NSX2!29) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8117])).
% 5.70/5.67 tff(8119,plain,
% 5.70/5.67 (pred(NSX2!29) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8118, 22])).
% 5.70/5.67 tff(8120,plain,
% 5.70/5.67 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8119, 8095])).
% 5.70/5.67 tff(8121,plain,
% 5.70/5.67 (Y3!54 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[425, 8120, 57])).
% 5.70/5.67 tff(8122,plain,
% 5.70/5.67 (pred(Y3!54) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8121])).
% 5.70/5.67 tff(8123,plain,
% 5.70/5.67 (pred(Y3!54) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8122, 22])).
% 5.70/5.67 tff(8124,plain,
% 5.70/5.67 (pred(pred(Y3!54)) = pred(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8123])).
% 5.70/5.67 tff(8125,plain,
% 5.70/5.67 (pred(pred(Y3!54)) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8124, 21])).
% 5.70/5.67 tff(8126,plain,
% 5.70/5.67 (pred(pred(pred(Y3!54))) = pred(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8125])).
% 5.70/5.67 tff(8127,plain,
% 5.70/5.67 (pred(pred(pred(Y3!54))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8126, 20])).
% 5.70/5.67 tff(8128,plain,
% 5.70/5.67 (pred(pred(pred(pred(Y3!54)))) = pred(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8127])).
% 5.70/5.67 tff(8129,plain,
% 5.70/5.67 (pred(pred(pred(pred(Y3!54)))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8128, 19])).
% 5.70/5.67 tff(8130,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8129])).
% 5.70/5.67 tff(8131,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(Y3!54))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[8130, 18])).
% 5.70/5.67 tff(8132,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8131])).
% 5.70/5.67 tff(8133,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[8132, 17])).
% 5.70/5.67 tff(8134,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8133])).
% 5.70/5.67 tff(8135,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[8134, 16])).
% 5.70/5.67 tff(8136,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8135])).
% 5.70/5.67 tff(8137,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[8136, 15])).
% 5.70/5.67 tff(8138,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8137])).
% 5.70/5.67 tff(8139,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[8138, 25])).
% 5.70/5.67 tff(8140,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8139])).
% 5.70/5.67 tff(8141,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8140, 24])).
% 5.70/5.67 tff(8142,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8141])).
% 5.70/5.67 tff(8143,plain,
% 5.70/5.67 (NPY3!26 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[462, 8142, 23])).
% 5.70/5.67 tff(8144,plain,
% 5.70/5.67 (succ(NPY3!26) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8143])).
% 5.70/5.67 tff(8145,plain,
% 5.70/5.67 (succ(NPY3!26) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8144, 58])).
% 5.70/5.67 tff(8146,plain,
% 5.70/5.67 (succ(Y3!54) = succ(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8121])).
% 5.70/5.67 tff(8147,plain,
% 5.70/5.67 (succ(Y3!54) = n1),
% 5.70/5.67 inference(transitivity,[status(thm)],[8146, 58])).
% 5.70/5.67 tff(8148,plain,
% 5.70/5.67 (succ(succ(Y3!54)) = succ(n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8147])).
% 5.70/5.67 tff(8149,plain,
% 5.70/5.67 (succ(succ(Y3!54)) = n2),
% 5.70/5.67 inference(transitivity,[status(thm)],[8148, 36])).
% 5.70/5.67 tff(8150,plain,
% 5.70/5.67 (succ(succ(succ(Y3!54))) = succ(n2)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8149])).
% 5.70/5.67 tff(8151,plain,
% 5.70/5.67 (succ(succ(succ(Y3!54))) = n3),
% 5.70/5.67 inference(transitivity,[status(thm)],[8150, 48])).
% 5.70/5.67 tff(8152,plain,
% 5.70/5.67 (succ(succ(succ(succ(Y3!54)))) = succ(n3)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8151])).
% 5.70/5.67 tff(8153,plain,
% 5.70/5.67 (succ(succ(succ(succ(Y3!54)))) = n4),
% 5.70/5.67 inference(transitivity,[status(thm)],[8152, 14])).
% 5.70/5.67 tff(8154,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n4)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8153])).
% 5.70/5.67 tff(8155,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(Y3!54))))) = n5),
% 5.70/5.67 inference(transitivity,[status(thm)],[8154, 33])).
% 5.70/5.67 tff(8156,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n5)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8155])).
% 5.70/5.67 tff(8157,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n6),
% 5.70/5.67 inference(transitivity,[status(thm)],[8156, 30])).
% 5.70/5.67 tff(8158,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n6)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8157])).
% 5.70/5.67 tff(8159,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8158, 39])).
% 5.70/5.67 tff(8160,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n7)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8159])).
% 5.70/5.67 tff(8161,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8160, 53])).
% 5.70/5.67 tff(8162,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8161])).
% 5.70/5.67 tff(8163,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8162, 45])).
% 5.70/5.67 tff(8164,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8163])).
% 5.70/5.67 tff(8165,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8164, 28])).
% 5.70/5.67 tff(8166,plain,
% 5.70/5.67 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8165])).
% 5.70/5.67 tff(8167,plain,
% 5.70/5.67 (NSY3!24 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[485, 8166, 42])).
% 5.70/5.67 tff(8168,plain,
% 5.70/5.67 (pred(NSY3!24) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8167])).
% 5.70/5.67 tff(8169,plain,
% 5.70/5.67 (pred(NSY3!24) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8168, 22])).
% 5.70/5.67 tff(8170,plain,
% 5.70/5.67 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8169, 8145])).
% 5.70/5.67 tff(8171,plain,
% 5.70/5.67 (sum(pred(NSY3!24), succ(NPY3!26)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[8170, 57])).
% 5.70/5.67 tff(8172,plain,
% 5.70/5.67 (sum(pred(Y2!56), succ(X2!57)) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8015, 8097])).
% 5.70/5.67 tff(8173,plain,
% 5.70/5.67 (sum(pred(Y2!56), succ(X2!57)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[8172, 57])).
% 5.70/5.67 tff(8174,plain,
% 5.70/5.67 (sum(pred(X2!57), succ(Y2!56)) = sum(n10, n1)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8071, 8039])).
% 5.70/5.67 tff(8175,plain,
% 5.70/5.67 (sum(pred(X2!57), succ(Y2!56)) = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[8174, 57])).
% 5.70/5.67 tff(8176,plain,
% 5.70/5.67 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n0, n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8175, 8173])).
% 5.70/5.67 tff(8177,plain,
% 5.70/5.67 (X3!55 = n0),
% 5.70/5.67 inference(transitivity,[status(thm)],[323, 8176, 59])).
% 5.70/5.67 tff(8178,plain,
% 5.70/5.67 (pred(X3!55) = pred(n0)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8177])).
% 5.70/5.67 tff(8179,plain,
% 5.70/5.67 (pred(X3!55) = n10),
% 5.70/5.67 inference(transitivity,[status(thm)],[8178, 22])).
% 5.70/5.67 tff(8180,plain,
% 5.70/5.67 (pred(pred(X3!55)) = pred(n10)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8179])).
% 5.70/5.67 tff(8181,plain,
% 5.70/5.67 (pred(pred(X3!55)) = n9),
% 5.70/5.67 inference(transitivity,[status(thm)],[8180, 21])).
% 5.70/5.67 tff(8182,plain,
% 5.70/5.67 (pred(pred(pred(X3!55))) = pred(n9)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8181])).
% 5.70/5.67 tff(8183,plain,
% 5.70/5.67 (pred(pred(pred(X3!55))) = n8),
% 5.70/5.67 inference(transitivity,[status(thm)],[8182, 20])).
% 5.70/5.67 tff(8184,plain,
% 5.70/5.67 (pred(pred(pred(pred(X3!55)))) = pred(n8)),
% 5.70/5.67 inference(monotonicity,[status(thm)],[8183])).
% 5.70/5.67 tff(8185,plain,
% 5.70/5.67 (pred(pred(pred(pred(X3!55)))) = n7),
% 5.70/5.67 inference(transitivity,[status(thm)],[8184, 19])).
% 5.70/5.67 tff(8186,plain,
% 5.70/5.67 (pred(pred(pred(pred(pred(X3!55))))) = pred(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8185])).
% 5.70/5.68 tff(8187,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(X3!55))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8186, 18])).
% 5.70/5.68 tff(8188,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8187])).
% 5.70/5.68 tff(8189,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8188, 17])).
% 5.70/5.68 tff(8190,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8189])).
% 5.70/5.68 tff(8191,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8190, 16])).
% 5.70/5.68 tff(8192,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8191])).
% 5.70/5.68 tff(8193,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8192, 15])).
% 5.70/5.68 tff(8194,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8193])).
% 5.70/5.68 tff(8195,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8194, 25])).
% 5.70/5.68 tff(8196,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8195])).
% 5.70/5.68 tff(8197,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8196, 24])).
% 5.70/5.68 tff(8198,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8197])).
% 5.70/5.68 tff(8199,plain,
% 5.70/5.68 (NPX3!27 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[510, 8198, 23])).
% 5.70/5.68 tff(8200,plain,
% 5.70/5.68 (succ(NPX3!27) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8199])).
% 5.70/5.68 tff(8201,plain,
% 5.70/5.68 (succ(NPX3!27) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8200, 58])).
% 5.70/5.68 tff(8202,plain,
% 5.70/5.68 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n1, n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8201, 8171])).
% 5.70/5.68 tff(8203,plain,
% 5.70/5.68 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8202, 56])).
% 5.70/5.68 tff(8204,plain,
% 5.70/5.68 (succ(X3!55) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8177])).
% 5.70/5.68 tff(8205,plain,
% 5.70/5.68 (succ(X3!55) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8204, 58])).
% 5.70/5.68 tff(8206,plain,
% 5.70/5.68 (succ(succ(X3!55)) = succ(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8205])).
% 5.70/5.68 tff(8207,plain,
% 5.70/5.68 (succ(succ(X3!55)) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8206, 36])).
% 5.70/5.68 tff(8208,plain,
% 5.70/5.68 (succ(succ(succ(X3!55))) = succ(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8207])).
% 5.70/5.68 tff(8209,plain,
% 5.70/5.68 (succ(succ(succ(X3!55))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8208, 48])).
% 5.70/5.68 tff(8210,plain,
% 5.70/5.68 (succ(succ(succ(succ(X3!55)))) = succ(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8209])).
% 5.70/5.68 tff(8211,plain,
% 5.70/5.68 (succ(succ(succ(succ(X3!55)))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8210, 14])).
% 5.70/5.68 tff(8212,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(X3!55))))) = succ(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8211])).
% 5.70/5.68 tff(8213,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(X3!55))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8212, 33])).
% 5.70/5.68 tff(8214,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8213])).
% 5.70/5.68 tff(8215,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8214, 30])).
% 5.70/5.68 tff(8216,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8215])).
% 5.70/5.68 tff(8217,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8216, 39])).
% 5.70/5.68 tff(8218,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8217])).
% 5.70/5.68 tff(8219,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8218, 53])).
% 5.70/5.68 tff(8220,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8219])).
% 5.70/5.68 tff(8221,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8220, 45])).
% 5.70/5.68 tff(8222,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8221])).
% 5.70/5.68 tff(8223,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8222, 28])).
% 5.70/5.68 tff(8224,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8223])).
% 5.70/5.68 tff(8225,plain,
% 5.70/5.68 (NSX3!25 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[535, 8224, 42])).
% 5.70/5.68 tff(8226,plain,
% 5.70/5.68 (pred(NSX3!25) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8225])).
% 5.70/5.68 tff(8227,plain,
% 5.70/5.68 (pred(NSX3!25) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8226, 22])).
% 5.70/5.68 tff(8228,plain,
% 5.70/5.68 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8227, 8203])).
% 5.70/5.68 tff(8229,plain,
% 5.70/5.68 (Y4!52 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[540, 8228, 57])).
% 5.70/5.68 tff(8230,plain,
% 5.70/5.68 (pred(Y4!52) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8229])).
% 5.70/5.68 tff(8231,plain,
% 5.70/5.68 (pred(Y4!52) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8230, 22])).
% 5.70/5.68 tff(8232,plain,
% 5.70/5.68 (pred(pred(Y4!52)) = pred(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8231])).
% 5.70/5.68 tff(8233,plain,
% 5.70/5.68 (pred(pred(Y4!52)) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8232, 21])).
% 5.70/5.68 tff(8234,plain,
% 5.70/5.68 (pred(pred(pred(Y4!52))) = pred(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8233])).
% 5.70/5.68 tff(8235,plain,
% 5.70/5.68 (pred(pred(pred(Y4!52))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8234, 20])).
% 5.70/5.68 tff(8236,plain,
% 5.70/5.68 (pred(pred(pred(pred(Y4!52)))) = pred(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8235])).
% 5.70/5.68 tff(8237,plain,
% 5.70/5.68 (pred(pred(pred(pred(Y4!52)))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8236, 19])).
% 5.70/5.68 tff(8238,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8237])).
% 5.70/5.68 tff(8239,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(Y4!52))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8238, 18])).
% 5.70/5.68 tff(8240,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8239])).
% 5.70/5.68 tff(8241,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8240, 17])).
% 5.70/5.68 tff(8242,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8241])).
% 5.70/5.68 tff(8243,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8242, 16])).
% 5.70/5.68 tff(8244,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8243])).
% 5.70/5.68 tff(8245,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8244, 15])).
% 5.70/5.68 tff(8246,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8245])).
% 5.70/5.68 tff(8247,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8246, 25])).
% 5.70/5.68 tff(8248,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8247])).
% 5.70/5.68 tff(8249,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8248, 24])).
% 5.70/5.68 tff(8250,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8249])).
% 5.70/5.68 tff(8251,plain,
% 5.70/5.68 (NPY4!22 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[578, 8250, 23])).
% 5.70/5.68 tff(8252,plain,
% 5.70/5.68 (succ(NPY4!22) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8251])).
% 5.70/5.68 tff(8253,plain,
% 5.70/5.68 (succ(NPY4!22) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8252, 58])).
% 5.70/5.68 tff(8254,plain,
% 5.70/5.68 (succ(Y4!52) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8229])).
% 5.70/5.68 tff(8255,plain,
% 5.70/5.68 (succ(Y4!52) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8254, 58])).
% 5.70/5.68 tff(8256,plain,
% 5.70/5.68 (succ(succ(Y4!52)) = succ(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8255])).
% 5.70/5.68 tff(8257,plain,
% 5.70/5.68 (succ(succ(Y4!52)) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8256, 36])).
% 5.70/5.68 tff(8258,plain,
% 5.70/5.68 (succ(succ(succ(Y4!52))) = succ(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8257])).
% 5.70/5.68 tff(8259,plain,
% 5.70/5.68 (succ(succ(succ(Y4!52))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8258, 48])).
% 5.70/5.68 tff(8260,plain,
% 5.70/5.68 (succ(succ(succ(succ(Y4!52)))) = succ(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8259])).
% 5.70/5.68 tff(8261,plain,
% 5.70/5.68 (succ(succ(succ(succ(Y4!52)))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8260, 14])).
% 5.70/5.68 tff(8262,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8261])).
% 5.70/5.68 tff(8263,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(Y4!52))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8262, 33])).
% 5.70/5.68 tff(8264,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8263])).
% 5.70/5.68 tff(8265,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8264, 30])).
% 5.70/5.68 tff(8266,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8265])).
% 5.70/5.68 tff(8267,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8266, 39])).
% 5.70/5.68 tff(8268,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8267])).
% 5.70/5.68 tff(8269,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8268, 53])).
% 5.70/5.68 tff(8270,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8269])).
% 5.70/5.68 tff(8271,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8270, 45])).
% 5.70/5.68 tff(8272,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8271])).
% 5.70/5.68 tff(8273,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8272, 28])).
% 5.70/5.68 tff(8274,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8273])).
% 5.70/5.68 tff(8275,plain,
% 5.70/5.68 (NSY4!20 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[601, 8274, 42])).
% 5.70/5.68 tff(8276,plain,
% 5.70/5.68 (pred(NSY4!20) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8275])).
% 5.70/5.68 tff(8277,plain,
% 5.70/5.68 (pred(NSY4!20) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8276, 22])).
% 5.70/5.68 tff(8278,plain,
% 5.70/5.68 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8277, 8253])).
% 5.70/5.68 tff(8279,plain,
% 5.70/5.68 (sum(pred(NSY4!20), succ(NPY4!22)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8278, 57])).
% 5.70/5.68 tff(8280,plain,
% 5.70/5.68 (sum(pred(Y3!54), succ(X3!55)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8123, 8205])).
% 5.70/5.68 tff(8281,plain,
% 5.70/5.68 (sum(pred(Y3!54), succ(X3!55)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8280, 57])).
% 5.70/5.68 tff(8282,plain,
% 5.70/5.68 (sum(pred(X3!55), succ(Y3!54)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8179, 8147])).
% 5.70/5.68 tff(8283,plain,
% 5.70/5.68 (sum(pred(X3!55), succ(Y3!54)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8282, 57])).
% 5.70/5.68 tff(8284,plain,
% 5.70/5.68 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n0, n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8283, 8281])).
% 5.70/5.68 tff(8285,plain,
% 5.70/5.68 (X4!53 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[438, 8284, 59])).
% 5.70/5.68 tff(8286,plain,
% 5.70/5.68 (pred(X4!53) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8285])).
% 5.70/5.68 tff(8287,plain,
% 5.70/5.68 (pred(X4!53) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8286, 22])).
% 5.70/5.68 tff(8288,plain,
% 5.70/5.68 (pred(pred(X4!53)) = pred(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8287])).
% 5.70/5.68 tff(8289,plain,
% 5.70/5.68 (pred(pred(X4!53)) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8288, 21])).
% 5.70/5.68 tff(8290,plain,
% 5.70/5.68 (pred(pred(pred(X4!53))) = pred(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8289])).
% 5.70/5.68 tff(8291,plain,
% 5.70/5.68 (pred(pred(pred(X4!53))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8290, 20])).
% 5.70/5.68 tff(8292,plain,
% 5.70/5.68 (pred(pred(pred(pred(X4!53)))) = pred(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8291])).
% 5.70/5.68 tff(8293,plain,
% 5.70/5.68 (pred(pred(pred(pred(X4!53)))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8292, 19])).
% 5.70/5.68 tff(8294,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(X4!53))))) = pred(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8293])).
% 5.70/5.68 tff(8295,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(X4!53))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8294, 18])).
% 5.70/5.68 tff(8296,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8295])).
% 5.70/5.68 tff(8297,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8296, 17])).
% 5.70/5.68 tff(8298,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8297])).
% 5.70/5.68 tff(8299,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8298, 16])).
% 5.70/5.68 tff(8300,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8299])).
% 5.70/5.68 tff(8301,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8300, 15])).
% 5.70/5.68 tff(8302,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8301])).
% 5.70/5.68 tff(8303,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8302, 25])).
% 5.70/5.68 tff(8304,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8303])).
% 5.70/5.68 tff(8305,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8304, 24])).
% 5.70/5.68 tff(8306,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8305])).
% 5.70/5.68 tff(8307,plain,
% 5.70/5.68 (NPX4!23 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[626, 8306, 23])).
% 5.70/5.68 tff(8308,plain,
% 5.70/5.68 (succ(NPX4!23) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8307])).
% 5.70/5.68 tff(8309,plain,
% 5.70/5.68 (succ(NPX4!23) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8308, 58])).
% 5.70/5.68 tff(8310,plain,
% 5.70/5.68 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n1, n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8309, 8279])).
% 5.70/5.68 tff(8311,plain,
% 5.70/5.68 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8310, 56])).
% 5.70/5.68 tff(8312,plain,
% 5.70/5.68 (succ(X4!53) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8285])).
% 5.70/5.68 tff(8313,plain,
% 5.70/5.68 (succ(X4!53) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8312, 58])).
% 5.70/5.68 tff(8314,plain,
% 5.70/5.68 (succ(succ(X4!53)) = succ(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8313])).
% 5.70/5.68 tff(8315,plain,
% 5.70/5.68 (succ(succ(X4!53)) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8314, 36])).
% 5.70/5.68 tff(8316,plain,
% 5.70/5.68 (succ(succ(succ(X4!53))) = succ(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8315])).
% 5.70/5.68 tff(8317,plain,
% 5.70/5.68 (succ(succ(succ(X4!53))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8316, 48])).
% 5.70/5.68 tff(8318,plain,
% 5.70/5.68 (succ(succ(succ(succ(X4!53)))) = succ(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8317])).
% 5.70/5.68 tff(8319,plain,
% 5.70/5.68 (succ(succ(succ(succ(X4!53)))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8318, 14])).
% 5.70/5.68 tff(8320,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(X4!53))))) = succ(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8319])).
% 5.70/5.68 tff(8321,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(X4!53))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8320, 33])).
% 5.70/5.68 tff(8322,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8321])).
% 5.70/5.68 tff(8323,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8322, 30])).
% 5.70/5.68 tff(8324,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8323])).
% 5.70/5.68 tff(8325,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8324, 39])).
% 5.70/5.68 tff(8326,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8325])).
% 5.70/5.68 tff(8327,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8326, 53])).
% 5.70/5.68 tff(8328,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8327])).
% 5.70/5.68 tff(8329,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8328, 45])).
% 5.70/5.68 tff(8330,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8329])).
% 5.70/5.68 tff(8331,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8330, 28])).
% 5.70/5.68 tff(8332,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8331])).
% 5.70/5.68 tff(8333,plain,
% 5.70/5.68 (NSX4!21 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[651, 8332, 42])).
% 5.70/5.68 tff(8334,plain,
% 5.70/5.68 (pred(NSX4!21) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8333])).
% 5.70/5.68 tff(8335,plain,
% 5.70/5.68 (pred(NSX4!21) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8334, 22])).
% 5.70/5.68 tff(8336,plain,
% 5.70/5.68 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8335, 8311])).
% 5.70/5.68 tff(8337,plain,
% 5.70/5.68 (Y5!50 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[656, 8336, 57])).
% 5.70/5.68 tff(8338,plain,
% 5.70/5.68 (pred(Y5!50) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8337])).
% 5.70/5.68 tff(8339,plain,
% 5.70/5.68 (pred(Y5!50) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8338, 22])).
% 5.70/5.68 tff(8340,plain,
% 5.70/5.68 (pred(pred(Y5!50)) = pred(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8339])).
% 5.70/5.68 tff(8341,plain,
% 5.70/5.68 (pred(pred(Y5!50)) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8340, 21])).
% 5.70/5.68 tff(8342,plain,
% 5.70/5.68 (pred(pred(pred(Y5!50))) = pred(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8341])).
% 5.70/5.68 tff(8343,plain,
% 5.70/5.68 (pred(pred(pred(Y5!50))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8342, 20])).
% 5.70/5.68 tff(8344,plain,
% 5.70/5.68 (pred(pred(pred(pred(Y5!50)))) = pred(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8343])).
% 5.70/5.68 tff(8345,plain,
% 5.70/5.68 (pred(pred(pred(pred(Y5!50)))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8344, 19])).
% 5.70/5.68 tff(8346,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8345])).
% 5.70/5.68 tff(8347,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(Y5!50))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8346, 18])).
% 5.70/5.68 tff(8348,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8347])).
% 5.70/5.68 tff(8349,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8348, 17])).
% 5.70/5.68 tff(8350,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8349])).
% 5.70/5.68 tff(8351,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8350, 16])).
% 5.70/5.68 tff(8352,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8351])).
% 5.70/5.68 tff(8353,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8352, 15])).
% 5.70/5.68 tff(8354,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8353])).
% 5.70/5.68 tff(8355,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8354, 25])).
% 5.70/5.68 tff(8356,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8355])).
% 5.70/5.68 tff(8357,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8356, 24])).
% 5.70/5.68 tff(8358,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8357])).
% 5.70/5.68 tff(8359,plain,
% 5.70/5.68 (NPY5!18 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[694, 8358, 23])).
% 5.70/5.68 tff(8360,plain,
% 5.70/5.68 (succ(NPY5!18) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8359])).
% 5.70/5.68 tff(8361,plain,
% 5.70/5.68 (succ(NPY5!18) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8360, 58])).
% 5.70/5.68 tff(8362,plain,
% 5.70/5.68 (succ(Y5!50) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8337])).
% 5.70/5.68 tff(8363,plain,
% 5.70/5.68 (succ(Y5!50) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8362, 58])).
% 5.70/5.68 tff(8364,plain,
% 5.70/5.68 (succ(succ(Y5!50)) = succ(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8363])).
% 5.70/5.68 tff(8365,plain,
% 5.70/5.68 (succ(succ(Y5!50)) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8364, 36])).
% 5.70/5.68 tff(8366,plain,
% 5.70/5.68 (succ(succ(succ(Y5!50))) = succ(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8365])).
% 5.70/5.68 tff(8367,plain,
% 5.70/5.68 (succ(succ(succ(Y5!50))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8366, 48])).
% 5.70/5.68 tff(8368,plain,
% 5.70/5.68 (succ(succ(succ(succ(Y5!50)))) = succ(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8367])).
% 5.70/5.68 tff(8369,plain,
% 5.70/5.68 (succ(succ(succ(succ(Y5!50)))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8368, 14])).
% 5.70/5.68 tff(8370,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8369])).
% 5.70/5.68 tff(8371,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(Y5!50))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8370, 33])).
% 5.70/5.68 tff(8372,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8371])).
% 5.70/5.68 tff(8373,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8372, 30])).
% 5.70/5.68 tff(8374,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8373])).
% 5.70/5.68 tff(8375,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8374, 39])).
% 5.70/5.68 tff(8376,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8375])).
% 5.70/5.68 tff(8377,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8376, 53])).
% 5.70/5.68 tff(8378,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8377])).
% 5.70/5.68 tff(8379,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8378, 45])).
% 5.70/5.68 tff(8380,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8379])).
% 5.70/5.68 tff(8381,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8380, 28])).
% 5.70/5.68 tff(8382,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8381])).
% 5.70/5.68 tff(8383,plain,
% 5.70/5.68 (NSY5!16 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[717, 8382, 42])).
% 5.70/5.68 tff(8384,plain,
% 5.70/5.68 (pred(NSY5!16) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8383])).
% 5.70/5.68 tff(8385,plain,
% 5.70/5.68 (pred(NSY5!16) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8384, 22])).
% 5.70/5.68 tff(8386,plain,
% 5.70/5.68 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8385, 8361])).
% 5.70/5.68 tff(8387,plain,
% 5.70/5.68 (sum(pred(NSY5!16), succ(NPY5!18)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8386, 57])).
% 5.70/5.68 tff(8388,plain,
% 5.70/5.68 (sum(pred(Y4!52), succ(X4!53)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8231, 8313])).
% 5.70/5.68 tff(8389,plain,
% 5.70/5.68 (sum(pred(Y4!52), succ(X4!53)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8388, 57])).
% 5.70/5.68 tff(8390,plain,
% 5.70/5.68 (sum(pred(X4!53), succ(Y4!52)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8287, 8255])).
% 5.70/5.68 tff(8391,plain,
% 5.70/5.68 (sum(pred(X4!53), succ(Y4!52)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8390, 57])).
% 5.70/5.68 tff(8392,plain,
% 5.70/5.68 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n0, n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8391, 8389])).
% 5.70/5.68 tff(8393,plain,
% 5.70/5.68 (X5!51 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[553, 8392, 59])).
% 5.70/5.68 tff(8394,plain,
% 5.70/5.68 (pred(X5!51) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8393])).
% 5.70/5.68 tff(8395,plain,
% 5.70/5.68 (pred(X5!51) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8394, 22])).
% 5.70/5.68 tff(8396,plain,
% 5.70/5.68 (pred(pred(X5!51)) = pred(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8395])).
% 5.70/5.68 tff(8397,plain,
% 5.70/5.68 (pred(pred(X5!51)) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8396, 21])).
% 5.70/5.68 tff(8398,plain,
% 5.70/5.68 (pred(pred(pred(X5!51))) = pred(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8397])).
% 5.70/5.68 tff(8399,plain,
% 5.70/5.68 (pred(pred(pred(X5!51))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8398, 20])).
% 5.70/5.68 tff(8400,plain,
% 5.70/5.68 (pred(pred(pred(pred(X5!51)))) = pred(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8399])).
% 5.70/5.68 tff(8401,plain,
% 5.70/5.68 (pred(pred(pred(pred(X5!51)))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8400, 19])).
% 5.70/5.68 tff(8402,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(X5!51))))) = pred(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8401])).
% 5.70/5.68 tff(8403,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(X5!51))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8402, 18])).
% 5.70/5.68 tff(8404,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8403])).
% 5.70/5.68 tff(8405,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8404, 17])).
% 5.70/5.68 tff(8406,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8405])).
% 5.70/5.68 tff(8407,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8406, 16])).
% 5.70/5.68 tff(8408,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8407])).
% 5.70/5.68 tff(8409,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8408, 15])).
% 5.70/5.68 tff(8410,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8409])).
% 5.70/5.68 tff(8411,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8410, 25])).
% 5.70/5.68 tff(8412,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8411])).
% 5.70/5.68 tff(8413,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8412, 24])).
% 5.70/5.68 tff(8414,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8413])).
% 5.70/5.68 tff(8415,plain,
% 5.70/5.68 (NPX5!19 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[742, 8414, 23])).
% 5.70/5.68 tff(8416,plain,
% 5.70/5.68 (succ(NPX5!19) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8415])).
% 5.70/5.68 tff(8417,plain,
% 5.70/5.68 (succ(NPX5!19) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8416, 58])).
% 5.70/5.68 tff(8418,plain,
% 5.70/5.68 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n1, n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8417, 8387])).
% 5.70/5.68 tff(8419,plain,
% 5.70/5.68 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8418, 56])).
% 5.70/5.68 tff(8420,plain,
% 5.70/5.68 (succ(X5!51) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8393])).
% 5.70/5.68 tff(8421,plain,
% 5.70/5.68 (succ(X5!51) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8420, 58])).
% 5.70/5.68 tff(8422,plain,
% 5.70/5.68 (succ(succ(X5!51)) = succ(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8421])).
% 5.70/5.68 tff(8423,plain,
% 5.70/5.68 (succ(succ(X5!51)) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8422, 36])).
% 5.70/5.68 tff(8424,plain,
% 5.70/5.68 (succ(succ(succ(X5!51))) = succ(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8423])).
% 5.70/5.68 tff(8425,plain,
% 5.70/5.68 (succ(succ(succ(X5!51))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8424, 48])).
% 5.70/5.68 tff(8426,plain,
% 5.70/5.68 (succ(succ(succ(succ(X5!51)))) = succ(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8425])).
% 5.70/5.68 tff(8427,plain,
% 5.70/5.68 (succ(succ(succ(succ(X5!51)))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8426, 14])).
% 5.70/5.68 tff(8428,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(X5!51))))) = succ(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8427])).
% 5.70/5.68 tff(8429,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(X5!51))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8428, 33])).
% 5.70/5.68 tff(8430,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8429])).
% 5.70/5.68 tff(8431,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8430, 30])).
% 5.70/5.68 tff(8432,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8431])).
% 5.70/5.68 tff(8433,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8432, 39])).
% 5.70/5.68 tff(8434,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8433])).
% 5.70/5.68 tff(8435,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8434, 53])).
% 5.70/5.68 tff(8436,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8435])).
% 5.70/5.68 tff(8437,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8436, 45])).
% 5.70/5.68 tff(8438,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8437])).
% 5.70/5.68 tff(8439,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8438, 28])).
% 5.70/5.68 tff(8440,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8439])).
% 5.70/5.68 tff(8441,plain,
% 5.70/5.68 (NSX5!17 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[767, 8440, 42])).
% 5.70/5.68 tff(8442,plain,
% 5.70/5.68 (pred(NSX5!17) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8441])).
% 5.70/5.68 tff(8443,plain,
% 5.70/5.68 (pred(NSX5!17) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8442, 22])).
% 5.70/5.68 tff(8444,plain,
% 5.70/5.68 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8443, 8419])).
% 5.70/5.68 tff(8445,plain,
% 5.70/5.68 (Y6!48 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[772, 8444, 57])).
% 5.70/5.68 tff(8446,plain,
% 5.70/5.68 (pred(Y6!48) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8445])).
% 5.70/5.68 tff(8447,plain,
% 5.70/5.68 (pred(Y6!48) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8446, 22])).
% 5.70/5.68 tff(8448,plain,
% 5.70/5.68 (pred(pred(Y6!48)) = pred(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8447])).
% 5.70/5.68 tff(8449,plain,
% 5.70/5.68 (pred(pred(Y6!48)) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8448, 21])).
% 5.70/5.68 tff(8450,plain,
% 5.70/5.68 (pred(pred(pred(Y6!48))) = pred(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8449])).
% 5.70/5.68 tff(8451,plain,
% 5.70/5.68 (pred(pred(pred(Y6!48))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8450, 20])).
% 5.70/5.68 tff(8452,plain,
% 5.70/5.68 (pred(pred(pred(pred(Y6!48)))) = pred(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8451])).
% 5.70/5.68 tff(8453,plain,
% 5.70/5.68 (pred(pred(pred(pred(Y6!48)))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8452, 19])).
% 5.70/5.68 tff(8454,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8453])).
% 5.70/5.68 tff(8455,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(Y6!48))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8454, 18])).
% 5.70/5.68 tff(8456,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8455])).
% 5.70/5.68 tff(8457,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8456, 17])).
% 5.70/5.68 tff(8458,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8457])).
% 5.70/5.68 tff(8459,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8458, 16])).
% 5.70/5.68 tff(8460,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8459])).
% 5.70/5.68 tff(8461,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8460, 15])).
% 5.70/5.68 tff(8462,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8461])).
% 5.70/5.68 tff(8463,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8462, 25])).
% 5.70/5.68 tff(8464,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8463])).
% 5.70/5.68 tff(8465,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8464, 24])).
% 5.70/5.68 tff(8466,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8465])).
% 5.70/5.68 tff(8467,plain,
% 5.70/5.68 (NPY6!14 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[1465, 8466, 23])).
% 5.70/5.68 tff(8468,plain,
% 5.70/5.68 (succ(NPY6!14) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8467])).
% 5.70/5.68 tff(8469,plain,
% 5.70/5.68 (succ(NPY6!14) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8468, 58])).
% 5.70/5.68 tff(8470,plain,
% 5.70/5.68 (succ(Y6!48) = succ(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8445])).
% 5.70/5.68 tff(8471,plain,
% 5.70/5.68 (succ(Y6!48) = n1),
% 5.70/5.68 inference(transitivity,[status(thm)],[8470, 58])).
% 5.70/5.68 tff(8472,plain,
% 5.70/5.68 (succ(succ(Y6!48)) = succ(n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8471])).
% 5.70/5.68 tff(8473,plain,
% 5.70/5.68 (succ(succ(Y6!48)) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8472, 36])).
% 5.70/5.68 tff(8474,plain,
% 5.70/5.68 (succ(succ(succ(Y6!48))) = succ(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8473])).
% 5.70/5.68 tff(8475,plain,
% 5.70/5.68 (succ(succ(succ(Y6!48))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8474, 48])).
% 5.70/5.68 tff(8476,plain,
% 5.70/5.68 (succ(succ(succ(succ(Y6!48)))) = succ(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8475])).
% 5.70/5.68 tff(8477,plain,
% 5.70/5.68 (succ(succ(succ(succ(Y6!48)))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8476, 14])).
% 5.70/5.68 tff(8478,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8477])).
% 5.70/5.68 tff(8479,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(Y6!48))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8478, 33])).
% 5.70/5.68 tff(8480,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8479])).
% 5.70/5.68 tff(8481,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8480, 30])).
% 5.70/5.68 tff(8482,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8481])).
% 5.70/5.68 tff(8483,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8482, 39])).
% 5.70/5.68 tff(8484,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8483])).
% 5.70/5.68 tff(8485,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8484, 53])).
% 5.70/5.68 tff(8486,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8485])).
% 5.70/5.68 tff(8487,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8486, 45])).
% 5.70/5.68 tff(8488,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8487])).
% 5.70/5.68 tff(8489,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8488, 28])).
% 5.70/5.68 tff(8490,plain,
% 5.70/5.68 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8489])).
% 5.70/5.68 tff(8491,plain,
% 5.70/5.68 (NSY6!12 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[1490, 8490, 42])).
% 5.70/5.68 tff(8492,plain,
% 5.70/5.68 (pred(NSY6!12) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8491])).
% 5.70/5.68 tff(8493,plain,
% 5.70/5.68 (pred(NSY6!12) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8492, 22])).
% 5.70/5.68 tff(8494,plain,
% 5.70/5.68 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8493, 8469])).
% 5.70/5.68 tff(8495,plain,
% 5.70/5.68 (sum(pred(NSY6!12), succ(NPY6!14)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8494, 57])).
% 5.70/5.68 tff(8496,plain,
% 5.70/5.68 (sum(pred(Y5!50), succ(X5!51)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8339, 8421])).
% 5.70/5.68 tff(8497,plain,
% 5.70/5.68 (sum(pred(Y5!50), succ(X5!51)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8496, 57])).
% 5.70/5.68 tff(8498,plain,
% 5.70/5.68 (sum(pred(X5!51), succ(Y5!50)) = sum(n10, n1)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8395, 8363])).
% 5.70/5.68 tff(8499,plain,
% 5.70/5.68 (sum(pred(X5!51), succ(Y5!50)) = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[8498, 57])).
% 5.70/5.68 tff(8500,plain,
% 5.70/5.68 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n0, n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8499, 8497])).
% 5.70/5.68 tff(8501,plain,
% 5.70/5.68 (X6!49 = n0),
% 5.70/5.68 inference(transitivity,[status(thm)],[669, 8500, 59])).
% 5.70/5.68 tff(8502,plain,
% 5.70/5.68 (pred(X6!49) = pred(n0)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8501])).
% 5.70/5.68 tff(8503,plain,
% 5.70/5.68 (pred(X6!49) = n10),
% 5.70/5.68 inference(transitivity,[status(thm)],[8502, 22])).
% 5.70/5.68 tff(8504,plain,
% 5.70/5.68 (pred(pred(X6!49)) = pred(n10)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8503])).
% 5.70/5.68 tff(8505,plain,
% 5.70/5.68 (pred(pred(X6!49)) = n9),
% 5.70/5.68 inference(transitivity,[status(thm)],[8504, 21])).
% 5.70/5.68 tff(8506,plain,
% 5.70/5.68 (pred(pred(pred(X6!49))) = pred(n9)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8505])).
% 5.70/5.68 tff(8507,plain,
% 5.70/5.68 (pred(pred(pred(X6!49))) = n8),
% 5.70/5.68 inference(transitivity,[status(thm)],[8506, 20])).
% 5.70/5.68 tff(8508,plain,
% 5.70/5.68 (pred(pred(pred(pred(X6!49)))) = pred(n8)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8507])).
% 5.70/5.68 tff(8509,plain,
% 5.70/5.68 (pred(pred(pred(pred(X6!49)))) = n7),
% 5.70/5.68 inference(transitivity,[status(thm)],[8508, 19])).
% 5.70/5.68 tff(8510,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(X6!49))))) = pred(n7)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8509])).
% 5.70/5.68 tff(8511,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(X6!49))))) = n6),
% 5.70/5.68 inference(transitivity,[status(thm)],[8510, 18])).
% 5.70/5.68 tff(8512,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n6)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8511])).
% 5.70/5.68 tff(8513,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n5),
% 5.70/5.68 inference(transitivity,[status(thm)],[8512, 17])).
% 5.70/5.68 tff(8514,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n5)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8513])).
% 5.70/5.68 tff(8515,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n4),
% 5.70/5.68 inference(transitivity,[status(thm)],[8514, 16])).
% 5.70/5.68 tff(8516,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n4)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8515])).
% 5.70/5.68 tff(8517,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n3),
% 5.70/5.68 inference(transitivity,[status(thm)],[8516, 15])).
% 5.70/5.68 tff(8518,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n3)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8517])).
% 5.70/5.68 tff(8519,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n2),
% 5.70/5.68 inference(transitivity,[status(thm)],[8518, 25])).
% 5.70/5.68 tff(8520,plain,
% 5.70/5.68 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n2)),
% 5.70/5.68 inference(monotonicity,[status(thm)],[8519])).
% 5.70/5.68 tff(8521,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8520, 24])).
% 5.70/5.69 tff(8522,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8521])).
% 5.70/5.69 tff(8523,plain,
% 5.70/5.69 (NPX6!15 = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[1523, 8522, 23])).
% 5.70/5.69 tff(8524,plain,
% 5.70/5.69 (succ(NPX6!15) = succ(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8523])).
% 5.70/5.69 tff(8525,plain,
% 5.70/5.69 (succ(NPX6!15) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8524, 58])).
% 5.70/5.69 tff(8526,plain,
% 5.70/5.69 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n1, n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8525, 8495])).
% 5.70/5.69 tff(8527,plain,
% 5.70/5.69 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8526, 56])).
% 5.70/5.69 tff(8528,plain,
% 5.70/5.69 (succ(X6!49) = succ(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8501])).
% 5.70/5.69 tff(8529,plain,
% 5.70/5.69 (succ(X6!49) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8528, 58])).
% 5.70/5.69 tff(8530,plain,
% 5.70/5.69 (succ(succ(X6!49)) = succ(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8529])).
% 5.70/5.69 tff(8531,plain,
% 5.70/5.69 (succ(succ(X6!49)) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8530, 36])).
% 5.70/5.69 tff(8532,plain,
% 5.70/5.69 (succ(succ(succ(X6!49))) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8531])).
% 5.70/5.69 tff(8533,plain,
% 5.70/5.69 (succ(succ(succ(X6!49))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8532, 48])).
% 5.70/5.69 tff(8534,plain,
% 5.70/5.69 (succ(succ(succ(succ(X6!49)))) = succ(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8533])).
% 5.70/5.69 tff(8535,plain,
% 5.70/5.69 (succ(succ(succ(succ(X6!49)))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8534, 14])).
% 5.70/5.69 tff(8536,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(X6!49))))) = succ(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8535])).
% 5.70/5.69 tff(8537,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(X6!49))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8536, 33])).
% 5.70/5.69 tff(8538,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8537])).
% 5.70/5.69 tff(8539,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8538, 30])).
% 5.70/5.69 tff(8540,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8539])).
% 5.70/5.69 tff(8541,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8540, 39])).
% 5.70/5.69 tff(8542,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8541])).
% 5.70/5.69 tff(8543,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8542, 53])).
% 5.70/5.69 tff(8544,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8543])).
% 5.70/5.69 tff(8545,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8544, 45])).
% 5.70/5.69 tff(8546,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8545])).
% 5.70/5.69 tff(8547,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8546, 28])).
% 5.70/5.69 tff(8548,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8547])).
% 5.70/5.69 tff(8549,plain,
% 5.70/5.69 (NSX6!13 = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[1550, 8548, 42])).
% 5.70/5.69 tff(8550,plain,
% 5.70/5.69 (pred(NSX6!13) = pred(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8549])).
% 5.70/5.69 tff(8551,plain,
% 5.70/5.69 (pred(NSX6!13) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8550, 22])).
% 5.70/5.69 tff(8552,plain,
% 5.70/5.69 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n10, n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8551, 8527])).
% 5.70/5.69 tff(8553,plain,
% 5.70/5.69 (sum(n10, n1) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.70/5.69 inference(symmetry,[status(thm)],[8552])).
% 5.70/5.69 tff(8554,plain,
% 5.70/5.69 (sum(pred(Y6!48), succ(X6!49)) = sum(n10, n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8447, 8529])).
% 5.70/5.69 tff(8555,plain,
% 5.70/5.69 (sum(pred(Y6!48), succ(X6!49)) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8554, 57])).
% 5.70/5.69 tff(8556,plain,
% 5.70/5.69 (sum(pred(X6!49), succ(Y6!48)) = sum(n10, n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8503, 8471])).
% 5.70/5.69 tff(8557,plain,
% 5.70/5.69 (sum(pred(X6!49), succ(Y6!48)) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8556, 57])).
% 5.70/5.69 tff(8558,plain,
% 5.70/5.69 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n0, n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8557, 8555])).
% 5.70/5.69 tff(8559,plain,
% 5.70/5.69 (X7!47 = Y7!46),
% 5.70/5.69 inference(transitivity,[status(thm)],[785, 8558, 59, 5850, 8553, 794])).
% 5.70/5.69 tff(8560,plain,
% 5.70/5.69 ($false),
% 5.70/5.69 inference(unit_resolution,[status(thm)],[792, 8559])).
% 5.70/5.69 tff(8561,plain,((~(Y0!60 = n6)) | (X7!47 = Y7!46) | (~(X0!61 = n5))), inference(lemma,lemma(discharge,[]))).
% 5.70/5.69 tff(8562,plain,
% 5.70/5.69 (~(Y0!60 = n6)),
% 5.70/5.69 inference(unit_resolution,[status(thm)],[8561, 7190, 792])).
% 5.70/5.69 tff(8563,plain,
% 5.70/5.69 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n6, n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[7214, 2335])).
% 5.70/5.69 tff(8564,plain,
% 5.70/5.69 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8563, 97])).
% 5.70/5.69 tff(8565,plain,
% 5.70/5.69 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n4, n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[7240, 8564])).
% 5.70/5.69 tff(8566,plain,
% 5.70/5.69 (Y1!58 = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[196, 8565, 67])).
% 5.70/5.69 tff(8567,plain,
% 5.70/5.69 (pred(Y1!58) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8566])).
% 5.70/5.69 tff(8568,plain,
% 5.70/5.69 (pred(Y1!58) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8567, 24])).
% 5.70/5.69 tff(8569,plain,
% 5.70/5.69 (pred(pred(Y1!58)) = pred(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8568])).
% 5.70/5.69 tff(8570,plain,
% 5.70/5.69 (pred(pred(Y1!58)) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8569, 23])).
% 5.70/5.69 tff(8571,plain,
% 5.70/5.69 (pred(pred(pred(Y1!58))) = pred(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8570])).
% 5.70/5.69 tff(8572,plain,
% 5.70/5.69 (pred(pred(pred(Y1!58))) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8571, 22])).
% 5.70/5.69 tff(8573,plain,
% 5.70/5.69 (pred(pred(pred(pred(Y1!58)))) = pred(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8572])).
% 5.70/5.69 tff(8574,plain,
% 5.70/5.69 (pred(pred(pred(pred(Y1!58)))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8573, 21])).
% 5.70/5.69 tff(8575,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8574])).
% 5.70/5.69 tff(8576,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(Y1!58))))) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8575, 20])).
% 5.70/5.69 tff(8577,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8576])).
% 5.70/5.69 tff(8578,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8577, 19])).
% 5.70/5.69 tff(8579,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8578])).
% 5.70/5.69 tff(8580,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8579, 18])).
% 5.70/5.69 tff(8581,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8580])).
% 5.70/5.69 tff(8582,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8581, 17])).
% 5.70/5.69 tff(8583,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8582])).
% 5.70/5.69 tff(8584,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8583, 16])).
% 5.70/5.69 tff(8585,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8584])).
% 5.70/5.69 tff(8586,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8585, 15])).
% 5.70/5.69 tff(8587,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8586])).
% 5.70/5.69 tff(8588,plain,
% 5.70/5.69 (NPY1!34 = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[232, 8587, 25])).
% 5.70/5.69 tff(8589,plain,
% 5.70/5.69 (succ(NPY1!34) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8588])).
% 5.70/5.69 tff(8590,plain,
% 5.70/5.69 (succ(NPY1!34) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8589, 48])).
% 5.70/5.69 tff(8591,plain,
% 5.70/5.69 (succ(Y1!58) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8566])).
% 5.70/5.69 tff(8592,plain,
% 5.70/5.69 (succ(Y1!58) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8591, 48])).
% 5.70/5.69 tff(8593,plain,
% 5.70/5.69 (succ(succ(Y1!58)) = succ(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8592])).
% 5.70/5.69 tff(8594,plain,
% 5.70/5.69 (succ(succ(Y1!58)) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8593, 14])).
% 5.70/5.69 tff(8595,plain,
% 5.70/5.69 (succ(succ(succ(Y1!58))) = succ(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8594])).
% 5.70/5.69 tff(8596,plain,
% 5.70/5.69 (succ(succ(succ(Y1!58))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8595, 33])).
% 5.70/5.69 tff(8597,plain,
% 5.70/5.69 (succ(succ(succ(succ(Y1!58)))) = succ(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8596])).
% 5.70/5.69 tff(8598,plain,
% 5.70/5.69 (succ(succ(succ(succ(Y1!58)))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8597, 30])).
% 5.70/5.69 tff(8599,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8598])).
% 5.70/5.69 tff(8600,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(Y1!58))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8599, 39])).
% 5.70/5.69 tff(8601,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8600])).
% 5.70/5.69 tff(8602,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8601, 53])).
% 5.70/5.69 tff(8603,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8602])).
% 5.70/5.69 tff(8604,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8603, 45])).
% 5.70/5.69 tff(8605,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8604])).
% 5.70/5.69 tff(8606,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8605, 28])).
% 5.70/5.69 tff(8607,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8606])).
% 5.70/5.69 tff(8608,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8607, 42])).
% 5.70/5.69 tff(8609,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8608])).
% 5.70/5.69 tff(8610,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8609, 58])).
% 5.70/5.69 tff(8611,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8610])).
% 5.70/5.69 tff(8612,plain,
% 5.70/5.69 (NSY1!32 = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[255, 8611, 36])).
% 5.70/5.69 tff(8613,plain,
% 5.70/5.69 (pred(NSY1!32) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8612])).
% 5.70/5.69 tff(8614,plain,
% 5.70/5.69 (pred(NSY1!32) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8613, 24])).
% 5.70/5.69 tff(8615,plain,
% 5.70/5.69 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n1, n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8614, 8590])).
% 5.70/5.69 tff(8616,plain,
% 5.70/5.69 (sum(pred(NSY1!32), succ(NPY1!34)) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8615, 47])).
% 5.70/5.69 tff(8617,plain,
% 5.70/5.69 (sum(pred(Y0!60), succ(X0!61)) = sum(n6, n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[2287, 7218])).
% 5.70/5.69 tff(8618,plain,
% 5.70/5.69 (sum(pred(Y0!60), succ(X0!61)) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8617, 37])).
% 5.70/5.69 tff(8619,plain,
% 5.70/5.69 (sum(n4, n8) = n1),
% 5.70/5.69 inference(and_elim,[status(thm)],[9])).
% 5.70/5.69 tff(8620,plain,
% 5.70/5.69 (sum(pred(X0!61), succ(Y0!60)) = sum(n4, n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[7192, 2311])).
% 5.70/5.69 tff(8621,plain,
% 5.70/5.69 (sum(pred(X0!61), succ(Y0!60)) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8620, 8619])).
% 5.70/5.69 tff(8622,plain,
% 5.70/5.69 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n1, n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8621, 8618])).
% 5.70/5.69 tff(8623,plain,
% 5.70/5.69 (X1!59 = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[93, 8622, 49])).
% 5.70/5.69 tff(8624,plain,
% 5.70/5.69 (pred(X1!59) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8623])).
% 5.70/5.69 tff(8625,plain,
% 5.70/5.69 (pred(X1!59) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8624, 24])).
% 5.70/5.69 tff(8626,plain,
% 5.70/5.69 (pred(pred(X1!59)) = pred(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8625])).
% 5.70/5.69 tff(8627,plain,
% 5.70/5.69 (pred(pred(X1!59)) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8626, 23])).
% 5.70/5.69 tff(8628,plain,
% 5.70/5.69 (pred(pred(pred(X1!59))) = pred(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8627])).
% 5.70/5.69 tff(8629,plain,
% 5.70/5.69 (pred(pred(pred(X1!59))) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8628, 22])).
% 5.70/5.69 tff(8630,plain,
% 5.70/5.69 (pred(pred(pred(pred(X1!59)))) = pred(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8629])).
% 5.70/5.69 tff(8631,plain,
% 5.70/5.69 (pred(pred(pred(pred(X1!59)))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8630, 21])).
% 5.70/5.69 tff(8632,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(X1!59))))) = pred(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8631])).
% 5.70/5.69 tff(8633,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(X1!59))))) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8632, 20])).
% 5.70/5.69 tff(8634,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8633])).
% 5.70/5.69 tff(8635,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8634, 19])).
% 5.70/5.69 tff(8636,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8635])).
% 5.70/5.69 tff(8637,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8636, 18])).
% 5.70/5.69 tff(8638,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8637])).
% 5.70/5.69 tff(8639,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8638, 17])).
% 5.70/5.69 tff(8640,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8639])).
% 5.70/5.69 tff(8641,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8640, 16])).
% 5.70/5.69 tff(8642,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8641])).
% 5.70/5.69 tff(8643,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8642, 15])).
% 5.70/5.69 tff(8644,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8643])).
% 5.70/5.69 tff(8645,plain,
% 5.70/5.69 (NPX1!35 = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[280, 8644, 25])).
% 5.70/5.69 tff(8646,plain,
% 5.70/5.69 (succ(NPX1!35) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8645])).
% 5.70/5.69 tff(8647,plain,
% 5.70/5.69 (succ(NPX1!35) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8646, 48])).
% 5.70/5.69 tff(8648,plain,
% 5.70/5.69 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n3, n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8647, 8616])).
% 5.70/5.69 tff(8649,plain,
% 5.70/5.69 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8648, 786])).
% 5.70/5.69 tff(8650,plain,
% 5.70/5.69 (succ(X1!59) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8623])).
% 5.70/5.69 tff(8651,plain,
% 5.70/5.69 (succ(X1!59) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8650, 48])).
% 5.70/5.69 tff(8652,plain,
% 5.70/5.69 (succ(succ(X1!59)) = succ(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8651])).
% 5.70/5.69 tff(8653,plain,
% 5.70/5.69 (succ(succ(X1!59)) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8652, 14])).
% 5.70/5.69 tff(8654,plain,
% 5.70/5.69 (succ(succ(succ(X1!59))) = succ(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8653])).
% 5.70/5.69 tff(8655,plain,
% 5.70/5.69 (succ(succ(succ(X1!59))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8654, 33])).
% 5.70/5.69 tff(8656,plain,
% 5.70/5.69 (succ(succ(succ(succ(X1!59)))) = succ(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8655])).
% 5.70/5.69 tff(8657,plain,
% 5.70/5.69 (succ(succ(succ(succ(X1!59)))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8656, 30])).
% 5.70/5.69 tff(8658,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(X1!59))))) = succ(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8657])).
% 5.70/5.69 tff(8659,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(X1!59))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8658, 39])).
% 5.70/5.69 tff(8660,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8659])).
% 5.70/5.69 tff(8661,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8660, 53])).
% 5.70/5.69 tff(8662,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8661])).
% 5.70/5.69 tff(8663,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8662, 45])).
% 5.70/5.69 tff(8664,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8663])).
% 5.70/5.69 tff(8665,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8664, 28])).
% 5.70/5.69 tff(8666,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8665])).
% 5.70/5.69 tff(8667,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8666, 42])).
% 5.70/5.69 tff(8668,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8667])).
% 5.70/5.69 tff(8669,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8668, 58])).
% 5.70/5.69 tff(8670,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8669])).
% 5.70/5.69 tff(8671,plain,
% 5.70/5.69 (NSX1!33 = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[305, 8670, 36])).
% 5.70/5.69 tff(8672,plain,
% 5.70/5.69 (pred(NSX1!33) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8671])).
% 5.70/5.69 tff(8673,plain,
% 5.70/5.69 (pred(NSX1!33) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8672, 24])).
% 5.70/5.69 tff(8674,plain,
% 5.70/5.69 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n1, n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8673, 8649])).
% 5.70/5.69 tff(8675,plain,
% 5.70/5.69 (Y2!56 = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[310, 8674, 791])).
% 5.70/5.69 tff(8676,plain,
% 5.70/5.69 (pred(Y2!56) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8675])).
% 5.70/5.69 tff(8677,plain,
% 5.70/5.69 (pred(Y2!56) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8676, 19])).
% 5.70/5.69 tff(8678,plain,
% 5.70/5.69 (pred(pred(Y2!56)) = pred(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8677])).
% 5.70/5.69 tff(8679,plain,
% 5.70/5.69 (pred(pred(Y2!56)) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8678, 18])).
% 5.70/5.69 tff(8680,plain,
% 5.70/5.69 (pred(pred(pred(Y2!56))) = pred(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8679])).
% 5.70/5.69 tff(8681,plain,
% 5.70/5.69 (pred(pred(pred(Y2!56))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8680, 17])).
% 5.70/5.69 tff(8682,plain,
% 5.70/5.69 (pred(pred(pred(pred(Y2!56)))) = pred(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8681])).
% 5.70/5.69 tff(8683,plain,
% 5.70/5.69 (pred(pred(pred(pred(Y2!56)))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8682, 16])).
% 5.70/5.69 tff(8684,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8683])).
% 5.70/5.69 tff(8685,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(Y2!56))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8684, 15])).
% 5.70/5.69 tff(8686,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8685])).
% 5.70/5.69 tff(8687,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8686, 25])).
% 5.70/5.69 tff(8688,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8687])).
% 5.70/5.69 tff(8689,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8688, 24])).
% 5.70/5.69 tff(8690,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8689])).
% 5.70/5.69 tff(8691,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8690, 23])).
% 5.70/5.69 tff(8692,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8691])).
% 5.70/5.69 tff(8693,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8692, 22])).
% 5.70/5.69 tff(8694,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8693])).
% 5.70/5.69 tff(8695,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8694, 21])).
% 5.70/5.69 tff(8696,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8695])).
% 5.70/5.69 tff(8697,plain,
% 5.70/5.69 (NPY2!30 = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[347, 8696, 20])).
% 5.70/5.69 tff(8698,plain,
% 5.70/5.69 (succ(NPY2!30) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8697])).
% 5.70/5.69 tff(8699,plain,
% 5.70/5.69 (succ(NPY2!30) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8698, 45])).
% 5.70/5.69 tff(8700,plain,
% 5.70/5.69 (succ(Y2!56) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8675])).
% 5.70/5.69 tff(8701,plain,
% 5.70/5.69 (succ(Y2!56) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8700, 45])).
% 5.70/5.69 tff(8702,plain,
% 5.70/5.69 (succ(succ(Y2!56)) = succ(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8701])).
% 5.70/5.69 tff(8703,plain,
% 5.70/5.69 (succ(succ(Y2!56)) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8702, 28])).
% 5.70/5.69 tff(8704,plain,
% 5.70/5.69 (succ(succ(succ(Y2!56))) = succ(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8703])).
% 5.70/5.69 tff(8705,plain,
% 5.70/5.69 (succ(succ(succ(Y2!56))) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8704, 42])).
% 5.70/5.69 tff(8706,plain,
% 5.70/5.69 (succ(succ(succ(succ(Y2!56)))) = succ(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8705])).
% 5.70/5.69 tff(8707,plain,
% 5.70/5.69 (succ(succ(succ(succ(Y2!56)))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8706, 58])).
% 5.70/5.69 tff(8708,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8707])).
% 5.70/5.69 tff(8709,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(Y2!56))))) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8708, 36])).
% 5.70/5.69 tff(8710,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8709])).
% 5.70/5.69 tff(8711,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8710, 48])).
% 5.70/5.69 tff(8712,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8711])).
% 5.70/5.69 tff(8713,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8712, 14])).
% 5.70/5.69 tff(8714,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8713])).
% 5.70/5.69 tff(8715,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8714, 33])).
% 5.70/5.69 tff(8716,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8715])).
% 5.70/5.69 tff(8717,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8716, 30])).
% 5.70/5.69 tff(8718,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8717])).
% 5.70/5.69 tff(8719,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8718, 39])).
% 5.70/5.69 tff(8720,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8719])).
% 5.70/5.69 tff(8721,plain,
% 5.70/5.69 (NSY2!28 = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[370, 8720, 53])).
% 5.70/5.69 tff(8722,plain,
% 5.70/5.69 (pred(NSY2!28) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8721])).
% 5.70/5.69 tff(8723,plain,
% 5.70/5.69 (pred(NSY2!28) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8722, 19])).
% 5.70/5.69 tff(8724,plain,
% 5.70/5.69 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n7, n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8723, 8699])).
% 5.70/5.69 tff(8725,plain,
% 5.70/5.69 (sum(pred(NSY2!28), succ(NPY2!30)) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8724, 44])).
% 5.70/5.69 tff(8726,plain,
% 5.70/5.69 (sum(pred(Y1!58), succ(X1!59)) = sum(n1, n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8568, 8651])).
% 5.70/5.69 tff(8727,plain,
% 5.70/5.69 (sum(pred(Y1!58), succ(X1!59)) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8726, 47])).
% 5.70/5.69 tff(8728,plain,
% 5.70/5.69 (sum(pred(X1!59), succ(Y1!58)) = sum(n1, n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8625, 8592])).
% 5.70/5.69 tff(8729,plain,
% 5.70/5.69 (sum(pred(X1!59), succ(Y1!58)) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8728, 47])).
% 5.70/5.69 tff(8730,plain,
% 5.70/5.69 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n4, n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8729, 8727])).
% 5.70/5.69 tff(8731,plain,
% 5.70/5.69 (X2!57 = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[209, 8730, 46])).
% 5.70/5.69 tff(8732,plain,
% 5.70/5.69 (pred(X2!57) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8731])).
% 5.70/5.69 tff(8733,plain,
% 5.70/5.69 (pred(X2!57) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8732, 19])).
% 5.70/5.69 tff(8734,plain,
% 5.70/5.69 (pred(pred(X2!57)) = pred(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8733])).
% 5.70/5.69 tff(8735,plain,
% 5.70/5.69 (pred(pred(X2!57)) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8734, 18])).
% 5.70/5.69 tff(8736,plain,
% 5.70/5.69 (pred(pred(pred(X2!57))) = pred(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8735])).
% 5.70/5.69 tff(8737,plain,
% 5.70/5.69 (pred(pred(pred(X2!57))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8736, 17])).
% 5.70/5.69 tff(8738,plain,
% 5.70/5.69 (pred(pred(pred(pred(X2!57)))) = pred(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8737])).
% 5.70/5.69 tff(8739,plain,
% 5.70/5.69 (pred(pred(pred(pred(X2!57)))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8738, 16])).
% 5.70/5.69 tff(8740,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(X2!57))))) = pred(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8739])).
% 5.70/5.69 tff(8741,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(X2!57))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8740, 15])).
% 5.70/5.69 tff(8742,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8741])).
% 5.70/5.69 tff(8743,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8742, 25])).
% 5.70/5.69 tff(8744,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8743])).
% 5.70/5.69 tff(8745,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8744, 24])).
% 5.70/5.69 tff(8746,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8745])).
% 5.70/5.69 tff(8747,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8746, 23])).
% 5.70/5.69 tff(8748,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8747])).
% 5.70/5.69 tff(8749,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8748, 22])).
% 5.70/5.69 tff(8750,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8749])).
% 5.70/5.69 tff(8751,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8750, 21])).
% 5.70/5.69 tff(8752,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8751])).
% 5.70/5.69 tff(8753,plain,
% 5.70/5.69 (NPX2!31 = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[395, 8752, 20])).
% 5.70/5.69 tff(8754,plain,
% 5.70/5.69 (succ(NPX2!31) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8753])).
% 5.70/5.69 tff(8755,plain,
% 5.70/5.69 (succ(NPX2!31) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8754, 45])).
% 5.70/5.69 tff(8756,plain,
% 5.70/5.69 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n9, n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8755, 8725])).
% 5.70/5.69 tff(8757,plain,
% 5.70/5.69 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8756, 790])).
% 5.70/5.69 tff(8758,plain,
% 5.70/5.69 (succ(X2!57) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8731])).
% 5.70/5.69 tff(8759,plain,
% 5.70/5.69 (succ(X2!57) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8758, 45])).
% 5.70/5.69 tff(8760,plain,
% 5.70/5.69 (succ(succ(X2!57)) = succ(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8759])).
% 5.70/5.69 tff(8761,plain,
% 5.70/5.69 (succ(succ(X2!57)) = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[8760, 28])).
% 5.70/5.69 tff(8762,plain,
% 5.70/5.69 (succ(succ(succ(X2!57))) = succ(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8761])).
% 5.70/5.69 tff(8763,plain,
% 5.70/5.69 (succ(succ(succ(X2!57))) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8762, 42])).
% 5.70/5.69 tff(8764,plain,
% 5.70/5.69 (succ(succ(succ(succ(X2!57)))) = succ(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8763])).
% 5.70/5.69 tff(8765,plain,
% 5.70/5.69 (succ(succ(succ(succ(X2!57)))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8764, 58])).
% 5.70/5.69 tff(8766,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(X2!57))))) = succ(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8765])).
% 5.70/5.69 tff(8767,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(X2!57))))) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8766, 36])).
% 5.70/5.69 tff(8768,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8767])).
% 5.70/5.69 tff(8769,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8768, 48])).
% 5.70/5.69 tff(8770,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8769])).
% 5.70/5.69 tff(8771,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8770, 14])).
% 5.70/5.69 tff(8772,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8771])).
% 5.70/5.69 tff(8773,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8772, 33])).
% 5.70/5.69 tff(8774,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8773])).
% 5.70/5.69 tff(8775,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8774, 30])).
% 5.70/5.69 tff(8776,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8775])).
% 5.70/5.69 tff(8777,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8776, 39])).
% 5.70/5.69 tff(8778,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8777])).
% 5.70/5.69 tff(8779,plain,
% 5.70/5.69 (NSX2!29 = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[420, 8778, 53])).
% 5.70/5.69 tff(8780,plain,
% 5.70/5.69 (pred(NSX2!29) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8779])).
% 5.70/5.69 tff(8781,plain,
% 5.70/5.69 (pred(NSX2!29) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8780, 19])).
% 5.70/5.69 tff(8782,plain,
% 5.70/5.69 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n7, n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8781, 8757])).
% 5.70/5.69 tff(8783,plain,
% 5.70/5.69 (Y3!54 = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[425, 8782, 789])).
% 5.70/5.69 tff(8784,plain,
% 5.70/5.69 (pred(Y3!54) = pred(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8783])).
% 5.70/5.69 tff(8785,plain,
% 5.70/5.69 (pred(Y3!54) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8784, 21])).
% 5.70/5.69 tff(8786,plain,
% 5.70/5.69 (pred(pred(Y3!54)) = pred(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8785])).
% 5.70/5.69 tff(8787,plain,
% 5.70/5.69 (pred(pred(Y3!54)) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8786, 20])).
% 5.70/5.69 tff(8788,plain,
% 5.70/5.69 (pred(pred(pred(Y3!54))) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8787])).
% 5.70/5.69 tff(8789,plain,
% 5.70/5.69 (pred(pred(pred(Y3!54))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8788, 19])).
% 5.70/5.69 tff(8790,plain,
% 5.70/5.69 (pred(pred(pred(pred(Y3!54)))) = pred(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8789])).
% 5.70/5.69 tff(8791,plain,
% 5.70/5.69 (pred(pred(pred(pred(Y3!54)))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8790, 18])).
% 5.70/5.69 tff(8792,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8791])).
% 5.70/5.69 tff(8793,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(Y3!54))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8792, 17])).
% 5.70/5.69 tff(8794,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8793])).
% 5.70/5.69 tff(8795,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8794, 16])).
% 5.70/5.69 tff(8796,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8795])).
% 5.70/5.69 tff(8797,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8796, 15])).
% 5.70/5.69 tff(8798,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8797])).
% 5.70/5.69 tff(8799,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8798, 25])).
% 5.70/5.69 tff(8800,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8799])).
% 5.70/5.69 tff(8801,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8800, 24])).
% 5.70/5.69 tff(8802,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8801])).
% 5.70/5.69 tff(8803,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8802, 23])).
% 5.70/5.69 tff(8804,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8803])).
% 5.70/5.69 tff(8805,plain,
% 5.70/5.69 (NPY3!26 = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[462, 8804, 22])).
% 5.70/5.69 tff(8806,plain,
% 5.70/5.69 (succ(NPY3!26) = succ(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8805])).
% 5.70/5.69 tff(8807,plain,
% 5.70/5.69 (succ(NPY3!26) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8806, 42])).
% 5.70/5.69 tff(8808,plain,
% 5.70/5.69 (succ(Y3!54) = succ(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8783])).
% 5.70/5.69 tff(8809,plain,
% 5.70/5.69 (succ(Y3!54) = n0),
% 5.70/5.69 inference(transitivity,[status(thm)],[8808, 42])).
% 5.70/5.69 tff(8810,plain,
% 5.70/5.69 (succ(succ(Y3!54)) = succ(n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8809])).
% 5.70/5.69 tff(8811,plain,
% 5.70/5.69 (succ(succ(Y3!54)) = n1),
% 5.70/5.69 inference(transitivity,[status(thm)],[8810, 58])).
% 5.70/5.69 tff(8812,plain,
% 5.70/5.69 (succ(succ(succ(Y3!54))) = succ(n1)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8811])).
% 5.70/5.69 tff(8813,plain,
% 5.70/5.69 (succ(succ(succ(Y3!54))) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8812, 36])).
% 5.70/5.69 tff(8814,plain,
% 5.70/5.69 (succ(succ(succ(succ(Y3!54)))) = succ(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8813])).
% 5.70/5.69 tff(8815,plain,
% 5.70/5.69 (succ(succ(succ(succ(Y3!54)))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8814, 48])).
% 5.70/5.69 tff(8816,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8815])).
% 5.70/5.69 tff(8817,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(Y3!54))))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8816, 14])).
% 5.70/5.69 tff(8818,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8817])).
% 5.70/5.69 tff(8819,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8818, 33])).
% 5.70/5.69 tff(8820,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8819])).
% 5.70/5.69 tff(8821,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8820, 30])).
% 5.70/5.69 tff(8822,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8821])).
% 5.70/5.69 tff(8823,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8822, 39])).
% 5.70/5.69 tff(8824,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8823])).
% 5.70/5.69 tff(8825,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8824, 53])).
% 5.70/5.69 tff(8826,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8825])).
% 5.70/5.69 tff(8827,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8826, 45])).
% 5.70/5.69 tff(8828,plain,
% 5.70/5.69 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8827])).
% 5.70/5.69 tff(8829,plain,
% 5.70/5.69 (NSY3!24 = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[485, 8828, 28])).
% 5.70/5.69 tff(8830,plain,
% 5.70/5.69 (pred(NSY3!24) = pred(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8829])).
% 5.70/5.69 tff(8831,plain,
% 5.70/5.69 (pred(NSY3!24) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8830, 21])).
% 5.70/5.69 tff(8832,plain,
% 5.70/5.69 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n9, n0)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8831, 8807])).
% 5.70/5.69 tff(8833,plain,
% 5.70/5.69 (sum(pred(NSY3!24), succ(NPY3!26)) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8832, 41])).
% 5.70/5.69 tff(8834,plain,
% 5.70/5.69 (sum(pred(Y2!56), succ(X2!57)) = sum(n7, n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8677, 8759])).
% 5.70/5.69 tff(8835,plain,
% 5.70/5.69 (sum(pred(Y2!56), succ(X2!57)) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8834, 44])).
% 5.70/5.69 tff(8836,plain,
% 5.70/5.69 (sum(pred(X2!57), succ(Y2!56)) = sum(n7, n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8733, 8701])).
% 5.70/5.69 tff(8837,plain,
% 5.70/5.69 (sum(pred(X2!57), succ(Y2!56)) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8836, 44])).
% 5.70/5.69 tff(8838,plain,
% 5.70/5.69 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n5, n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8837, 8835])).
% 5.70/5.69 tff(8839,plain,
% 5.70/5.69 (X3!55 = n10),
% 5.70/5.69 inference(transitivity,[status(thm)],[323, 8838, 43])).
% 5.70/5.69 tff(8840,plain,
% 5.70/5.69 (pred(X3!55) = pred(n10)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8839])).
% 5.70/5.69 tff(8841,plain,
% 5.70/5.69 (pred(X3!55) = n9),
% 5.70/5.69 inference(transitivity,[status(thm)],[8840, 21])).
% 5.70/5.69 tff(8842,plain,
% 5.70/5.69 (pred(pred(X3!55)) = pred(n9)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8841])).
% 5.70/5.69 tff(8843,plain,
% 5.70/5.69 (pred(pred(X3!55)) = n8),
% 5.70/5.69 inference(transitivity,[status(thm)],[8842, 20])).
% 5.70/5.69 tff(8844,plain,
% 5.70/5.69 (pred(pred(pred(X3!55))) = pred(n8)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8843])).
% 5.70/5.69 tff(8845,plain,
% 5.70/5.69 (pred(pred(pred(X3!55))) = n7),
% 5.70/5.69 inference(transitivity,[status(thm)],[8844, 19])).
% 5.70/5.69 tff(8846,plain,
% 5.70/5.69 (pred(pred(pred(pred(X3!55)))) = pred(n7)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8845])).
% 5.70/5.69 tff(8847,plain,
% 5.70/5.69 (pred(pred(pred(pred(X3!55)))) = n6),
% 5.70/5.69 inference(transitivity,[status(thm)],[8846, 18])).
% 5.70/5.69 tff(8848,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(X3!55))))) = pred(n6)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8847])).
% 5.70/5.69 tff(8849,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(X3!55))))) = n5),
% 5.70/5.69 inference(transitivity,[status(thm)],[8848, 17])).
% 5.70/5.69 tff(8850,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n5)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8849])).
% 5.70/5.69 tff(8851,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n4),
% 5.70/5.69 inference(transitivity,[status(thm)],[8850, 16])).
% 5.70/5.69 tff(8852,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n4)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8851])).
% 5.70/5.69 tff(8853,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n3),
% 5.70/5.69 inference(transitivity,[status(thm)],[8852, 15])).
% 5.70/5.69 tff(8854,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n3)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8853])).
% 5.70/5.69 tff(8855,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n2),
% 5.70/5.69 inference(transitivity,[status(thm)],[8854, 25])).
% 5.70/5.69 tff(8856,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n2)),
% 5.70/5.69 inference(monotonicity,[status(thm)],[8855])).
% 5.70/5.69 tff(8857,plain,
% 5.70/5.69 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[8856, 24])).
% 5.70/5.70 tff(8858,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8857])).
% 5.70/5.70 tff(8859,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8858, 23])).
% 5.70/5.70 tff(8860,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8859])).
% 5.70/5.70 tff(8861,plain,
% 5.70/5.70 (NPX3!27 = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[510, 8860, 22])).
% 5.70/5.70 tff(8862,plain,
% 5.70/5.70 (succ(NPX3!27) = succ(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8861])).
% 5.70/5.70 tff(8863,plain,
% 5.70/5.70 (succ(NPX3!27) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8862, 42])).
% 5.70/5.70 tff(8864,plain,
% 5.70/5.70 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n0, n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8863, 8833])).
% 5.70/5.70 tff(8865,plain,
% 5.70/5.70 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8864, 40])).
% 5.70/5.70 tff(8866,plain,
% 5.70/5.70 (succ(X3!55) = succ(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8839])).
% 5.70/5.70 tff(8867,plain,
% 5.70/5.70 (succ(X3!55) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8866, 42])).
% 5.70/5.70 tff(8868,plain,
% 5.70/5.70 (succ(succ(X3!55)) = succ(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8867])).
% 5.70/5.70 tff(8869,plain,
% 5.70/5.70 (succ(succ(X3!55)) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[8868, 58])).
% 5.70/5.70 tff(8870,plain,
% 5.70/5.70 (succ(succ(succ(X3!55))) = succ(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8869])).
% 5.70/5.70 tff(8871,plain,
% 5.70/5.70 (succ(succ(succ(X3!55))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[8870, 36])).
% 5.70/5.70 tff(8872,plain,
% 5.70/5.70 (succ(succ(succ(succ(X3!55)))) = succ(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8871])).
% 5.70/5.70 tff(8873,plain,
% 5.70/5.70 (succ(succ(succ(succ(X3!55)))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[8872, 48])).
% 5.70/5.70 tff(8874,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(X3!55))))) = succ(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8873])).
% 5.70/5.70 tff(8875,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(X3!55))))) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[8874, 14])).
% 5.70/5.70 tff(8876,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8875])).
% 5.70/5.70 tff(8877,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[8876, 33])).
% 5.70/5.70 tff(8878,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8877])).
% 5.70/5.70 tff(8879,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[8878, 30])).
% 5.70/5.70 tff(8880,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8879])).
% 5.70/5.70 tff(8881,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[8880, 39])).
% 5.70/5.70 tff(8882,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8881])).
% 5.70/5.70 tff(8883,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[8882, 53])).
% 5.70/5.70 tff(8884,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8883])).
% 5.70/5.70 tff(8885,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8884, 45])).
% 5.70/5.70 tff(8886,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8885])).
% 5.70/5.70 tff(8887,plain,
% 5.70/5.70 (NSX3!25 = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[535, 8886, 28])).
% 5.70/5.70 tff(8888,plain,
% 5.70/5.70 (pred(NSX3!25) = pred(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8887])).
% 5.70/5.70 tff(8889,plain,
% 5.70/5.70 (pred(NSX3!25) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8888, 21])).
% 5.70/5.70 tff(8890,plain,
% 5.70/5.70 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n9, n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8889, 8865])).
% 5.70/5.70 tff(8891,plain,
% 5.70/5.70 (Y4!52 = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[540, 8890, 54])).
% 5.70/5.70 tff(8892,plain,
% 5.70/5.70 (pred(Y4!52) = pred(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8891])).
% 5.70/5.70 tff(8893,plain,
% 5.70/5.70 (pred(Y4!52) = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[8892, 18])).
% 5.70/5.70 tff(8894,plain,
% 5.70/5.70 (pred(pred(Y4!52)) = pred(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8893])).
% 5.70/5.70 tff(8895,plain,
% 5.70/5.70 (pred(pred(Y4!52)) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[8894, 17])).
% 5.70/5.70 tff(8896,plain,
% 5.70/5.70 (pred(pred(pred(Y4!52))) = pred(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8895])).
% 5.70/5.70 tff(8897,plain,
% 5.70/5.70 (pred(pred(pred(Y4!52))) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[8896, 16])).
% 5.70/5.70 tff(8898,plain,
% 5.70/5.70 (pred(pred(pred(pred(Y4!52)))) = pred(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8897])).
% 5.70/5.70 tff(8899,plain,
% 5.70/5.70 (pred(pred(pred(pred(Y4!52)))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[8898, 15])).
% 5.70/5.70 tff(8900,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8899])).
% 5.70/5.70 tff(8901,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(Y4!52))))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[8900, 25])).
% 5.70/5.70 tff(8902,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8901])).
% 5.70/5.70 tff(8903,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[8902, 24])).
% 5.70/5.70 tff(8904,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8903])).
% 5.70/5.70 tff(8905,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8904, 23])).
% 5.70/5.70 tff(8906,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8905])).
% 5.70/5.70 tff(8907,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[8906, 22])).
% 5.70/5.70 tff(8908,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8907])).
% 5.70/5.70 tff(8909,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8908, 21])).
% 5.70/5.70 tff(8910,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8909])).
% 5.70/5.70 tff(8911,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[8910, 20])).
% 5.70/5.70 tff(8912,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8911])).
% 5.70/5.70 tff(8913,plain,
% 5.70/5.70 (NPY4!22 = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[578, 8912, 19])).
% 5.70/5.70 tff(8914,plain,
% 5.70/5.70 (succ(NPY4!22) = succ(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8913])).
% 5.70/5.70 tff(8915,plain,
% 5.70/5.70 (succ(NPY4!22) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[8914, 53])).
% 5.70/5.70 tff(8916,plain,
% 5.70/5.70 (succ(Y4!52) = succ(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8891])).
% 5.70/5.70 tff(8917,plain,
% 5.70/5.70 (succ(Y4!52) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[8916, 53])).
% 5.70/5.70 tff(8918,plain,
% 5.70/5.70 (succ(succ(Y4!52)) = succ(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8917])).
% 5.70/5.70 tff(8919,plain,
% 5.70/5.70 (succ(succ(Y4!52)) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8918, 45])).
% 5.70/5.70 tff(8920,plain,
% 5.70/5.70 (succ(succ(succ(Y4!52))) = succ(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8919])).
% 5.70/5.70 tff(8921,plain,
% 5.70/5.70 (succ(succ(succ(Y4!52))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[8920, 28])).
% 5.70/5.70 tff(8922,plain,
% 5.70/5.70 (succ(succ(succ(succ(Y4!52)))) = succ(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8921])).
% 5.70/5.70 tff(8923,plain,
% 5.70/5.70 (succ(succ(succ(succ(Y4!52)))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8922, 42])).
% 5.70/5.70 tff(8924,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8923])).
% 5.70/5.70 tff(8925,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(Y4!52))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[8924, 58])).
% 5.70/5.70 tff(8926,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8925])).
% 5.70/5.70 tff(8927,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[8926, 36])).
% 5.70/5.70 tff(8928,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8927])).
% 5.70/5.70 tff(8929,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[8928, 48])).
% 5.70/5.70 tff(8930,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8929])).
% 5.70/5.70 tff(8931,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[8930, 14])).
% 5.70/5.70 tff(8932,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8931])).
% 5.70/5.70 tff(8933,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[8932, 33])).
% 5.70/5.70 tff(8934,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8933])).
% 5.70/5.70 tff(8935,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[8934, 30])).
% 5.70/5.70 tff(8936,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8935])).
% 5.70/5.70 tff(8937,plain,
% 5.70/5.70 (NSY4!20 = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[601, 8936, 39])).
% 5.70/5.70 tff(8938,plain,
% 5.70/5.70 (pred(NSY4!20) = pred(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8937])).
% 5.70/5.70 tff(8939,plain,
% 5.70/5.70 (pred(NSY4!20) = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[8938, 18])).
% 5.70/5.70 tff(8940,plain,
% 5.70/5.70 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n6, n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8939, 8915])).
% 5.70/5.70 tff(8941,plain,
% 5.70/5.70 (sum(pred(NSY4!20), succ(NPY4!22)) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[8940, 52])).
% 5.70/5.70 tff(8942,plain,
% 5.70/5.70 (sum(pred(Y3!54), succ(X3!55)) = sum(n9, n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8785, 8867])).
% 5.70/5.70 tff(8943,plain,
% 5.70/5.70 (sum(pred(Y3!54), succ(X3!55)) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8942, 41])).
% 5.70/5.70 tff(8944,plain,
% 5.70/5.70 (sum(pred(X3!55), succ(Y3!54)) = sum(n9, n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8841, 8809])).
% 5.70/5.70 tff(8945,plain,
% 5.70/5.70 (sum(pred(X3!55), succ(Y3!54)) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8944, 41])).
% 5.70/5.70 tff(8946,plain,
% 5.70/5.70 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n9, n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8945, 8943])).
% 5.70/5.70 tff(8947,plain,
% 5.70/5.70 (X4!53 = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[438, 8946, 54])).
% 5.70/5.70 tff(8948,plain,
% 5.70/5.70 (pred(X4!53) = pred(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8947])).
% 5.70/5.70 tff(8949,plain,
% 5.70/5.70 (pred(X4!53) = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[8948, 18])).
% 5.70/5.70 tff(8950,plain,
% 5.70/5.70 (pred(pred(X4!53)) = pred(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8949])).
% 5.70/5.70 tff(8951,plain,
% 5.70/5.70 (pred(pred(X4!53)) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[8950, 17])).
% 5.70/5.70 tff(8952,plain,
% 5.70/5.70 (pred(pred(pred(X4!53))) = pred(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8951])).
% 5.70/5.70 tff(8953,plain,
% 5.70/5.70 (pred(pred(pred(X4!53))) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[8952, 16])).
% 5.70/5.70 tff(8954,plain,
% 5.70/5.70 (pred(pred(pred(pred(X4!53)))) = pred(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8953])).
% 5.70/5.70 tff(8955,plain,
% 5.70/5.70 (pred(pred(pred(pred(X4!53)))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[8954, 15])).
% 5.70/5.70 tff(8956,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(X4!53))))) = pred(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8955])).
% 5.70/5.70 tff(8957,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(X4!53))))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[8956, 25])).
% 5.70/5.70 tff(8958,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8957])).
% 5.70/5.70 tff(8959,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[8958, 24])).
% 5.70/5.70 tff(8960,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8959])).
% 5.70/5.70 tff(8961,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8960, 23])).
% 5.70/5.70 tff(8962,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8961])).
% 5.70/5.70 tff(8963,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[8962, 22])).
% 5.70/5.70 tff(8964,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8963])).
% 5.70/5.70 tff(8965,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8964, 21])).
% 5.70/5.70 tff(8966,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8965])).
% 5.70/5.70 tff(8967,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[8966, 20])).
% 5.70/5.70 tff(8968,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8967])).
% 5.70/5.70 tff(8969,plain,
% 5.70/5.70 (NPX4!23 = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[626, 8968, 19])).
% 5.70/5.70 tff(8970,plain,
% 5.70/5.70 (succ(NPX4!23) = succ(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8969])).
% 5.70/5.70 tff(8971,plain,
% 5.70/5.70 (succ(NPX4!23) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[8970, 53])).
% 5.70/5.70 tff(8972,plain,
% 5.70/5.70 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n8, n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8971, 8941])).
% 5.70/5.70 tff(8973,plain,
% 5.70/5.70 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8972, 64])).
% 5.70/5.70 tff(8974,plain,
% 5.70/5.70 (succ(X4!53) = succ(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8947])).
% 5.70/5.70 tff(8975,plain,
% 5.70/5.70 (succ(X4!53) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[8974, 53])).
% 5.70/5.70 tff(8976,plain,
% 5.70/5.70 (succ(succ(X4!53)) = succ(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8975])).
% 5.70/5.70 tff(8977,plain,
% 5.70/5.70 (succ(succ(X4!53)) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[8976, 45])).
% 5.70/5.70 tff(8978,plain,
% 5.70/5.70 (succ(succ(succ(X4!53))) = succ(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8977])).
% 5.70/5.70 tff(8979,plain,
% 5.70/5.70 (succ(succ(succ(X4!53))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[8978, 28])).
% 5.70/5.70 tff(8980,plain,
% 5.70/5.70 (succ(succ(succ(succ(X4!53)))) = succ(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8979])).
% 5.70/5.70 tff(8981,plain,
% 5.70/5.70 (succ(succ(succ(succ(X4!53)))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[8980, 42])).
% 5.70/5.70 tff(8982,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(X4!53))))) = succ(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8981])).
% 5.70/5.70 tff(8983,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(X4!53))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[8982, 58])).
% 5.70/5.70 tff(8984,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8983])).
% 5.70/5.70 tff(8985,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[8984, 36])).
% 5.70/5.70 tff(8986,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8985])).
% 5.70/5.70 tff(8987,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[8986, 48])).
% 5.70/5.70 tff(8988,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8987])).
% 5.70/5.70 tff(8989,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[8988, 14])).
% 5.70/5.70 tff(8990,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8989])).
% 5.70/5.70 tff(8991,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[8990, 33])).
% 5.70/5.70 tff(8992,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8991])).
% 5.70/5.70 tff(8993,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[8992, 30])).
% 5.70/5.70 tff(8994,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8993])).
% 5.70/5.70 tff(8995,plain,
% 5.70/5.70 (NSX4!21 = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[651, 8994, 39])).
% 5.70/5.70 tff(8996,plain,
% 5.70/5.70 (pred(NSX4!21) = pred(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8995])).
% 5.70/5.70 tff(8997,plain,
% 5.70/5.70 (pred(NSX4!21) = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[8996, 18])).
% 5.70/5.70 tff(8998,plain,
% 5.70/5.70 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n6, n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8997, 8973])).
% 5.70/5.70 tff(8999,plain,
% 5.70/5.70 (Y5!50 = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[656, 8998, 788])).
% 5.70/5.70 tff(9000,plain,
% 5.70/5.70 (pred(Y5!50) = pred(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8999])).
% 5.70/5.70 tff(9001,plain,
% 5.70/5.70 (pred(Y5!50) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[9000, 17])).
% 5.70/5.70 tff(9002,plain,
% 5.70/5.70 (pred(pred(Y5!50)) = pred(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9001])).
% 5.70/5.70 tff(9003,plain,
% 5.70/5.70 (pred(pred(Y5!50)) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[9002, 16])).
% 5.70/5.70 tff(9004,plain,
% 5.70/5.70 (pred(pred(pred(Y5!50))) = pred(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9003])).
% 5.70/5.70 tff(9005,plain,
% 5.70/5.70 (pred(pred(pred(Y5!50))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[9004, 15])).
% 5.70/5.70 tff(9006,plain,
% 5.70/5.70 (pred(pred(pred(pred(Y5!50)))) = pred(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9005])).
% 5.70/5.70 tff(9007,plain,
% 5.70/5.70 (pred(pred(pred(pred(Y5!50)))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[9006, 25])).
% 5.70/5.70 tff(9008,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9007])).
% 5.70/5.70 tff(9009,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(Y5!50))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[9008, 24])).
% 5.70/5.70 tff(9010,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9009])).
% 5.70/5.70 tff(9011,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[9010, 23])).
% 5.70/5.70 tff(9012,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9011])).
% 5.70/5.70 tff(9013,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[9012, 22])).
% 5.70/5.70 tff(9014,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9013])).
% 5.70/5.70 tff(9015,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[9014, 21])).
% 5.70/5.70 tff(9016,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9015])).
% 5.70/5.70 tff(9017,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[9016, 20])).
% 5.70/5.70 tff(9018,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9017])).
% 5.70/5.70 tff(9019,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[9018, 19])).
% 5.70/5.70 tff(9020,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9019])).
% 5.70/5.70 tff(9021,plain,
% 5.70/5.70 (NPY5!18 = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[694, 9020, 18])).
% 5.70/5.70 tff(9022,plain,
% 5.70/5.70 (succ(NPY5!18) = succ(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9021])).
% 5.70/5.70 tff(9023,plain,
% 5.70/5.70 (succ(NPY5!18) = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[9022, 39])).
% 5.70/5.70 tff(9024,plain,
% 5.70/5.70 (succ(Y5!50) = succ(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8999])).
% 5.70/5.70 tff(9025,plain,
% 5.70/5.70 (succ(Y5!50) = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[9024, 39])).
% 5.70/5.70 tff(9026,plain,
% 5.70/5.70 (succ(succ(Y5!50)) = succ(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9025])).
% 5.70/5.70 tff(9027,plain,
% 5.70/5.70 (succ(succ(Y5!50)) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[9026, 53])).
% 5.70/5.70 tff(9028,plain,
% 5.70/5.70 (succ(succ(succ(Y5!50))) = succ(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9027])).
% 5.70/5.70 tff(9029,plain,
% 5.70/5.70 (succ(succ(succ(Y5!50))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[9028, 45])).
% 5.70/5.70 tff(9030,plain,
% 5.70/5.70 (succ(succ(succ(succ(Y5!50)))) = succ(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9029])).
% 5.70/5.70 tff(9031,plain,
% 5.70/5.70 (succ(succ(succ(succ(Y5!50)))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[9030, 28])).
% 5.70/5.70 tff(9032,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9031])).
% 5.70/5.70 tff(9033,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(Y5!50))))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[9032, 42])).
% 5.70/5.70 tff(9034,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9033])).
% 5.70/5.70 tff(9035,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[9034, 58])).
% 5.70/5.70 tff(9036,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9035])).
% 5.70/5.70 tff(9037,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[9036, 36])).
% 5.70/5.70 tff(9038,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9037])).
% 5.70/5.70 tff(9039,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[9038, 48])).
% 5.70/5.70 tff(9040,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9039])).
% 5.70/5.70 tff(9041,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[9040, 14])).
% 5.70/5.70 tff(9042,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9041])).
% 5.70/5.70 tff(9043,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[9042, 33])).
% 5.70/5.70 tff(9044,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9043])).
% 5.70/5.70 tff(9045,plain,
% 5.70/5.70 (NSY5!16 = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[717, 9044, 30])).
% 5.70/5.70 tff(9046,plain,
% 5.70/5.70 (pred(NSY5!16) = pred(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9045])).
% 5.70/5.70 tff(9047,plain,
% 5.70/5.70 (pred(NSY5!16) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[9046, 17])).
% 5.70/5.70 tff(9048,plain,
% 5.70/5.70 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n5, n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9047, 9023])).
% 5.70/5.70 tff(9049,plain,
% 5.70/5.70 (sum(pred(NSY5!16), succ(NPY5!18)) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[9048, 50])).
% 5.70/5.70 tff(9050,plain,
% 5.70/5.70 (sum(pred(Y4!52), succ(X4!53)) = sum(n6, n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8893, 8975])).
% 5.70/5.70 tff(9051,plain,
% 5.70/5.70 (sum(pred(Y4!52), succ(X4!53)) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[9050, 52])).
% 5.70/5.70 tff(9052,plain,
% 5.70/5.70 (sum(pred(X4!53), succ(Y4!52)) = sum(n6, n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[8949, 8917])).
% 5.70/5.70 tff(9053,plain,
% 5.70/5.70 (sum(pred(X4!53), succ(Y4!52)) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[9052, 52])).
% 5.70/5.70 tff(9054,plain,
% 5.70/5.70 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n3, n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9053, 9051])).
% 5.70/5.70 tff(9055,plain,
% 5.70/5.70 (X5!51 = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[553, 9054, 51])).
% 5.70/5.70 tff(9056,plain,
% 5.70/5.70 (pred(X5!51) = pred(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9055])).
% 5.70/5.70 tff(9057,plain,
% 5.70/5.70 (pred(X5!51) = n5),
% 5.70/5.70 inference(transitivity,[status(thm)],[9056, 17])).
% 5.70/5.70 tff(9058,plain,
% 5.70/5.70 (pred(pred(X5!51)) = pred(n5)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9057])).
% 5.70/5.70 tff(9059,plain,
% 5.70/5.70 (pred(pred(X5!51)) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[9058, 16])).
% 5.70/5.70 tff(9060,plain,
% 5.70/5.70 (pred(pred(pred(X5!51))) = pred(n4)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9059])).
% 5.70/5.70 tff(9061,plain,
% 5.70/5.70 (pred(pred(pred(X5!51))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[9060, 15])).
% 5.70/5.70 tff(9062,plain,
% 5.70/5.70 (pred(pred(pred(pred(X5!51)))) = pred(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9061])).
% 5.70/5.70 tff(9063,plain,
% 5.70/5.70 (pred(pred(pred(pred(X5!51)))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[9062, 25])).
% 5.70/5.70 tff(9064,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(X5!51))))) = pred(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9063])).
% 5.70/5.70 tff(9065,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(X5!51))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[9064, 24])).
% 5.70/5.70 tff(9066,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9065])).
% 5.70/5.70 tff(9067,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[9066, 23])).
% 5.70/5.70 tff(9068,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9067])).
% 5.70/5.70 tff(9069,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[9068, 22])).
% 5.70/5.70 tff(9070,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9069])).
% 5.70/5.70 tff(9071,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[9070, 21])).
% 5.70/5.70 tff(9072,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9071])).
% 5.70/5.70 tff(9073,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[9072, 20])).
% 5.70/5.70 tff(9074,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9073])).
% 5.70/5.70 tff(9075,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[9074, 19])).
% 5.70/5.70 tff(9076,plain,
% 5.70/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9075])).
% 5.70/5.70 tff(9077,plain,
% 5.70/5.70 (NPX5!19 = n6),
% 5.70/5.70 inference(transitivity,[status(thm)],[742, 9076, 18])).
% 5.70/5.70 tff(9078,plain,
% 5.70/5.70 (succ(NPX5!19) = succ(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9077])).
% 5.70/5.70 tff(9079,plain,
% 5.70/5.70 (succ(NPX5!19) = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[9078, 39])).
% 5.70/5.70 tff(9080,plain,
% 5.70/5.70 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n7, n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9079, 9049])).
% 5.70/5.70 tff(9081,plain,
% 5.70/5.70 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[9080, 787])).
% 5.70/5.70 tff(9082,plain,
% 5.70/5.70 (succ(X5!51) = succ(n6)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9055])).
% 5.70/5.70 tff(9083,plain,
% 5.70/5.70 (succ(X5!51) = n7),
% 5.70/5.70 inference(transitivity,[status(thm)],[9082, 39])).
% 5.70/5.70 tff(9084,plain,
% 5.70/5.70 (succ(succ(X5!51)) = succ(n7)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9083])).
% 5.70/5.70 tff(9085,plain,
% 5.70/5.70 (succ(succ(X5!51)) = n8),
% 5.70/5.70 inference(transitivity,[status(thm)],[9084, 53])).
% 5.70/5.70 tff(9086,plain,
% 5.70/5.70 (succ(succ(succ(X5!51))) = succ(n8)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9085])).
% 5.70/5.70 tff(9087,plain,
% 5.70/5.70 (succ(succ(succ(X5!51))) = n9),
% 5.70/5.70 inference(transitivity,[status(thm)],[9086, 45])).
% 5.70/5.70 tff(9088,plain,
% 5.70/5.70 (succ(succ(succ(succ(X5!51)))) = succ(n9)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9087])).
% 5.70/5.70 tff(9089,plain,
% 5.70/5.70 (succ(succ(succ(succ(X5!51)))) = n10),
% 5.70/5.70 inference(transitivity,[status(thm)],[9088, 28])).
% 5.70/5.70 tff(9090,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(X5!51))))) = succ(n10)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9089])).
% 5.70/5.70 tff(9091,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(X5!51))))) = n0),
% 5.70/5.70 inference(transitivity,[status(thm)],[9090, 42])).
% 5.70/5.70 tff(9092,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n0)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9091])).
% 5.70/5.70 tff(9093,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n1),
% 5.70/5.70 inference(transitivity,[status(thm)],[9092, 58])).
% 5.70/5.70 tff(9094,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n1)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9093])).
% 5.70/5.70 tff(9095,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n2),
% 5.70/5.70 inference(transitivity,[status(thm)],[9094, 36])).
% 5.70/5.70 tff(9096,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n2)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9095])).
% 5.70/5.70 tff(9097,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n3),
% 5.70/5.70 inference(transitivity,[status(thm)],[9096, 48])).
% 5.70/5.70 tff(9098,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n3)),
% 5.70/5.70 inference(monotonicity,[status(thm)],[9097])).
% 5.70/5.70 tff(9099,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n4),
% 5.70/5.70 inference(transitivity,[status(thm)],[9098, 14])).
% 5.70/5.70 tff(9100,plain,
% 5.70/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n4)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9099])).
% 5.77/5.70 tff(9101,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n5),
% 5.77/5.70 inference(transitivity,[status(thm)],[9100, 33])).
% 5.77/5.70 tff(9102,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n5)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9101])).
% 5.77/5.70 tff(9103,plain,
% 5.77/5.70 (NSX5!17 = n6),
% 5.77/5.70 inference(transitivity,[status(thm)],[767, 9102, 30])).
% 5.77/5.70 tff(9104,plain,
% 5.77/5.70 (pred(NSX5!17) = pred(n6)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9103])).
% 5.77/5.70 tff(9105,plain,
% 5.77/5.70 (pred(NSX5!17) = n5),
% 5.77/5.70 inference(transitivity,[status(thm)],[9104, 17])).
% 5.77/5.70 tff(9106,plain,
% 5.77/5.70 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n5, n8)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9105, 9081])).
% 5.77/5.70 tff(9107,plain,
% 5.77/5.70 (Y6!48 = n2),
% 5.77/5.70 inference(transitivity,[status(thm)],[772, 9106, 558])).
% 5.77/5.70 tff(9108,plain,
% 5.77/5.70 (pred(Y6!48) = pred(n2)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9107])).
% 5.77/5.70 tff(9109,plain,
% 5.77/5.70 (pred(Y6!48) = n1),
% 5.77/5.70 inference(transitivity,[status(thm)],[9108, 24])).
% 5.77/5.70 tff(9110,plain,
% 5.77/5.70 (pred(pred(Y6!48)) = pred(n1)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9109])).
% 5.77/5.70 tff(9111,plain,
% 5.77/5.70 (pred(pred(Y6!48)) = n0),
% 5.77/5.70 inference(transitivity,[status(thm)],[9110, 23])).
% 5.77/5.70 tff(9112,plain,
% 5.77/5.70 (pred(pred(pred(Y6!48))) = pred(n0)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9111])).
% 5.77/5.70 tff(9113,plain,
% 5.77/5.70 (pred(pred(pred(Y6!48))) = n10),
% 5.77/5.70 inference(transitivity,[status(thm)],[9112, 22])).
% 5.77/5.70 tff(9114,plain,
% 5.77/5.70 (pred(pred(pred(pred(Y6!48)))) = pred(n10)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9113])).
% 5.77/5.70 tff(9115,plain,
% 5.77/5.70 (pred(pred(pred(pred(Y6!48)))) = n9),
% 5.77/5.70 inference(transitivity,[status(thm)],[9114, 21])).
% 5.77/5.70 tff(9116,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n9)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9115])).
% 5.77/5.70 tff(9117,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(Y6!48))))) = n8),
% 5.77/5.70 inference(transitivity,[status(thm)],[9116, 20])).
% 5.77/5.70 tff(9118,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n8)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9117])).
% 5.77/5.70 tff(9119,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n7),
% 5.77/5.70 inference(transitivity,[status(thm)],[9118, 19])).
% 5.77/5.70 tff(9120,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n7)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9119])).
% 5.77/5.70 tff(9121,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n6),
% 5.77/5.70 inference(transitivity,[status(thm)],[9120, 18])).
% 5.77/5.70 tff(9122,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n6)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9121])).
% 5.77/5.70 tff(9123,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n5),
% 5.77/5.70 inference(transitivity,[status(thm)],[9122, 17])).
% 5.77/5.70 tff(9124,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n5)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9123])).
% 5.77/5.70 tff(9125,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n4),
% 5.77/5.70 inference(transitivity,[status(thm)],[9124, 16])).
% 5.77/5.70 tff(9126,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n4)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9125])).
% 5.77/5.70 tff(9127,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n3),
% 5.77/5.70 inference(transitivity,[status(thm)],[9126, 15])).
% 5.77/5.70 tff(9128,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n3)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9127])).
% 5.77/5.70 tff(9129,plain,
% 5.77/5.70 (NPY6!14 = n2),
% 5.77/5.70 inference(transitivity,[status(thm)],[1465, 9128, 25])).
% 5.77/5.70 tff(9130,plain,
% 5.77/5.70 (succ(NPY6!14) = succ(n2)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9129])).
% 5.77/5.70 tff(9131,plain,
% 5.77/5.70 (succ(NPY6!14) = n3),
% 5.77/5.70 inference(transitivity,[status(thm)],[9130, 48])).
% 5.77/5.70 tff(9132,plain,
% 5.77/5.70 (succ(Y6!48) = succ(n2)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9107])).
% 5.77/5.70 tff(9133,plain,
% 5.77/5.70 (succ(Y6!48) = n3),
% 5.77/5.70 inference(transitivity,[status(thm)],[9132, 48])).
% 5.77/5.70 tff(9134,plain,
% 5.77/5.70 (succ(succ(Y6!48)) = succ(n3)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9133])).
% 5.77/5.70 tff(9135,plain,
% 5.77/5.70 (succ(succ(Y6!48)) = n4),
% 5.77/5.70 inference(transitivity,[status(thm)],[9134, 14])).
% 5.77/5.70 tff(9136,plain,
% 5.77/5.70 (succ(succ(succ(Y6!48))) = succ(n4)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9135])).
% 5.77/5.70 tff(9137,plain,
% 5.77/5.70 (succ(succ(succ(Y6!48))) = n5),
% 5.77/5.70 inference(transitivity,[status(thm)],[9136, 33])).
% 5.77/5.70 tff(9138,plain,
% 5.77/5.70 (succ(succ(succ(succ(Y6!48)))) = succ(n5)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9137])).
% 5.77/5.70 tff(9139,plain,
% 5.77/5.70 (succ(succ(succ(succ(Y6!48)))) = n6),
% 5.77/5.70 inference(transitivity,[status(thm)],[9138, 30])).
% 5.77/5.70 tff(9140,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n6)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9139])).
% 5.77/5.70 tff(9141,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(Y6!48))))) = n7),
% 5.77/5.70 inference(transitivity,[status(thm)],[9140, 39])).
% 5.77/5.70 tff(9142,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n7)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9141])).
% 5.77/5.70 tff(9143,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n8),
% 5.77/5.70 inference(transitivity,[status(thm)],[9142, 53])).
% 5.77/5.70 tff(9144,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n8)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9143])).
% 5.77/5.70 tff(9145,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n9),
% 5.77/5.70 inference(transitivity,[status(thm)],[9144, 45])).
% 5.77/5.70 tff(9146,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n9)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9145])).
% 5.77/5.70 tff(9147,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n10),
% 5.77/5.70 inference(transitivity,[status(thm)],[9146, 28])).
% 5.77/5.70 tff(9148,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n10)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9147])).
% 5.77/5.70 tff(9149,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n0),
% 5.77/5.70 inference(transitivity,[status(thm)],[9148, 42])).
% 5.77/5.70 tff(9150,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n0)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9149])).
% 5.77/5.70 tff(9151,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n1),
% 5.77/5.70 inference(transitivity,[status(thm)],[9150, 58])).
% 5.77/5.70 tff(9152,plain,
% 5.77/5.70 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n1)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9151])).
% 5.77/5.70 tff(9153,plain,
% 5.77/5.70 (NSY6!12 = n2),
% 5.77/5.70 inference(transitivity,[status(thm)],[1490, 9152, 36])).
% 5.77/5.70 tff(9154,plain,
% 5.77/5.70 (pred(NSY6!12) = pred(n2)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9153])).
% 5.77/5.70 tff(9155,plain,
% 5.77/5.70 (pred(NSY6!12) = n1),
% 5.77/5.70 inference(transitivity,[status(thm)],[9154, 24])).
% 5.77/5.70 tff(9156,plain,
% 5.77/5.70 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n1, n3)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9155, 9131])).
% 5.77/5.70 tff(9157,plain,
% 5.77/5.70 (sum(pred(NSY6!12), succ(NPY6!14)) = n4),
% 5.77/5.70 inference(transitivity,[status(thm)],[9156, 47])).
% 5.77/5.70 tff(9158,plain,
% 5.77/5.70 (sum(pred(Y5!50), succ(X5!51)) = sum(n5, n7)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9001, 9083])).
% 5.77/5.70 tff(9159,plain,
% 5.77/5.70 (sum(pred(Y5!50), succ(X5!51)) = n1),
% 5.77/5.70 inference(transitivity,[status(thm)],[9158, 50])).
% 5.77/5.70 tff(9160,plain,
% 5.77/5.70 (sum(pred(X5!51), succ(Y5!50)) = sum(n5, n7)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9057, 9025])).
% 5.77/5.70 tff(9161,plain,
% 5.77/5.70 (sum(pred(X5!51), succ(Y5!50)) = n1),
% 5.77/5.70 inference(transitivity,[status(thm)],[9160, 50])).
% 5.77/5.70 tff(9162,plain,
% 5.77/5.70 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n1, n1)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9161, 9159])).
% 5.77/5.70 tff(9163,plain,
% 5.77/5.70 (X6!49 = n2),
% 5.77/5.70 inference(transitivity,[status(thm)],[669, 9162, 49])).
% 5.77/5.70 tff(9164,plain,
% 5.77/5.70 (pred(X6!49) = pred(n2)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9163])).
% 5.77/5.70 tff(9165,plain,
% 5.77/5.70 (pred(X6!49) = n1),
% 5.77/5.70 inference(transitivity,[status(thm)],[9164, 24])).
% 5.77/5.70 tff(9166,plain,
% 5.77/5.70 (pred(pred(X6!49)) = pred(n1)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9165])).
% 5.77/5.70 tff(9167,plain,
% 5.77/5.70 (pred(pred(X6!49)) = n0),
% 5.77/5.70 inference(transitivity,[status(thm)],[9166, 23])).
% 5.77/5.70 tff(9168,plain,
% 5.77/5.70 (pred(pred(pred(X6!49))) = pred(n0)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9167])).
% 5.77/5.70 tff(9169,plain,
% 5.77/5.70 (pred(pred(pred(X6!49))) = n10),
% 5.77/5.70 inference(transitivity,[status(thm)],[9168, 22])).
% 5.77/5.70 tff(9170,plain,
% 5.77/5.70 (pred(pred(pred(pred(X6!49)))) = pred(n10)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9169])).
% 5.77/5.70 tff(9171,plain,
% 5.77/5.70 (pred(pred(pred(pred(X6!49)))) = n9),
% 5.77/5.70 inference(transitivity,[status(thm)],[9170, 21])).
% 5.77/5.70 tff(9172,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(X6!49))))) = pred(n9)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9171])).
% 5.77/5.70 tff(9173,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(X6!49))))) = n8),
% 5.77/5.70 inference(transitivity,[status(thm)],[9172, 20])).
% 5.77/5.70 tff(9174,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n8)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9173])).
% 5.77/5.70 tff(9175,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n7),
% 5.77/5.70 inference(transitivity,[status(thm)],[9174, 19])).
% 5.77/5.70 tff(9176,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n7)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9175])).
% 5.77/5.70 tff(9177,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n6),
% 5.77/5.70 inference(transitivity,[status(thm)],[9176, 18])).
% 5.77/5.70 tff(9178,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n6)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9177])).
% 5.77/5.70 tff(9179,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n5),
% 5.77/5.70 inference(transitivity,[status(thm)],[9178, 17])).
% 5.77/5.70 tff(9180,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n5)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9179])).
% 5.77/5.70 tff(9181,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n4),
% 5.77/5.70 inference(transitivity,[status(thm)],[9180, 16])).
% 5.77/5.70 tff(9182,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n4)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9181])).
% 5.77/5.70 tff(9183,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n3),
% 5.77/5.70 inference(transitivity,[status(thm)],[9182, 15])).
% 5.77/5.70 tff(9184,plain,
% 5.77/5.70 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n3)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9183])).
% 5.77/5.70 tff(9185,plain,
% 5.77/5.70 (NPX6!15 = n2),
% 5.77/5.70 inference(transitivity,[status(thm)],[1523, 9184, 25])).
% 5.77/5.70 tff(9186,plain,
% 5.77/5.70 (succ(NPX6!15) = succ(n2)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9185])).
% 5.77/5.70 tff(9187,plain,
% 5.77/5.70 (succ(NPX6!15) = n3),
% 5.77/5.70 inference(transitivity,[status(thm)],[9186, 48])).
% 5.77/5.70 tff(9188,plain,
% 5.77/5.70 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n3, n4)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9187, 9157])).
% 5.77/5.70 tff(9189,plain,
% 5.77/5.70 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n7),
% 5.77/5.70 inference(transitivity,[status(thm)],[9188, 786])).
% 5.77/5.70 tff(9190,plain,
% 5.77/5.70 (succ(X6!49) = succ(n2)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9163])).
% 5.77/5.70 tff(9191,plain,
% 5.77/5.70 (succ(X6!49) = n3),
% 5.77/5.70 inference(transitivity,[status(thm)],[9190, 48])).
% 5.77/5.70 tff(9192,plain,
% 5.77/5.70 (succ(succ(X6!49)) = succ(n3)),
% 5.77/5.70 inference(monotonicity,[status(thm)],[9191])).
% 5.77/5.70 tff(9193,plain,
% 5.77/5.71 (succ(succ(X6!49)) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9192, 14])).
% 5.77/5.71 tff(9194,plain,
% 5.77/5.71 (succ(succ(succ(X6!49))) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9193])).
% 5.77/5.71 tff(9195,plain,
% 5.77/5.71 (succ(succ(succ(X6!49))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9194, 33])).
% 5.77/5.71 tff(9196,plain,
% 5.77/5.71 (succ(succ(succ(succ(X6!49)))) = succ(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9195])).
% 5.77/5.71 tff(9197,plain,
% 5.77/5.71 (succ(succ(succ(succ(X6!49)))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9196, 30])).
% 5.77/5.71 tff(9198,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(X6!49))))) = succ(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9197])).
% 5.77/5.71 tff(9199,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(X6!49))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9198, 39])).
% 5.77/5.71 tff(9200,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9199])).
% 5.77/5.71 tff(9201,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9200, 53])).
% 5.77/5.71 tff(9202,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9201])).
% 5.77/5.71 tff(9203,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9202, 45])).
% 5.77/5.71 tff(9204,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9203])).
% 5.77/5.71 tff(9205,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9204, 28])).
% 5.77/5.71 tff(9206,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9205])).
% 5.77/5.71 tff(9207,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9206, 42])).
% 5.77/5.71 tff(9208,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9207])).
% 5.77/5.71 tff(9209,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9208, 58])).
% 5.77/5.71 tff(9210,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9209])).
% 5.77/5.71 tff(9211,plain,
% 5.77/5.71 (NSX6!13 = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[1550, 9210, 36])).
% 5.77/5.71 tff(9212,plain,
% 5.77/5.71 (pred(NSX6!13) = pred(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9211])).
% 5.77/5.71 tff(9213,plain,
% 5.77/5.71 (pred(NSX6!13) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9212, 24])).
% 5.77/5.71 tff(9214,plain,
% 5.77/5.71 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n1, n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9213, 9189])).
% 5.77/5.71 tff(9215,plain,
% 5.77/5.71 (sum(n1, n7) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.77/5.71 inference(symmetry,[status(thm)],[9214])).
% 5.77/5.71 tff(9216,plain,
% 5.77/5.71 (sum(pred(Y6!48), succ(X6!49)) = sum(n1, n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9109, 9191])).
% 5.77/5.71 tff(9217,plain,
% 5.77/5.71 (sum(pred(Y6!48), succ(X6!49)) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9216, 47])).
% 5.77/5.71 tff(9218,plain,
% 5.77/5.71 (sum(pred(X6!49), succ(Y6!48)) = sum(n1, n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9165, 9133])).
% 5.77/5.71 tff(9219,plain,
% 5.77/5.71 (sum(pred(X6!49), succ(Y6!48)) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9218, 47])).
% 5.77/5.71 tff(9220,plain,
% 5.77/5.71 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n4, n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9219, 9217])).
% 5.77/5.71 tff(9221,plain,
% 5.77/5.71 (X7!47 = Y7!46),
% 5.77/5.71 inference(transitivity,[status(thm)],[785, 9220, 46, 6515, 9215, 794])).
% 5.77/5.71 tff(9222,plain,
% 5.77/5.71 ($false),
% 5.77/5.71 inference(unit_resolution,[status(thm)],[792, 9221])).
% 5.77/5.71 tff(9223,plain,((~(Y0!60 = n7)) | (X7!47 = Y7!46) | (~(X0!61 = n5))), inference(lemma,lemma(discharge,[]))).
% 5.77/5.71 tff(9224,plain,
% 5.77/5.71 (~(Y0!60 = n7)),
% 5.77/5.71 inference(unit_resolution,[status(thm)],[9223, 7190, 792])).
% 5.77/5.71 tff(9225,assumption,(Y0!60 = n0), introduced(assumption)).
% 5.77/5.71 tff(9226,plain,
% 5.77/5.71 (pred(Y0!60) = pred(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9225])).
% 5.77/5.71 tff(9227,plain,
% 5.77/5.71 (pred(Y0!60) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9226, 22])).
% 5.77/5.71 tff(9228,plain,
% 5.77/5.71 (pred(pred(Y0!60)) = pred(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9227])).
% 5.77/5.71 tff(9229,plain,
% 5.77/5.71 (pred(pred(Y0!60)) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9228, 21])).
% 5.77/5.71 tff(9230,plain,
% 5.77/5.71 (pred(pred(pred(Y0!60))) = pred(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9229])).
% 5.77/5.71 tff(9231,plain,
% 5.77/5.71 (pred(pred(pred(Y0!60))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9230, 20])).
% 5.77/5.71 tff(9232,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y0!60)))) = pred(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9231])).
% 5.77/5.71 tff(9233,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y0!60)))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9232, 19])).
% 5.77/5.71 tff(9234,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9233])).
% 5.77/5.71 tff(9235,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y0!60))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9234, 18])).
% 5.77/5.71 tff(9236,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9235])).
% 5.77/5.71 tff(9237,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9236, 17])).
% 5.77/5.71 tff(9238,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9237])).
% 5.77/5.71 tff(9239,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9238, 16])).
% 5.77/5.71 tff(9240,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9239])).
% 5.77/5.71 tff(9241,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[9240, 15])).
% 5.77/5.71 tff(9242,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9241])).
% 5.77/5.71 tff(9243,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9242, 25])).
% 5.77/5.71 tff(9244,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9243])).
% 5.77/5.71 tff(9245,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9244, 24])).
% 5.77/5.71 tff(9246,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9245])).
% 5.77/5.71 tff(9247,plain,
% 5.77/5.71 (NPY0!38 = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[118, 9246, 23])).
% 5.77/5.71 tff(9248,plain,
% 5.77/5.71 (succ(NPY0!38) = succ(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9247])).
% 5.77/5.71 tff(9249,plain,
% 5.77/5.71 (succ(NPY0!38) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9248, 58])).
% 5.77/5.71 tff(9250,plain,
% 5.77/5.71 (succ(Y0!60) = succ(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9225])).
% 5.77/5.71 tff(9251,plain,
% 5.77/5.71 (succ(Y0!60) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9250, 58])).
% 5.77/5.71 tff(9252,plain,
% 5.77/5.71 (succ(succ(Y0!60)) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9251])).
% 5.77/5.71 tff(9253,plain,
% 5.77/5.71 (succ(succ(Y0!60)) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9252, 36])).
% 5.77/5.71 tff(9254,plain,
% 5.77/5.71 (succ(succ(succ(Y0!60))) = succ(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9253])).
% 5.77/5.71 tff(9255,plain,
% 5.77/5.71 (succ(succ(succ(Y0!60))) = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[9254, 48])).
% 5.77/5.71 tff(9256,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y0!60)))) = succ(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9255])).
% 5.77/5.71 tff(9257,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y0!60)))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9256, 14])).
% 5.77/5.71 tff(9258,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9257])).
% 5.77/5.71 tff(9259,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(Y0!60))))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9258, 33])).
% 5.77/5.71 tff(9260,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9259])).
% 5.77/5.71 tff(9261,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9260, 30])).
% 5.77/5.71 tff(9262,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9261])).
% 5.77/5.71 tff(9263,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9262, 39])).
% 5.77/5.71 tff(9264,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9263])).
% 5.77/5.71 tff(9265,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9264, 53])).
% 5.77/5.71 tff(9266,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9265])).
% 5.77/5.71 tff(9267,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9266, 45])).
% 5.77/5.71 tff(9268,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9267])).
% 5.77/5.71 tff(9269,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9268, 28])).
% 5.77/5.71 tff(9270,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9269])).
% 5.77/5.71 tff(9271,plain,
% 5.77/5.71 (NSY0!36 = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[141, 9270, 42])).
% 5.77/5.71 tff(9272,plain,
% 5.77/5.71 (pred(NSY0!36) = pred(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9271])).
% 5.77/5.71 tff(9273,plain,
% 5.77/5.71 (pred(NSY0!36) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9272, 22])).
% 5.77/5.71 tff(9274,plain,
% 5.77/5.71 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n10, n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9273, 9249])).
% 5.77/5.71 tff(9275,plain,
% 5.77/5.71 (sum(pred(NSY0!36), succ(NPY0!38)) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9274, 57])).
% 5.77/5.71 tff(9276,plain,
% 5.77/5.71 (sum(n8, n0) = n8),
% 5.77/5.71 inference(and_elim,[status(thm)],[9])).
% 5.77/5.71 tff(9277,plain,
% 5.77/5.71 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n8, n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[169, 9275])).
% 5.77/5.71 tff(9278,plain,
% 5.77/5.71 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9277, 9276])).
% 5.77/5.71 tff(9279,plain,
% 5.77/5.71 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n6, n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[194, 9278])).
% 5.77/5.71 tff(9280,plain,
% 5.77/5.71 (Y1!58 = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[196, 9279, 52])).
% 5.77/5.71 tff(9281,plain,
% 5.77/5.71 (pred(Y1!58) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9280])).
% 5.77/5.71 tff(9282,plain,
% 5.77/5.71 (pred(Y1!58) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9281, 25])).
% 5.77/5.71 tff(9283,plain,
% 5.77/5.71 (pred(pred(Y1!58)) = pred(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9282])).
% 5.77/5.71 tff(9284,plain,
% 5.77/5.71 (pred(pred(Y1!58)) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9283, 24])).
% 5.77/5.71 tff(9285,plain,
% 5.77/5.71 (pred(pred(pred(Y1!58))) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9284])).
% 5.77/5.71 tff(9286,plain,
% 5.77/5.71 (pred(pred(pred(Y1!58))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9285, 23])).
% 5.77/5.71 tff(9287,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y1!58)))) = pred(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9286])).
% 5.77/5.71 tff(9288,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y1!58)))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9287, 22])).
% 5.77/5.71 tff(9289,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9288])).
% 5.77/5.71 tff(9290,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y1!58))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9289, 21])).
% 5.77/5.71 tff(9291,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9290])).
% 5.77/5.71 tff(9292,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9291, 20])).
% 5.77/5.71 tff(9293,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9292])).
% 5.77/5.71 tff(9294,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9293, 19])).
% 5.77/5.71 tff(9295,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9294])).
% 5.77/5.71 tff(9296,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9295, 18])).
% 5.77/5.71 tff(9297,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9296])).
% 5.77/5.71 tff(9298,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9297, 17])).
% 5.77/5.71 tff(9299,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9298])).
% 5.77/5.71 tff(9300,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9299, 16])).
% 5.77/5.71 tff(9301,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9300])).
% 5.77/5.71 tff(9302,plain,
% 5.77/5.71 (NPY1!34 = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[232, 9301, 15])).
% 5.77/5.71 tff(9303,plain,
% 5.77/5.71 (succ(NPY1!34) = succ(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9302])).
% 5.77/5.71 tff(9304,plain,
% 5.77/5.71 (succ(NPY1!34) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9303, 14])).
% 5.77/5.71 tff(9305,plain,
% 5.77/5.71 (succ(Y1!58) = succ(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9280])).
% 5.77/5.71 tff(9306,plain,
% 5.77/5.71 (succ(Y1!58) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9305, 14])).
% 5.77/5.71 tff(9307,plain,
% 5.77/5.71 (succ(succ(Y1!58)) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9306])).
% 5.77/5.71 tff(9308,plain,
% 5.77/5.71 (succ(succ(Y1!58)) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9307, 33])).
% 5.77/5.71 tff(9309,plain,
% 5.77/5.71 (succ(succ(succ(Y1!58))) = succ(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9308])).
% 5.77/5.71 tff(9310,plain,
% 5.77/5.71 (succ(succ(succ(Y1!58))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9309, 30])).
% 5.77/5.71 tff(9311,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y1!58)))) = succ(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9310])).
% 5.77/5.71 tff(9312,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y1!58)))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9311, 39])).
% 5.77/5.71 tff(9313,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9312])).
% 5.77/5.71 tff(9314,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(Y1!58))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9313, 53])).
% 5.77/5.71 tff(9315,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9314])).
% 5.77/5.71 tff(9316,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9315, 45])).
% 5.77/5.71 tff(9317,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9316])).
% 5.77/5.71 tff(9318,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9317, 28])).
% 5.77/5.71 tff(9319,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9318])).
% 5.77/5.71 tff(9320,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9319, 42])).
% 5.77/5.71 tff(9321,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9320])).
% 5.77/5.71 tff(9322,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9321, 58])).
% 5.77/5.71 tff(9323,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9322])).
% 5.77/5.71 tff(9324,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9323, 36])).
% 5.77/5.71 tff(9325,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9324])).
% 5.77/5.71 tff(9326,plain,
% 5.77/5.71 (NSY1!32 = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[255, 9325, 48])).
% 5.77/5.71 tff(9327,plain,
% 5.77/5.71 (pred(NSY1!32) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9326])).
% 5.77/5.71 tff(9328,plain,
% 5.77/5.71 (pred(NSY1!32) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9327, 25])).
% 5.77/5.71 tff(9329,plain,
% 5.77/5.71 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n2, n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9328, 9304])).
% 5.77/5.71 tff(9330,plain,
% 5.77/5.71 (sum(pred(NSY1!32), succ(NPY1!34)) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9329, 13])).
% 5.77/5.71 tff(9331,plain,
% 5.77/5.71 (sum(n10, n8) = n7),
% 5.77/5.71 inference(and_elim,[status(thm)],[9])).
% 5.77/5.71 tff(9332,plain,
% 5.77/5.71 (sum(pred(Y0!60), succ(X0!61)) = sum(n10, n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9227, 75])).
% 5.77/5.71 tff(9333,plain,
% 5.77/5.71 (sum(pred(Y0!60), succ(X0!61)) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9332, 9331])).
% 5.77/5.71 tff(9334,plain,
% 5.77/5.71 (sum(pred(X0!61), succ(Y0!60)) = sum(n6, n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[89, 9251])).
% 5.77/5.71 tff(9335,plain,
% 5.77/5.71 (sum(pred(X0!61), succ(Y0!60)) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9334, 7901])).
% 5.77/5.71 tff(9336,plain,
% 5.77/5.71 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n7, n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9335, 9333])).
% 5.77/5.71 tff(9337,plain,
% 5.77/5.71 (X1!59 = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[93, 9336, 26])).
% 5.77/5.71 tff(9338,plain,
% 5.77/5.71 (pred(X1!59) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9337])).
% 5.77/5.71 tff(9339,plain,
% 5.77/5.71 (pred(X1!59) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9338, 25])).
% 5.77/5.71 tff(9340,plain,
% 5.77/5.71 (pred(pred(X1!59)) = pred(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9339])).
% 5.77/5.71 tff(9341,plain,
% 5.77/5.71 (pred(pred(X1!59)) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9340, 24])).
% 5.77/5.71 tff(9342,plain,
% 5.77/5.71 (pred(pred(pred(X1!59))) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9341])).
% 5.77/5.71 tff(9343,plain,
% 5.77/5.71 (pred(pred(pred(X1!59))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9342, 23])).
% 5.77/5.71 tff(9344,plain,
% 5.77/5.71 (pred(pred(pred(pred(X1!59)))) = pred(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9343])).
% 5.77/5.71 tff(9345,plain,
% 5.77/5.71 (pred(pred(pred(pred(X1!59)))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9344, 22])).
% 5.77/5.71 tff(9346,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(X1!59))))) = pred(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9345])).
% 5.77/5.71 tff(9347,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(X1!59))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9346, 21])).
% 5.77/5.71 tff(9348,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9347])).
% 5.77/5.71 tff(9349,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9348, 20])).
% 5.77/5.71 tff(9350,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9349])).
% 5.77/5.71 tff(9351,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9350, 19])).
% 5.77/5.71 tff(9352,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9351])).
% 5.77/5.71 tff(9353,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9352, 18])).
% 5.77/5.71 tff(9354,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9353])).
% 5.77/5.71 tff(9355,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9354, 17])).
% 5.77/5.71 tff(9356,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9355])).
% 5.77/5.71 tff(9357,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9356, 16])).
% 5.77/5.71 tff(9358,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9357])).
% 5.77/5.71 tff(9359,plain,
% 5.77/5.71 (NPX1!35 = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[280, 9358, 15])).
% 5.77/5.71 tff(9360,plain,
% 5.77/5.71 (succ(NPX1!35) = succ(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9359])).
% 5.77/5.71 tff(9361,plain,
% 5.77/5.71 (succ(NPX1!35) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9360, 14])).
% 5.77/5.71 tff(9362,plain,
% 5.77/5.71 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n4, n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9361, 9330])).
% 5.77/5.71 tff(9363,plain,
% 5.77/5.71 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9362, 12])).
% 5.77/5.71 tff(9364,plain,
% 5.77/5.71 (succ(X1!59) = succ(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9337])).
% 5.77/5.71 tff(9365,plain,
% 5.77/5.71 (succ(X1!59) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9364, 14])).
% 5.77/5.71 tff(9366,plain,
% 5.77/5.71 (succ(succ(X1!59)) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9365])).
% 5.77/5.71 tff(9367,plain,
% 5.77/5.71 (succ(succ(X1!59)) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9366, 33])).
% 5.77/5.71 tff(9368,plain,
% 5.77/5.71 (succ(succ(succ(X1!59))) = succ(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9367])).
% 5.77/5.71 tff(9369,plain,
% 5.77/5.71 (succ(succ(succ(X1!59))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9368, 30])).
% 5.77/5.71 tff(9370,plain,
% 5.77/5.71 (succ(succ(succ(succ(X1!59)))) = succ(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9369])).
% 5.77/5.71 tff(9371,plain,
% 5.77/5.71 (succ(succ(succ(succ(X1!59)))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9370, 39])).
% 5.77/5.71 tff(9372,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(X1!59))))) = succ(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9371])).
% 5.77/5.71 tff(9373,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(X1!59))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9372, 53])).
% 5.77/5.71 tff(9374,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9373])).
% 5.77/5.71 tff(9375,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9374, 45])).
% 5.77/5.71 tff(9376,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9375])).
% 5.77/5.71 tff(9377,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9376, 28])).
% 5.77/5.71 tff(9378,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9377])).
% 5.77/5.71 tff(9379,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9378, 42])).
% 5.77/5.71 tff(9380,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9379])).
% 5.77/5.71 tff(9381,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9380, 58])).
% 5.77/5.71 tff(9382,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9381])).
% 5.77/5.71 tff(9383,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9382, 36])).
% 5.77/5.71 tff(9384,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9383])).
% 5.77/5.71 tff(9385,plain,
% 5.77/5.71 (NSX1!33 = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[305, 9384, 48])).
% 5.77/5.71 tff(9386,plain,
% 5.77/5.71 (pred(NSX1!33) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9385])).
% 5.77/5.71 tff(9387,plain,
% 5.77/5.71 (pred(NSX1!33) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9386, 25])).
% 5.77/5.71 tff(9388,plain,
% 5.77/5.71 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n2, n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9387, 9363])).
% 5.77/5.71 tff(9389,plain,
% 5.77/5.71 (Y2!56 = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[310, 9388, 327])).
% 5.77/5.71 tff(9390,plain,
% 5.77/5.71 (pred(Y2!56) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9389])).
% 5.77/5.71 tff(9391,plain,
% 5.77/5.71 (pred(Y2!56) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9390, 23])).
% 5.77/5.71 tff(9392,plain,
% 5.77/5.71 (pred(pred(Y2!56)) = pred(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9391])).
% 5.77/5.71 tff(9393,plain,
% 5.77/5.71 (pred(pred(Y2!56)) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9392, 22])).
% 5.77/5.71 tff(9394,plain,
% 5.77/5.71 (pred(pred(pred(Y2!56))) = pred(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9393])).
% 5.77/5.71 tff(9395,plain,
% 5.77/5.71 (pred(pred(pred(Y2!56))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9394, 21])).
% 5.77/5.71 tff(9396,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y2!56)))) = pred(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9395])).
% 5.77/5.71 tff(9397,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y2!56)))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9396, 20])).
% 5.77/5.71 tff(9398,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9397])).
% 5.77/5.71 tff(9399,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y2!56))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9398, 19])).
% 5.77/5.71 tff(9400,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9399])).
% 5.77/5.71 tff(9401,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9400, 18])).
% 5.77/5.71 tff(9402,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9401])).
% 5.77/5.71 tff(9403,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9402, 17])).
% 5.77/5.71 tff(9404,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9403])).
% 5.77/5.71 tff(9405,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9404, 16])).
% 5.77/5.71 tff(9406,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9405])).
% 5.77/5.71 tff(9407,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[9406, 15])).
% 5.77/5.71 tff(9408,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9407])).
% 5.77/5.71 tff(9409,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9408, 25])).
% 5.77/5.71 tff(9410,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9409])).
% 5.77/5.71 tff(9411,plain,
% 5.77/5.71 (NPY2!30 = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[347, 9410, 24])).
% 5.77/5.71 tff(9412,plain,
% 5.77/5.71 (succ(NPY2!30) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9411])).
% 5.77/5.71 tff(9413,plain,
% 5.77/5.71 (succ(NPY2!30) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9412, 36])).
% 5.77/5.71 tff(9414,plain,
% 5.77/5.71 (succ(Y2!56) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9389])).
% 5.77/5.71 tff(9415,plain,
% 5.77/5.71 (succ(Y2!56) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9414, 36])).
% 5.77/5.71 tff(9416,plain,
% 5.77/5.71 (succ(succ(Y2!56)) = succ(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9415])).
% 5.77/5.71 tff(9417,plain,
% 5.77/5.71 (succ(succ(Y2!56)) = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[9416, 48])).
% 5.77/5.71 tff(9418,plain,
% 5.77/5.71 (succ(succ(succ(Y2!56))) = succ(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9417])).
% 5.77/5.71 tff(9419,plain,
% 5.77/5.71 (succ(succ(succ(Y2!56))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9418, 14])).
% 5.77/5.71 tff(9420,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y2!56)))) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9419])).
% 5.77/5.71 tff(9421,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y2!56)))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9420, 33])).
% 5.77/5.71 tff(9422,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9421])).
% 5.77/5.71 tff(9423,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(Y2!56))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9422, 30])).
% 5.77/5.71 tff(9424,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9423])).
% 5.77/5.71 tff(9425,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9424, 39])).
% 5.77/5.71 tff(9426,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9425])).
% 5.77/5.71 tff(9427,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9426, 53])).
% 5.77/5.71 tff(9428,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9427])).
% 5.77/5.71 tff(9429,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9428, 45])).
% 5.77/5.71 tff(9430,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9429])).
% 5.77/5.71 tff(9431,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9430, 28])).
% 5.77/5.71 tff(9432,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9431])).
% 5.77/5.71 tff(9433,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9432, 42])).
% 5.77/5.71 tff(9434,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9433])).
% 5.77/5.71 tff(9435,plain,
% 5.77/5.71 (NSY2!28 = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[370, 9434, 58])).
% 5.77/5.71 tff(9436,plain,
% 5.77/5.71 (pred(NSY2!28) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9435])).
% 5.77/5.71 tff(9437,plain,
% 5.77/5.71 (pred(NSY2!28) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9436, 23])).
% 5.77/5.71 tff(9438,plain,
% 5.77/5.71 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n0, n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9437, 9413])).
% 5.77/5.71 tff(9439,plain,
% 5.77/5.71 (sum(pred(NSY2!28), succ(NPY2!30)) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9438, 35])).
% 5.77/5.71 tff(9440,plain,
% 5.77/5.71 (sum(pred(Y1!58), succ(X1!59)) = sum(n2, n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9282, 9365])).
% 5.77/5.71 tff(9441,plain,
% 5.77/5.71 (sum(pred(Y1!58), succ(X1!59)) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9440, 13])).
% 5.77/5.71 tff(9442,plain,
% 5.77/5.71 (sum(pred(X1!59), succ(Y1!58)) = sum(n2, n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9339, 9306])).
% 5.77/5.71 tff(9443,plain,
% 5.77/5.71 (sum(pred(X1!59), succ(Y1!58)) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9442, 13])).
% 5.77/5.71 tff(9444,plain,
% 5.77/5.71 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n6, n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9443, 9441])).
% 5.77/5.71 tff(9445,plain,
% 5.77/5.71 (X2!57 = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[209, 9444, 37])).
% 5.77/5.71 tff(9446,plain,
% 5.77/5.71 (pred(X2!57) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9445])).
% 5.77/5.71 tff(9447,plain,
% 5.77/5.71 (pred(X2!57) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9446, 23])).
% 5.77/5.71 tff(9448,plain,
% 5.77/5.71 (pred(pred(X2!57)) = pred(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9447])).
% 5.77/5.71 tff(9449,plain,
% 5.77/5.71 (pred(pred(X2!57)) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9448, 22])).
% 5.77/5.71 tff(9450,plain,
% 5.77/5.71 (pred(pred(pred(X2!57))) = pred(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9449])).
% 5.77/5.71 tff(9451,plain,
% 5.77/5.71 (pred(pred(pred(X2!57))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9450, 21])).
% 5.77/5.71 tff(9452,plain,
% 5.77/5.71 (pred(pred(pred(pred(X2!57)))) = pred(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9451])).
% 5.77/5.71 tff(9453,plain,
% 5.77/5.71 (pred(pred(pred(pred(X2!57)))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9452, 20])).
% 5.77/5.71 tff(9454,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(X2!57))))) = pred(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9453])).
% 5.77/5.71 tff(9455,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(X2!57))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9454, 19])).
% 5.77/5.71 tff(9456,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9455])).
% 5.77/5.71 tff(9457,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9456, 18])).
% 5.77/5.71 tff(9458,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9457])).
% 5.77/5.71 tff(9459,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9458, 17])).
% 5.77/5.71 tff(9460,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9459])).
% 5.77/5.71 tff(9461,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9460, 16])).
% 5.77/5.71 tff(9462,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9461])).
% 5.77/5.71 tff(9463,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[9462, 15])).
% 5.77/5.71 tff(9464,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9463])).
% 5.77/5.71 tff(9465,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9464, 25])).
% 5.77/5.71 tff(9466,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9465])).
% 5.77/5.71 tff(9467,plain,
% 5.77/5.71 (NPX2!31 = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[395, 9466, 24])).
% 5.77/5.71 tff(9468,plain,
% 5.77/5.71 (succ(NPX2!31) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9467])).
% 5.77/5.71 tff(9469,plain,
% 5.77/5.71 (succ(NPX2!31) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9468, 36])).
% 5.77/5.71 tff(9470,plain,
% 5.77/5.71 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n2, n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9469, 9439])).
% 5.77/5.71 tff(9471,plain,
% 5.77/5.71 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9470, 34])).
% 5.77/5.71 tff(9472,plain,
% 5.77/5.71 (succ(X2!57) = succ(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9445])).
% 5.77/5.71 tff(9473,plain,
% 5.77/5.71 (succ(X2!57) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9472, 36])).
% 5.77/5.71 tff(9474,plain,
% 5.77/5.71 (succ(succ(X2!57)) = succ(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9473])).
% 5.77/5.71 tff(9475,plain,
% 5.77/5.71 (succ(succ(X2!57)) = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[9474, 48])).
% 5.77/5.71 tff(9476,plain,
% 5.77/5.71 (succ(succ(succ(X2!57))) = succ(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9475])).
% 5.77/5.71 tff(9477,plain,
% 5.77/5.71 (succ(succ(succ(X2!57))) = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[9476, 14])).
% 5.77/5.71 tff(9478,plain,
% 5.77/5.71 (succ(succ(succ(succ(X2!57)))) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9477])).
% 5.77/5.71 tff(9479,plain,
% 5.77/5.71 (succ(succ(succ(succ(X2!57)))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9478, 33])).
% 5.77/5.71 tff(9480,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(X2!57))))) = succ(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9479])).
% 5.77/5.71 tff(9481,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(X2!57))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9480, 30])).
% 5.77/5.71 tff(9482,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9481])).
% 5.77/5.71 tff(9483,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9482, 39])).
% 5.77/5.71 tff(9484,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9483])).
% 5.77/5.71 tff(9485,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9484, 53])).
% 5.77/5.71 tff(9486,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9485])).
% 5.77/5.71 tff(9487,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9486, 45])).
% 5.77/5.71 tff(9488,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9487])).
% 5.77/5.71 tff(9489,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9488, 28])).
% 5.77/5.71 tff(9490,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9489])).
% 5.77/5.71 tff(9491,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9490, 42])).
% 5.77/5.71 tff(9492,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9491])).
% 5.77/5.71 tff(9493,plain,
% 5.77/5.71 (NSX2!29 = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[420, 9492, 58])).
% 5.77/5.71 tff(9494,plain,
% 5.77/5.71 (pred(NSX2!29) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9493])).
% 5.77/5.71 tff(9495,plain,
% 5.77/5.71 (pred(NSX2!29) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9494, 23])).
% 5.77/5.71 tff(9496,plain,
% 5.77/5.71 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n0, n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9495, 9471])).
% 5.77/5.71 tff(9497,plain,
% 5.77/5.71 (Y3!54 = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[425, 9496, 442])).
% 5.77/5.71 tff(9498,plain,
% 5.77/5.71 (pred(Y3!54) = pred(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9497])).
% 5.77/5.71 tff(9499,plain,
% 5.77/5.71 (pred(Y3!54) = n3),
% 5.77/5.71 inference(transitivity,[status(thm)],[9498, 15])).
% 5.77/5.71 tff(9500,plain,
% 5.77/5.71 (pred(pred(Y3!54)) = pred(n3)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9499])).
% 5.77/5.71 tff(9501,plain,
% 5.77/5.71 (pred(pred(Y3!54)) = n2),
% 5.77/5.71 inference(transitivity,[status(thm)],[9500, 25])).
% 5.77/5.71 tff(9502,plain,
% 5.77/5.71 (pred(pred(pred(Y3!54))) = pred(n2)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9501])).
% 5.77/5.71 tff(9503,plain,
% 5.77/5.71 (pred(pred(pred(Y3!54))) = n1),
% 5.77/5.71 inference(transitivity,[status(thm)],[9502, 24])).
% 5.77/5.71 tff(9504,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y3!54)))) = pred(n1)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9503])).
% 5.77/5.71 tff(9505,plain,
% 5.77/5.71 (pred(pred(pred(pred(Y3!54)))) = n0),
% 5.77/5.71 inference(transitivity,[status(thm)],[9504, 23])).
% 5.77/5.71 tff(9506,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n0)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9505])).
% 5.77/5.71 tff(9507,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(Y3!54))))) = n10),
% 5.77/5.71 inference(transitivity,[status(thm)],[9506, 22])).
% 5.77/5.71 tff(9508,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n10)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9507])).
% 5.77/5.71 tff(9509,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n9),
% 5.77/5.71 inference(transitivity,[status(thm)],[9508, 21])).
% 5.77/5.71 tff(9510,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n9)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9509])).
% 5.77/5.71 tff(9511,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9510, 20])).
% 5.77/5.71 tff(9512,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n8)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9511])).
% 5.77/5.71 tff(9513,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9512, 19])).
% 5.77/5.71 tff(9514,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9513])).
% 5.77/5.71 tff(9515,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9514, 18])).
% 5.77/5.71 tff(9516,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9515])).
% 5.77/5.71 tff(9517,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9516, 17])).
% 5.77/5.71 tff(9518,plain,
% 5.77/5.71 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9517])).
% 5.77/5.71 tff(9519,plain,
% 5.77/5.71 (NPY3!26 = n4),
% 5.77/5.71 inference(transitivity,[status(thm)],[462, 9518, 16])).
% 5.77/5.71 tff(9520,plain,
% 5.77/5.71 (succ(NPY3!26) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9519])).
% 5.77/5.71 tff(9521,plain,
% 5.77/5.71 (succ(NPY3!26) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9520, 33])).
% 5.77/5.71 tff(9522,plain,
% 5.77/5.71 (succ(Y3!54) = succ(n4)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9497])).
% 5.77/5.71 tff(9523,plain,
% 5.77/5.71 (succ(Y3!54) = n5),
% 5.77/5.71 inference(transitivity,[status(thm)],[9522, 33])).
% 5.77/5.71 tff(9524,plain,
% 5.77/5.71 (succ(succ(Y3!54)) = succ(n5)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9523])).
% 5.77/5.71 tff(9525,plain,
% 5.77/5.71 (succ(succ(Y3!54)) = n6),
% 5.77/5.71 inference(transitivity,[status(thm)],[9524, 30])).
% 5.77/5.71 tff(9526,plain,
% 5.77/5.71 (succ(succ(succ(Y3!54))) = succ(n6)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9525])).
% 5.77/5.71 tff(9527,plain,
% 5.77/5.71 (succ(succ(succ(Y3!54))) = n7),
% 5.77/5.71 inference(transitivity,[status(thm)],[9526, 39])).
% 5.77/5.71 tff(9528,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y3!54)))) = succ(n7)),
% 5.77/5.71 inference(monotonicity,[status(thm)],[9527])).
% 5.77/5.71 tff(9529,plain,
% 5.77/5.71 (succ(succ(succ(succ(Y3!54)))) = n8),
% 5.77/5.71 inference(transitivity,[status(thm)],[9528, 53])).
% 5.77/5.71 tff(9530,plain,
% 5.77/5.71 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9529])).
% 5.77/5.72 tff(9531,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(Y3!54))))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9530, 45])).
% 5.77/5.72 tff(9532,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9531])).
% 5.77/5.72 tff(9533,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9532, 28])).
% 5.77/5.72 tff(9534,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9533])).
% 5.77/5.72 tff(9535,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9534, 42])).
% 5.77/5.72 tff(9536,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9535])).
% 5.77/5.72 tff(9537,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9536, 58])).
% 5.77/5.72 tff(9538,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9537])).
% 5.77/5.72 tff(9539,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9538, 36])).
% 5.77/5.72 tff(9540,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9539])).
% 5.77/5.72 tff(9541,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9540, 48])).
% 5.77/5.72 tff(9542,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9541])).
% 5.77/5.72 tff(9543,plain,
% 5.77/5.72 (NSY3!24 = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[485, 9542, 14])).
% 5.77/5.72 tff(9544,plain,
% 5.77/5.72 (pred(NSY3!24) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9543])).
% 5.77/5.72 tff(9545,plain,
% 5.77/5.72 (pred(NSY3!24) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9544, 15])).
% 5.77/5.72 tff(9546,plain,
% 5.77/5.72 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n3, n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9545, 9521])).
% 5.77/5.72 tff(9547,plain,
% 5.77/5.72 (sum(pred(NSY3!24), succ(NPY3!26)) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9546, 32])).
% 5.77/5.72 tff(9548,plain,
% 5.77/5.72 (sum(pred(Y2!56), succ(X2!57)) = sum(n0, n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9391, 9473])).
% 5.77/5.72 tff(9549,plain,
% 5.77/5.72 (sum(pred(Y2!56), succ(X2!57)) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9548, 35])).
% 5.77/5.72 tff(9550,plain,
% 5.77/5.72 (sum(pred(X2!57), succ(Y2!56)) = sum(n0, n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9447, 9415])).
% 5.77/5.72 tff(9551,plain,
% 5.77/5.72 (sum(pred(X2!57), succ(Y2!56)) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9550, 35])).
% 5.77/5.72 tff(9552,plain,
% 5.77/5.72 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n2, n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9551, 9549])).
% 5.77/5.72 tff(9553,plain,
% 5.77/5.72 (X3!55 = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[323, 9552, 34])).
% 5.77/5.72 tff(9554,plain,
% 5.77/5.72 (pred(X3!55) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9553])).
% 5.77/5.72 tff(9555,plain,
% 5.77/5.72 (pred(X3!55) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9554, 15])).
% 5.77/5.72 tff(9556,plain,
% 5.77/5.72 (pred(pred(X3!55)) = pred(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9555])).
% 5.77/5.72 tff(9557,plain,
% 5.77/5.72 (pred(pred(X3!55)) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9556, 25])).
% 5.77/5.72 tff(9558,plain,
% 5.77/5.72 (pred(pred(pred(X3!55))) = pred(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9557])).
% 5.77/5.72 tff(9559,plain,
% 5.77/5.72 (pred(pred(pred(X3!55))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9558, 24])).
% 5.77/5.72 tff(9560,plain,
% 5.77/5.72 (pred(pred(pred(pred(X3!55)))) = pred(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9559])).
% 5.77/5.72 tff(9561,plain,
% 5.77/5.72 (pred(pred(pred(pred(X3!55)))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9560, 23])).
% 5.77/5.72 tff(9562,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(X3!55))))) = pred(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9561])).
% 5.77/5.72 tff(9563,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(X3!55))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9562, 22])).
% 5.77/5.72 tff(9564,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9563])).
% 5.77/5.72 tff(9565,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9564, 21])).
% 5.77/5.72 tff(9566,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9565])).
% 5.77/5.72 tff(9567,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9566, 20])).
% 5.77/5.72 tff(9568,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9567])).
% 5.77/5.72 tff(9569,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9568, 19])).
% 5.77/5.72 tff(9570,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9569])).
% 5.77/5.72 tff(9571,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9570, 18])).
% 5.77/5.72 tff(9572,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9571])).
% 5.77/5.72 tff(9573,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9572, 17])).
% 5.77/5.72 tff(9574,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9573])).
% 5.77/5.72 tff(9575,plain,
% 5.77/5.72 (NPX3!27 = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[510, 9574, 16])).
% 5.77/5.72 tff(9576,plain,
% 5.77/5.72 (succ(NPX3!27) = succ(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9575])).
% 5.77/5.72 tff(9577,plain,
% 5.77/5.72 (succ(NPX3!27) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9576, 33])).
% 5.77/5.72 tff(9578,plain,
% 5.77/5.72 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n5, n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9577, 9547])).
% 5.77/5.72 tff(9579,plain,
% 5.77/5.72 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9578, 558])).
% 5.77/5.72 tff(9580,plain,
% 5.77/5.72 (succ(X3!55) = succ(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9553])).
% 5.77/5.72 tff(9581,plain,
% 5.77/5.72 (succ(X3!55) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9580, 33])).
% 5.77/5.72 tff(9582,plain,
% 5.77/5.72 (succ(succ(X3!55)) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9581])).
% 5.77/5.72 tff(9583,plain,
% 5.77/5.72 (succ(succ(X3!55)) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9582, 30])).
% 5.77/5.72 tff(9584,plain,
% 5.77/5.72 (succ(succ(succ(X3!55))) = succ(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9583])).
% 5.77/5.72 tff(9585,plain,
% 5.77/5.72 (succ(succ(succ(X3!55))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9584, 39])).
% 5.77/5.72 tff(9586,plain,
% 5.77/5.72 (succ(succ(succ(succ(X3!55)))) = succ(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9585])).
% 5.77/5.72 tff(9587,plain,
% 5.77/5.72 (succ(succ(succ(succ(X3!55)))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9586, 53])).
% 5.77/5.72 tff(9588,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(X3!55))))) = succ(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9587])).
% 5.77/5.72 tff(9589,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(X3!55))))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9588, 45])).
% 5.77/5.72 tff(9590,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9589])).
% 5.77/5.72 tff(9591,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9590, 28])).
% 5.77/5.72 tff(9592,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9591])).
% 5.77/5.72 tff(9593,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9592, 42])).
% 5.77/5.72 tff(9594,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9593])).
% 5.77/5.72 tff(9595,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9594, 58])).
% 5.77/5.72 tff(9596,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9595])).
% 5.77/5.72 tff(9597,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9596, 36])).
% 5.77/5.72 tff(9598,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9597])).
% 5.77/5.72 tff(9599,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9598, 48])).
% 5.77/5.72 tff(9600,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9599])).
% 5.77/5.72 tff(9601,plain,
% 5.77/5.72 (NSX3!25 = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[535, 9600, 14])).
% 5.77/5.72 tff(9602,plain,
% 5.77/5.72 (pred(NSX3!25) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9601])).
% 5.77/5.72 tff(9603,plain,
% 5.77/5.72 (pred(NSX3!25) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9602, 15])).
% 5.77/5.72 tff(9604,plain,
% 5.77/5.72 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n3, n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9603, 9579])).
% 5.77/5.72 tff(9605,plain,
% 5.77/5.72 (Y4!52 = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[540, 9604, 557])).
% 5.77/5.72 tff(9606,plain,
% 5.77/5.72 (pred(Y4!52) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9605])).
% 5.77/5.72 tff(9607,plain,
% 5.77/5.72 (pred(Y4!52) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9606, 16])).
% 5.77/5.72 tff(9608,plain,
% 5.77/5.72 (pred(pred(Y4!52)) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9607])).
% 5.77/5.72 tff(9609,plain,
% 5.77/5.72 (pred(pred(Y4!52)) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9608, 15])).
% 5.77/5.72 tff(9610,plain,
% 5.77/5.72 (pred(pred(pred(Y4!52))) = pred(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9609])).
% 5.77/5.72 tff(9611,plain,
% 5.77/5.72 (pred(pred(pred(Y4!52))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9610, 25])).
% 5.77/5.72 tff(9612,plain,
% 5.77/5.72 (pred(pred(pred(pred(Y4!52)))) = pred(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9611])).
% 5.77/5.72 tff(9613,plain,
% 5.77/5.72 (pred(pred(pred(pred(Y4!52)))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9612, 24])).
% 5.77/5.72 tff(9614,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9613])).
% 5.77/5.72 tff(9615,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(Y4!52))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9614, 23])).
% 5.77/5.72 tff(9616,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9615])).
% 5.77/5.72 tff(9617,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9616, 22])).
% 5.77/5.72 tff(9618,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9617])).
% 5.77/5.72 tff(9619,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9618, 21])).
% 5.77/5.72 tff(9620,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9619])).
% 5.77/5.72 tff(9621,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9620, 20])).
% 5.77/5.72 tff(9622,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9621])).
% 5.77/5.72 tff(9623,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9622, 19])).
% 5.77/5.72 tff(9624,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9623])).
% 5.77/5.72 tff(9625,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9624, 18])).
% 5.77/5.72 tff(9626,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9625])).
% 5.77/5.72 tff(9627,plain,
% 5.77/5.72 (NPY4!22 = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[578, 9626, 17])).
% 5.77/5.72 tff(9628,plain,
% 5.77/5.72 (succ(NPY4!22) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9627])).
% 5.77/5.72 tff(9629,plain,
% 5.77/5.72 (succ(NPY4!22) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9628, 30])).
% 5.77/5.72 tff(9630,plain,
% 5.77/5.72 (succ(Y4!52) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9605])).
% 5.77/5.72 tff(9631,plain,
% 5.77/5.72 (succ(Y4!52) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9630, 30])).
% 5.77/5.72 tff(9632,plain,
% 5.77/5.72 (succ(succ(Y4!52)) = succ(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9631])).
% 5.77/5.72 tff(9633,plain,
% 5.77/5.72 (succ(succ(Y4!52)) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9632, 39])).
% 5.77/5.72 tff(9634,plain,
% 5.77/5.72 (succ(succ(succ(Y4!52))) = succ(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9633])).
% 5.77/5.72 tff(9635,plain,
% 5.77/5.72 (succ(succ(succ(Y4!52))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9634, 53])).
% 5.77/5.72 tff(9636,plain,
% 5.77/5.72 (succ(succ(succ(succ(Y4!52)))) = succ(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9635])).
% 5.77/5.72 tff(9637,plain,
% 5.77/5.72 (succ(succ(succ(succ(Y4!52)))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9636, 45])).
% 5.77/5.72 tff(9638,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9637])).
% 5.77/5.72 tff(9639,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(Y4!52))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9638, 28])).
% 5.77/5.72 tff(9640,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9639])).
% 5.77/5.72 tff(9641,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9640, 42])).
% 5.77/5.72 tff(9642,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9641])).
% 5.77/5.72 tff(9643,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9642, 58])).
% 5.77/5.72 tff(9644,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9643])).
% 5.77/5.72 tff(9645,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9644, 36])).
% 5.77/5.72 tff(9646,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9645])).
% 5.77/5.72 tff(9647,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9646, 48])).
% 5.77/5.72 tff(9648,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9647])).
% 5.77/5.72 tff(9649,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9648, 14])).
% 5.77/5.72 tff(9650,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9649])).
% 5.77/5.72 tff(9651,plain,
% 5.77/5.72 (NSY4!20 = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[601, 9650, 33])).
% 5.77/5.72 tff(9652,plain,
% 5.77/5.72 (pred(NSY4!20) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9651])).
% 5.77/5.72 tff(9653,plain,
% 5.77/5.72 (pred(NSY4!20) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9652, 16])).
% 5.77/5.72 tff(9654,plain,
% 5.77/5.72 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n4, n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9653, 9629])).
% 5.77/5.72 tff(9655,plain,
% 5.77/5.72 (sum(pred(NSY4!20), succ(NPY4!22)) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9654, 12])).
% 5.77/5.72 tff(9656,plain,
% 5.77/5.72 (sum(pred(Y3!54), succ(X3!55)) = sum(n3, n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9499, 9581])).
% 5.77/5.72 tff(9657,plain,
% 5.77/5.72 (sum(pred(Y3!54), succ(X3!55)) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9656, 32])).
% 5.77/5.72 tff(9658,plain,
% 5.77/5.72 (sum(pred(X3!55), succ(Y3!54)) = sum(n3, n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9555, 9523])).
% 5.77/5.72 tff(9659,plain,
% 5.77/5.72 (sum(pred(X3!55), succ(Y3!54)) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9658, 32])).
% 5.77/5.72 tff(9660,plain,
% 5.77/5.72 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n8, n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9659, 9657])).
% 5.77/5.72 tff(9661,plain,
% 5.77/5.72 (X4!53 = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[438, 9660, 31])).
% 5.77/5.72 tff(9662,plain,
% 5.77/5.72 (pred(X4!53) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9661])).
% 5.77/5.72 tff(9663,plain,
% 5.77/5.72 (pred(X4!53) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9662, 16])).
% 5.77/5.72 tff(9664,plain,
% 5.77/5.72 (pred(pred(X4!53)) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9663])).
% 5.77/5.72 tff(9665,plain,
% 5.77/5.72 (pred(pred(X4!53)) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9664, 15])).
% 5.77/5.72 tff(9666,plain,
% 5.77/5.72 (pred(pred(pred(X4!53))) = pred(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9665])).
% 5.77/5.72 tff(9667,plain,
% 5.77/5.72 (pred(pred(pred(X4!53))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9666, 25])).
% 5.77/5.72 tff(9668,plain,
% 5.77/5.72 (pred(pred(pred(pred(X4!53)))) = pred(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9667])).
% 5.77/5.72 tff(9669,plain,
% 5.77/5.72 (pred(pred(pred(pred(X4!53)))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9668, 24])).
% 5.77/5.72 tff(9670,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(X4!53))))) = pred(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9669])).
% 5.77/5.72 tff(9671,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(X4!53))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9670, 23])).
% 5.77/5.72 tff(9672,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9671])).
% 5.77/5.72 tff(9673,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9672, 22])).
% 5.77/5.72 tff(9674,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9673])).
% 5.77/5.72 tff(9675,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9674, 21])).
% 5.77/5.72 tff(9676,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9675])).
% 5.77/5.72 tff(9677,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9676, 20])).
% 5.77/5.72 tff(9678,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9677])).
% 5.77/5.72 tff(9679,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9678, 19])).
% 5.77/5.72 tff(9680,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9679])).
% 5.77/5.72 tff(9681,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9680, 18])).
% 5.77/5.72 tff(9682,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9681])).
% 5.77/5.72 tff(9683,plain,
% 5.77/5.72 (NPX4!23 = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[626, 9682, 17])).
% 5.77/5.72 tff(9684,plain,
% 5.77/5.72 (succ(NPX4!23) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9683])).
% 5.77/5.72 tff(9685,plain,
% 5.77/5.72 (succ(NPX4!23) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9684, 30])).
% 5.77/5.72 tff(9686,plain,
% 5.77/5.72 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n6, n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9685, 9655])).
% 5.77/5.72 tff(9687,plain,
% 5.77/5.72 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9686, 674])).
% 5.77/5.72 tff(9688,plain,
% 5.77/5.72 (succ(X4!53) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9661])).
% 5.77/5.72 tff(9689,plain,
% 5.77/5.72 (succ(X4!53) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9688, 30])).
% 5.77/5.72 tff(9690,plain,
% 5.77/5.72 (succ(succ(X4!53)) = succ(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9689])).
% 5.77/5.72 tff(9691,plain,
% 5.77/5.72 (succ(succ(X4!53)) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9690, 39])).
% 5.77/5.72 tff(9692,plain,
% 5.77/5.72 (succ(succ(succ(X4!53))) = succ(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9691])).
% 5.77/5.72 tff(9693,plain,
% 5.77/5.72 (succ(succ(succ(X4!53))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9692, 53])).
% 5.77/5.72 tff(9694,plain,
% 5.77/5.72 (succ(succ(succ(succ(X4!53)))) = succ(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9693])).
% 5.77/5.72 tff(9695,plain,
% 5.77/5.72 (succ(succ(succ(succ(X4!53)))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9694, 45])).
% 5.77/5.72 tff(9696,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(X4!53))))) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9695])).
% 5.77/5.72 tff(9697,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(X4!53))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9696, 28])).
% 5.77/5.72 tff(9698,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9697])).
% 5.77/5.72 tff(9699,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9698, 42])).
% 5.77/5.72 tff(9700,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9699])).
% 5.77/5.72 tff(9701,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9700, 58])).
% 5.77/5.72 tff(9702,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9701])).
% 5.77/5.72 tff(9703,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9702, 36])).
% 5.77/5.72 tff(9704,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9703])).
% 5.77/5.72 tff(9705,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9704, 48])).
% 5.77/5.72 tff(9706,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9705])).
% 5.77/5.72 tff(9707,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9706, 14])).
% 5.77/5.72 tff(9708,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9707])).
% 5.77/5.72 tff(9709,plain,
% 5.77/5.72 (NSX4!21 = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[651, 9708, 33])).
% 5.77/5.72 tff(9710,plain,
% 5.77/5.72 (pred(NSX4!21) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9709])).
% 5.77/5.72 tff(9711,plain,
% 5.77/5.72 (pred(NSX4!21) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9710, 16])).
% 5.77/5.72 tff(9712,plain,
% 5.77/5.72 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n4, n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9711, 9687])).
% 5.77/5.72 tff(9713,plain,
% 5.77/5.72 (Y5!50 = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[656, 9712, 673])).
% 5.77/5.72 tff(9714,plain,
% 5.77/5.72 (pred(Y5!50) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9713])).
% 5.77/5.72 tff(9715,plain,
% 5.77/5.72 (pred(Y5!50) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9714, 20])).
% 5.77/5.72 tff(9716,plain,
% 5.77/5.72 (pred(pred(Y5!50)) = pred(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9715])).
% 5.77/5.72 tff(9717,plain,
% 5.77/5.72 (pred(pred(Y5!50)) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9716, 19])).
% 5.77/5.72 tff(9718,plain,
% 5.77/5.72 (pred(pred(pred(Y5!50))) = pred(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9717])).
% 5.77/5.72 tff(9719,plain,
% 5.77/5.72 (pred(pred(pred(Y5!50))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9718, 18])).
% 5.77/5.72 tff(9720,plain,
% 5.77/5.72 (pred(pred(pred(pred(Y5!50)))) = pred(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9719])).
% 5.77/5.72 tff(9721,plain,
% 5.77/5.72 (pred(pred(pred(pred(Y5!50)))) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9720, 17])).
% 5.77/5.72 tff(9722,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9721])).
% 5.77/5.72 tff(9723,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(Y5!50))))) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9722, 16])).
% 5.77/5.72 tff(9724,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9723])).
% 5.77/5.72 tff(9725,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9724, 15])).
% 5.77/5.72 tff(9726,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9725])).
% 5.77/5.72 tff(9727,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9726, 25])).
% 5.77/5.72 tff(9728,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9727])).
% 5.77/5.72 tff(9729,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9728, 24])).
% 5.77/5.72 tff(9730,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9729])).
% 5.77/5.72 tff(9731,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9730, 23])).
% 5.77/5.72 tff(9732,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9731])).
% 5.77/5.72 tff(9733,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9732, 22])).
% 5.77/5.72 tff(9734,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9733])).
% 5.77/5.72 tff(9735,plain,
% 5.77/5.72 (NPY5!18 = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[694, 9734, 21])).
% 5.77/5.72 tff(9736,plain,
% 5.77/5.72 (succ(NPY5!18) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9735])).
% 5.77/5.72 tff(9737,plain,
% 5.77/5.72 (succ(NPY5!18) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9736, 28])).
% 5.77/5.72 tff(9738,plain,
% 5.77/5.72 (succ(Y5!50) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9713])).
% 5.77/5.72 tff(9739,plain,
% 5.77/5.72 (succ(Y5!50) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9738, 28])).
% 5.77/5.72 tff(9740,plain,
% 5.77/5.72 (succ(succ(Y5!50)) = succ(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9739])).
% 5.77/5.72 tff(9741,plain,
% 5.77/5.72 (succ(succ(Y5!50)) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9740, 42])).
% 5.77/5.72 tff(9742,plain,
% 5.77/5.72 (succ(succ(succ(Y5!50))) = succ(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9741])).
% 5.77/5.72 tff(9743,plain,
% 5.77/5.72 (succ(succ(succ(Y5!50))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9742, 58])).
% 5.77/5.72 tff(9744,plain,
% 5.77/5.72 (succ(succ(succ(succ(Y5!50)))) = succ(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9743])).
% 5.77/5.72 tff(9745,plain,
% 5.77/5.72 (succ(succ(succ(succ(Y5!50)))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9744, 36])).
% 5.77/5.72 tff(9746,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9745])).
% 5.77/5.72 tff(9747,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(Y5!50))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9746, 48])).
% 5.77/5.72 tff(9748,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9747])).
% 5.77/5.72 tff(9749,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9748, 14])).
% 5.77/5.72 tff(9750,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9749])).
% 5.77/5.72 tff(9751,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9750, 33])).
% 5.77/5.72 tff(9752,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9751])).
% 5.77/5.72 tff(9753,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9752, 30])).
% 5.77/5.72 tff(9754,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9753])).
% 5.77/5.72 tff(9755,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9754, 39])).
% 5.77/5.72 tff(9756,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9755])).
% 5.77/5.72 tff(9757,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9756, 53])).
% 5.77/5.72 tff(9758,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9757])).
% 5.77/5.72 tff(9759,plain,
% 5.77/5.72 (NSY5!16 = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[717, 9758, 45])).
% 5.77/5.72 tff(9760,plain,
% 5.77/5.72 (pred(NSY5!16) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9759])).
% 5.77/5.72 tff(9761,plain,
% 5.77/5.72 (pred(NSY5!16) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9760, 20])).
% 5.77/5.72 tff(9762,plain,
% 5.77/5.72 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n8, n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9761, 9737])).
% 5.77/5.72 tff(9763,plain,
% 5.77/5.72 (sum(pred(NSY5!16), succ(NPY5!18)) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9762, 27])).
% 5.77/5.72 tff(9764,plain,
% 5.77/5.72 (sum(pred(Y4!52), succ(X4!53)) = sum(n4, n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9607, 9689])).
% 5.77/5.72 tff(9765,plain,
% 5.77/5.72 (sum(pred(Y4!52), succ(X4!53)) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9764, 12])).
% 5.77/5.72 tff(9766,plain,
% 5.77/5.72 (sum(pred(X4!53), succ(Y4!52)) = sum(n4, n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9663, 9631])).
% 5.77/5.72 tff(9767,plain,
% 5.77/5.72 (sum(pred(X4!53), succ(Y4!52)) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9766, 12])).
% 5.77/5.72 tff(9768,plain,
% 5.77/5.72 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n10, n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9767, 9765])).
% 5.77/5.72 tff(9769,plain,
% 5.77/5.72 (X5!51 = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[553, 9768, 29])).
% 5.77/5.72 tff(9770,plain,
% 5.77/5.72 (pred(X5!51) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9769])).
% 5.77/5.72 tff(9771,plain,
% 5.77/5.72 (pred(X5!51) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9770, 20])).
% 5.77/5.72 tff(9772,plain,
% 5.77/5.72 (pred(pred(X5!51)) = pred(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9771])).
% 5.77/5.72 tff(9773,plain,
% 5.77/5.72 (pred(pred(X5!51)) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9772, 19])).
% 5.77/5.72 tff(9774,plain,
% 5.77/5.72 (pred(pred(pred(X5!51))) = pred(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9773])).
% 5.77/5.72 tff(9775,plain,
% 5.77/5.72 (pred(pred(pred(X5!51))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9774, 18])).
% 5.77/5.72 tff(9776,plain,
% 5.77/5.72 (pred(pred(pred(pred(X5!51)))) = pred(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9775])).
% 5.77/5.72 tff(9777,plain,
% 5.77/5.72 (pred(pred(pred(pred(X5!51)))) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9776, 17])).
% 5.77/5.72 tff(9778,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(X5!51))))) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9777])).
% 5.77/5.72 tff(9779,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(X5!51))))) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9778, 16])).
% 5.77/5.72 tff(9780,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9779])).
% 5.77/5.72 tff(9781,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9780, 15])).
% 5.77/5.72 tff(9782,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9781])).
% 5.77/5.72 tff(9783,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9782, 25])).
% 5.77/5.72 tff(9784,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9783])).
% 5.77/5.72 tff(9785,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9784, 24])).
% 5.77/5.72 tff(9786,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9785])).
% 5.77/5.72 tff(9787,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9786, 23])).
% 5.77/5.72 tff(9788,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9787])).
% 5.77/5.72 tff(9789,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9788, 22])).
% 5.77/5.72 tff(9790,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9789])).
% 5.77/5.72 tff(9791,plain,
% 5.77/5.72 (NPX5!19 = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[742, 9790, 21])).
% 5.77/5.72 tff(9792,plain,
% 5.77/5.72 (succ(NPX5!19) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9791])).
% 5.77/5.72 tff(9793,plain,
% 5.77/5.72 (succ(NPX5!19) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9792, 28])).
% 5.77/5.72 tff(9794,plain,
% 5.77/5.72 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n10, n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9793, 9763])).
% 5.77/5.72 tff(9795,plain,
% 5.77/5.72 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9794, 69])).
% 5.77/5.72 tff(9796,plain,
% 5.77/5.72 (succ(X5!51) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9769])).
% 5.77/5.72 tff(9797,plain,
% 5.77/5.72 (succ(X5!51) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9796, 28])).
% 5.77/5.72 tff(9798,plain,
% 5.77/5.72 (succ(succ(X5!51)) = succ(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9797])).
% 5.77/5.72 tff(9799,plain,
% 5.77/5.72 (succ(succ(X5!51)) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9798, 42])).
% 5.77/5.72 tff(9800,plain,
% 5.77/5.72 (succ(succ(succ(X5!51))) = succ(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9799])).
% 5.77/5.72 tff(9801,plain,
% 5.77/5.72 (succ(succ(succ(X5!51))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9800, 58])).
% 5.77/5.72 tff(9802,plain,
% 5.77/5.72 (succ(succ(succ(succ(X5!51)))) = succ(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9801])).
% 5.77/5.72 tff(9803,plain,
% 5.77/5.72 (succ(succ(succ(succ(X5!51)))) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9802, 36])).
% 5.77/5.72 tff(9804,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(X5!51))))) = succ(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9803])).
% 5.77/5.72 tff(9805,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(X5!51))))) = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[9804, 48])).
% 5.77/5.72 tff(9806,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9805])).
% 5.77/5.72 tff(9807,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9806, 14])).
% 5.77/5.72 tff(9808,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9807])).
% 5.77/5.72 tff(9809,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9808, 33])).
% 5.77/5.72 tff(9810,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9809])).
% 5.77/5.72 tff(9811,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9810, 30])).
% 5.77/5.72 tff(9812,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9811])).
% 5.77/5.72 tff(9813,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9812, 39])).
% 5.77/5.72 tff(9814,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9813])).
% 5.77/5.72 tff(9815,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9814, 53])).
% 5.77/5.72 tff(9816,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9815])).
% 5.77/5.72 tff(9817,plain,
% 5.77/5.72 (NSX5!17 = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[767, 9816, 45])).
% 5.77/5.72 tff(9818,plain,
% 5.77/5.72 (pred(NSX5!17) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9817])).
% 5.77/5.72 tff(9819,plain,
% 5.77/5.72 (pred(NSX5!17) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9818, 20])).
% 5.77/5.72 tff(9820,plain,
% 5.77/5.72 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n8, n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9819, 9795])).
% 5.77/5.72 tff(9821,plain,
% 5.77/5.72 (Y6!48 = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[772, 9820, 98])).
% 5.77/5.72 tff(9822,plain,
% 5.77/5.72 (pred(Y6!48) = pred(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9821])).
% 5.77/5.72 tff(9823,plain,
% 5.77/5.72 (pred(Y6!48) = n2),
% 5.77/5.72 inference(transitivity,[status(thm)],[9822, 25])).
% 5.77/5.72 tff(9824,plain,
% 5.77/5.72 (pred(pred(Y6!48)) = pred(n2)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9823])).
% 5.77/5.72 tff(9825,plain,
% 5.77/5.72 (pred(pred(Y6!48)) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9824, 24])).
% 5.77/5.72 tff(9826,plain,
% 5.77/5.72 (pred(pred(pred(Y6!48))) = pred(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9825])).
% 5.77/5.72 tff(9827,plain,
% 5.77/5.72 (pred(pred(pred(Y6!48))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9826, 23])).
% 5.77/5.72 tff(9828,plain,
% 5.77/5.72 (pred(pred(pred(pred(Y6!48)))) = pred(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9827])).
% 5.77/5.72 tff(9829,plain,
% 5.77/5.72 (pred(pred(pred(pred(Y6!48)))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9828, 22])).
% 5.77/5.72 tff(9830,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9829])).
% 5.77/5.72 tff(9831,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(Y6!48))))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9830, 21])).
% 5.77/5.72 tff(9832,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9831])).
% 5.77/5.72 tff(9833,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9832, 20])).
% 5.77/5.72 tff(9834,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9833])).
% 5.77/5.72 tff(9835,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9834, 19])).
% 5.77/5.72 tff(9836,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9835])).
% 5.77/5.72 tff(9837,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9836, 18])).
% 5.77/5.72 tff(9838,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9837])).
% 5.77/5.72 tff(9839,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9838, 17])).
% 5.77/5.72 tff(9840,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9839])).
% 5.77/5.72 tff(9841,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9840, 16])).
% 5.77/5.72 tff(9842,plain,
% 5.77/5.72 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9841])).
% 5.77/5.72 tff(9843,plain,
% 5.77/5.72 (NPY6!14 = n3),
% 5.77/5.72 inference(transitivity,[status(thm)],[1465, 9842, 15])).
% 5.77/5.72 tff(9844,plain,
% 5.77/5.72 (succ(NPY6!14) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9843])).
% 5.77/5.72 tff(9845,plain,
% 5.77/5.72 (succ(NPY6!14) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9844, 14])).
% 5.77/5.72 tff(9846,plain,
% 5.77/5.72 (succ(Y6!48) = succ(n3)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9821])).
% 5.77/5.72 tff(9847,plain,
% 5.77/5.72 (succ(Y6!48) = n4),
% 5.77/5.72 inference(transitivity,[status(thm)],[9846, 14])).
% 5.77/5.72 tff(9848,plain,
% 5.77/5.72 (succ(succ(Y6!48)) = succ(n4)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9847])).
% 5.77/5.72 tff(9849,plain,
% 5.77/5.72 (succ(succ(Y6!48)) = n5),
% 5.77/5.72 inference(transitivity,[status(thm)],[9848, 33])).
% 5.77/5.72 tff(9850,plain,
% 5.77/5.72 (succ(succ(succ(Y6!48))) = succ(n5)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9849])).
% 5.77/5.72 tff(9851,plain,
% 5.77/5.72 (succ(succ(succ(Y6!48))) = n6),
% 5.77/5.72 inference(transitivity,[status(thm)],[9850, 30])).
% 5.77/5.72 tff(9852,plain,
% 5.77/5.72 (succ(succ(succ(succ(Y6!48)))) = succ(n6)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9851])).
% 5.77/5.72 tff(9853,plain,
% 5.77/5.72 (succ(succ(succ(succ(Y6!48)))) = n7),
% 5.77/5.72 inference(transitivity,[status(thm)],[9852, 39])).
% 5.77/5.72 tff(9854,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n7)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9853])).
% 5.77/5.72 tff(9855,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(Y6!48))))) = n8),
% 5.77/5.72 inference(transitivity,[status(thm)],[9854, 53])).
% 5.77/5.72 tff(9856,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n8)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9855])).
% 5.77/5.72 tff(9857,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n9),
% 5.77/5.72 inference(transitivity,[status(thm)],[9856, 45])).
% 5.77/5.72 tff(9858,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n9)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9857])).
% 5.77/5.72 tff(9859,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n10),
% 5.77/5.72 inference(transitivity,[status(thm)],[9858, 28])).
% 5.77/5.72 tff(9860,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n10)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9859])).
% 5.77/5.72 tff(9861,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n0),
% 5.77/5.72 inference(transitivity,[status(thm)],[9860, 42])).
% 5.77/5.72 tff(9862,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n0)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9861])).
% 5.77/5.72 tff(9863,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n1),
% 5.77/5.72 inference(transitivity,[status(thm)],[9862, 58])).
% 5.77/5.72 tff(9864,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n1)),
% 5.77/5.72 inference(monotonicity,[status(thm)],[9863])).
% 5.77/5.72 tff(9865,plain,
% 5.77/5.72 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[9864, 36])).
% 5.77/5.73 tff(9866,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9865])).
% 5.77/5.73 tff(9867,plain,
% 5.77/5.73 (NSY6!12 = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[1490, 9866, 48])).
% 5.77/5.73 tff(9868,plain,
% 5.77/5.73 (pred(NSY6!12) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9867])).
% 5.77/5.73 tff(9869,plain,
% 5.77/5.73 (pred(NSY6!12) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[9868, 25])).
% 5.77/5.73 tff(9870,plain,
% 5.77/5.73 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n2, n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9869, 9845])).
% 5.77/5.73 tff(9871,plain,
% 5.77/5.73 (sum(pred(NSY6!12), succ(NPY6!14)) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9870, 13])).
% 5.77/5.73 tff(9872,plain,
% 5.77/5.73 (sum(pred(Y5!50), succ(X5!51)) = sum(n8, n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9715, 9797])).
% 5.77/5.73 tff(9873,plain,
% 5.77/5.73 (sum(pred(Y5!50), succ(X5!51)) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[9872, 27])).
% 5.77/5.73 tff(9874,plain,
% 5.77/5.73 (sum(pred(X5!51), succ(Y5!50)) = sum(n8, n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9771, 9739])).
% 5.77/5.73 tff(9875,plain,
% 5.77/5.73 (sum(pred(X5!51), succ(Y5!50)) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[9874, 27])).
% 5.77/5.73 tff(9876,plain,
% 5.77/5.73 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n7, n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9875, 9873])).
% 5.77/5.73 tff(9877,plain,
% 5.77/5.73 (X6!49 = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[669, 9876, 26])).
% 5.77/5.73 tff(9878,plain,
% 5.77/5.73 (pred(X6!49) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9877])).
% 5.77/5.73 tff(9879,plain,
% 5.77/5.73 (pred(X6!49) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[9878, 25])).
% 5.77/5.73 tff(9880,plain,
% 5.77/5.73 (pred(pred(X6!49)) = pred(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9879])).
% 5.77/5.73 tff(9881,plain,
% 5.77/5.73 (pred(pred(X6!49)) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[9880, 24])).
% 5.77/5.73 tff(9882,plain,
% 5.77/5.73 (pred(pred(pred(X6!49))) = pred(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9881])).
% 5.77/5.73 tff(9883,plain,
% 5.77/5.73 (pred(pred(pred(X6!49))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[9882, 23])).
% 5.77/5.73 tff(9884,plain,
% 5.77/5.73 (pred(pred(pred(pred(X6!49)))) = pred(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9883])).
% 5.77/5.73 tff(9885,plain,
% 5.77/5.73 (pred(pred(pred(pred(X6!49)))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[9884, 22])).
% 5.77/5.73 tff(9886,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(X6!49))))) = pred(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9885])).
% 5.77/5.73 tff(9887,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(X6!49))))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[9886, 21])).
% 5.77/5.73 tff(9888,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9887])).
% 5.77/5.73 tff(9889,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[9888, 20])).
% 5.77/5.73 tff(9890,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9889])).
% 5.77/5.73 tff(9891,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[9890, 19])).
% 5.77/5.73 tff(9892,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9891])).
% 5.77/5.73 tff(9893,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9892, 18])).
% 5.77/5.73 tff(9894,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9893])).
% 5.77/5.73 tff(9895,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[9894, 17])).
% 5.77/5.73 tff(9896,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9895])).
% 5.77/5.73 tff(9897,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[9896, 16])).
% 5.77/5.73 tff(9898,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9897])).
% 5.77/5.73 tff(9899,plain,
% 5.77/5.73 (NPX6!15 = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[1523, 9898, 15])).
% 5.77/5.73 tff(9900,plain,
% 5.77/5.73 (succ(NPX6!15) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9899])).
% 5.77/5.73 tff(9901,plain,
% 5.77/5.73 (succ(NPX6!15) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[9900, 14])).
% 5.77/5.73 tff(9902,plain,
% 5.77/5.73 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n4, n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9901, 9871])).
% 5.77/5.73 tff(9903,plain,
% 5.77/5.73 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[9902, 12])).
% 5.77/5.73 tff(9904,plain,
% 5.77/5.73 (succ(X6!49) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9877])).
% 5.77/5.73 tff(9905,plain,
% 5.77/5.73 (succ(X6!49) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[9904, 14])).
% 5.77/5.73 tff(9906,plain,
% 5.77/5.73 (succ(succ(X6!49)) = succ(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9905])).
% 5.77/5.73 tff(9907,plain,
% 5.77/5.73 (succ(succ(X6!49)) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[9906, 33])).
% 5.77/5.73 tff(9908,plain,
% 5.77/5.73 (succ(succ(succ(X6!49))) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9907])).
% 5.77/5.73 tff(9909,plain,
% 5.77/5.73 (succ(succ(succ(X6!49))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9908, 30])).
% 5.77/5.73 tff(9910,plain,
% 5.77/5.73 (succ(succ(succ(succ(X6!49)))) = succ(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9909])).
% 5.77/5.73 tff(9911,plain,
% 5.77/5.73 (succ(succ(succ(succ(X6!49)))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[9910, 39])).
% 5.77/5.73 tff(9912,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(X6!49))))) = succ(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9911])).
% 5.77/5.73 tff(9913,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(X6!49))))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[9912, 53])).
% 5.77/5.73 tff(9914,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9913])).
% 5.77/5.73 tff(9915,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[9914, 45])).
% 5.77/5.73 tff(9916,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9915])).
% 5.77/5.73 tff(9917,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[9916, 28])).
% 5.77/5.73 tff(9918,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9917])).
% 5.77/5.73 tff(9919,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[9918, 42])).
% 5.77/5.73 tff(9920,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9919])).
% 5.77/5.73 tff(9921,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[9920, 58])).
% 5.77/5.73 tff(9922,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9921])).
% 5.77/5.73 tff(9923,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[9922, 36])).
% 5.77/5.73 tff(9924,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9923])).
% 5.77/5.73 tff(9925,plain,
% 5.77/5.73 (NSX6!13 = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[1550, 9924, 48])).
% 5.77/5.73 tff(9926,plain,
% 5.77/5.73 (pred(NSX6!13) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9925])).
% 5.77/5.73 tff(9927,plain,
% 5.77/5.73 (pred(NSX6!13) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[9926, 25])).
% 5.77/5.73 tff(9928,plain,
% 5.77/5.73 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n2, n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9927, 9903])).
% 5.77/5.73 tff(9929,plain,
% 5.77/5.73 (sum(n2, n10) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.77/5.73 inference(symmetry,[status(thm)],[9928])).
% 5.77/5.73 tff(9930,plain,
% 5.77/5.73 (n1 = sum(n2, n10)),
% 5.77/5.73 inference(symmetry,[status(thm)],[327])).
% 5.77/5.73 tff(9931,plain,
% 5.77/5.73 (sum(pred(Y6!48), succ(X6!49)) = sum(n2, n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9823, 9905])).
% 5.77/5.73 tff(9932,plain,
% 5.77/5.73 (sum(pred(Y6!48), succ(X6!49)) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9931, 13])).
% 5.77/5.73 tff(9933,plain,
% 5.77/5.73 (sum(pred(X6!49), succ(Y6!48)) = sum(n2, n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9879, 9847])).
% 5.77/5.73 tff(9934,plain,
% 5.77/5.73 (sum(pred(X6!49), succ(Y6!48)) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9933, 13])).
% 5.77/5.73 tff(9935,plain,
% 5.77/5.73 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n6, n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9934, 9932])).
% 5.77/5.73 tff(9936,plain,
% 5.77/5.73 (X7!47 = sum(n2, n10)),
% 5.77/5.73 inference(transitivity,[status(thm)],[785, 9935, 37, 9930])).
% 5.77/5.73 tff(9937,plain,
% 5.77/5.73 ((X7!47 = Y7!46) <=> (sum(n2, n10) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))))),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9936, 793])).
% 5.77/5.73 tff(9938,plain,
% 5.77/5.73 ((~(X7!47 = Y7!46)) <=> (~(sum(n2, n10) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))))),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9937])).
% 5.77/5.73 tff(9939,plain,
% 5.77/5.73 (~(sum(n2, n10) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))))),
% 5.77/5.73 inference(modus_ponens,[status(thm)],[792, 9938])).
% 5.77/5.73 tff(9940,plain,
% 5.77/5.73 ($false),
% 5.77/5.73 inference(unit_resolution,[status(thm)],[9939, 9929])).
% 5.77/5.73 tff(9941,plain,((~(X0!61 = n7)) | (~(Y0!60 = n0)) | (X7!47 = Y7!46)), inference(lemma,lemma(discharge,[]))).
% 5.77/5.73 tff(9942,plain,
% 5.77/5.73 (~(X0!61 = n7)),
% 5.77/5.73 inference(unit_resolution,[status(thm)],[9941, 9225, 792])).
% 5.77/5.73 tff(9943,plain,
% 5.77/5.73 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n9, n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[5172, 9275])).
% 5.77/5.73 tff(9944,plain,
% 5.77/5.73 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[9943, 41])).
% 5.77/5.73 tff(9945,plain,
% 5.77/5.73 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n7, n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[5198, 9944])).
% 5.77/5.73 tff(9946,plain,
% 5.77/5.73 (Y1!58 = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[196, 9945, 44])).
% 5.77/5.73 tff(9947,plain,
% 5.77/5.73 (pred(Y1!58) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9946])).
% 5.77/5.73 tff(9948,plain,
% 5.77/5.73 (pred(Y1!58) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[9947, 16])).
% 5.77/5.73 tff(9949,plain,
% 5.77/5.73 (pred(pred(Y1!58)) = pred(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9948])).
% 5.77/5.73 tff(9950,plain,
% 5.77/5.73 (pred(pred(Y1!58)) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[9949, 15])).
% 5.77/5.73 tff(9951,plain,
% 5.77/5.73 (pred(pred(pred(Y1!58))) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9950])).
% 5.77/5.73 tff(9952,plain,
% 5.77/5.73 (pred(pred(pred(Y1!58))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[9951, 25])).
% 5.77/5.73 tff(9953,plain,
% 5.77/5.73 (pred(pred(pred(pred(Y1!58)))) = pred(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9952])).
% 5.77/5.73 tff(9954,plain,
% 5.77/5.73 (pred(pred(pred(pred(Y1!58)))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[9953, 24])).
% 5.77/5.73 tff(9955,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9954])).
% 5.77/5.73 tff(9956,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(Y1!58))))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[9955, 23])).
% 5.77/5.73 tff(9957,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9956])).
% 5.77/5.73 tff(9958,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[9957, 22])).
% 5.77/5.73 tff(9959,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9958])).
% 5.77/5.73 tff(9960,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[9959, 21])).
% 5.77/5.73 tff(9961,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9960])).
% 5.77/5.73 tff(9962,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[9961, 20])).
% 5.77/5.73 tff(9963,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9962])).
% 5.77/5.73 tff(9964,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[9963, 19])).
% 5.77/5.73 tff(9965,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9964])).
% 5.77/5.73 tff(9966,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9965, 18])).
% 5.77/5.73 tff(9967,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9966])).
% 5.77/5.73 tff(9968,plain,
% 5.77/5.73 (NPY1!34 = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[232, 9967, 17])).
% 5.77/5.73 tff(9969,plain,
% 5.77/5.73 (succ(NPY1!34) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9968])).
% 5.77/5.73 tff(9970,plain,
% 5.77/5.73 (succ(NPY1!34) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9969, 30])).
% 5.77/5.73 tff(9971,plain,
% 5.77/5.73 (succ(Y1!58) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9946])).
% 5.77/5.73 tff(9972,plain,
% 5.77/5.73 (succ(Y1!58) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[9971, 30])).
% 5.77/5.73 tff(9973,plain,
% 5.77/5.73 (succ(succ(Y1!58)) = succ(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9972])).
% 5.77/5.73 tff(9974,plain,
% 5.77/5.73 (succ(succ(Y1!58)) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[9973, 39])).
% 5.77/5.73 tff(9975,plain,
% 5.77/5.73 (succ(succ(succ(Y1!58))) = succ(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9974])).
% 5.77/5.73 tff(9976,plain,
% 5.77/5.73 (succ(succ(succ(Y1!58))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[9975, 53])).
% 5.77/5.73 tff(9977,plain,
% 5.77/5.73 (succ(succ(succ(succ(Y1!58)))) = succ(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9976])).
% 5.77/5.73 tff(9978,plain,
% 5.77/5.73 (succ(succ(succ(succ(Y1!58)))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[9977, 45])).
% 5.77/5.73 tff(9979,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9978])).
% 5.77/5.73 tff(9980,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(Y1!58))))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[9979, 28])).
% 5.77/5.73 tff(9981,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9980])).
% 5.77/5.73 tff(9982,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[9981, 42])).
% 5.77/5.73 tff(9983,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9982])).
% 5.77/5.73 tff(9984,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[9983, 58])).
% 5.77/5.73 tff(9985,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9984])).
% 5.77/5.73 tff(9986,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[9985, 36])).
% 5.77/5.73 tff(9987,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9986])).
% 5.77/5.73 tff(9988,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[9987, 48])).
% 5.77/5.73 tff(9989,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9988])).
% 5.77/5.73 tff(9990,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[9989, 14])).
% 5.77/5.73 tff(9991,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9990])).
% 5.77/5.73 tff(9992,plain,
% 5.77/5.73 (NSY1!32 = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[255, 9991, 33])).
% 5.77/5.73 tff(9993,plain,
% 5.77/5.73 (pred(NSY1!32) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9992])).
% 5.77/5.73 tff(9994,plain,
% 5.77/5.73 (pred(NSY1!32) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[9993, 16])).
% 5.77/5.73 tff(9995,plain,
% 5.77/5.73 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n4, n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9994, 9970])).
% 5.77/5.73 tff(9996,plain,
% 5.77/5.73 (sum(pred(NSY1!32), succ(NPY1!34)) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[9995, 12])).
% 5.77/5.73 tff(9997,plain,
% 5.77/5.73 (sum(n10, n9) = n8),
% 5.77/5.73 inference(and_elim,[status(thm)],[9])).
% 5.77/5.73 tff(9998,plain,
% 5.77/5.73 (sum(pred(Y0!60), succ(X0!61)) = sum(n10, n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9227, 5176])).
% 5.77/5.73 tff(9999,plain,
% 5.77/5.73 (sum(pred(Y0!60), succ(X0!61)) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[9998, 9997])).
% 5.77/5.73 tff(10000,plain,
% 5.77/5.73 (sum(pred(X0!61), succ(Y0!60)) = sum(n7, n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[5150, 9251])).
% 5.77/5.73 tff(10001,plain,
% 5.77/5.73 (sum(pred(X0!61), succ(Y0!60)) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10000, 787])).
% 5.77/5.73 tff(10002,plain,
% 5.77/5.73 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n8, n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10001, 9999])).
% 5.77/5.73 tff(10003,plain,
% 5.77/5.73 (X1!59 = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[93, 10002, 31])).
% 5.77/5.73 tff(10004,plain,
% 5.77/5.73 (pred(X1!59) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10003])).
% 5.77/5.73 tff(10005,plain,
% 5.77/5.73 (pred(X1!59) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10004, 16])).
% 5.77/5.73 tff(10006,plain,
% 5.77/5.73 (pred(pred(X1!59)) = pred(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10005])).
% 5.77/5.73 tff(10007,plain,
% 5.77/5.73 (pred(pred(X1!59)) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[10006, 15])).
% 5.77/5.73 tff(10008,plain,
% 5.77/5.73 (pred(pred(pred(X1!59))) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10007])).
% 5.77/5.73 tff(10009,plain,
% 5.77/5.73 (pred(pred(pred(X1!59))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[10008, 25])).
% 5.77/5.73 tff(10010,plain,
% 5.77/5.73 (pred(pred(pred(pred(X1!59)))) = pred(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10009])).
% 5.77/5.73 tff(10011,plain,
% 5.77/5.73 (pred(pred(pred(pred(X1!59)))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[10010, 24])).
% 5.77/5.73 tff(10012,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(X1!59))))) = pred(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10011])).
% 5.77/5.73 tff(10013,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(X1!59))))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[10012, 23])).
% 5.77/5.73 tff(10014,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10013])).
% 5.77/5.73 tff(10015,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10014, 22])).
% 5.77/5.73 tff(10016,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10015])).
% 5.77/5.73 tff(10017,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[10016, 21])).
% 5.77/5.73 tff(10018,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10017])).
% 5.77/5.73 tff(10019,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10018, 20])).
% 5.77/5.73 tff(10020,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10019])).
% 5.77/5.73 tff(10021,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10020, 19])).
% 5.77/5.73 tff(10022,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10021])).
% 5.77/5.73 tff(10023,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10022, 18])).
% 5.77/5.73 tff(10024,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10023])).
% 5.77/5.73 tff(10025,plain,
% 5.77/5.73 (NPX1!35 = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[280, 10024, 17])).
% 5.77/5.73 tff(10026,plain,
% 5.77/5.73 (succ(NPX1!35) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10025])).
% 5.77/5.73 tff(10027,plain,
% 5.77/5.73 (succ(NPX1!35) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10026, 30])).
% 5.77/5.73 tff(10028,plain,
% 5.77/5.73 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n6, n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10027, 9996])).
% 5.77/5.73 tff(10029,plain,
% 5.77/5.73 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[10028, 674])).
% 5.77/5.73 tff(10030,plain,
% 5.77/5.73 (succ(X1!59) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10003])).
% 5.77/5.73 tff(10031,plain,
% 5.77/5.73 (succ(X1!59) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10030, 30])).
% 5.77/5.73 tff(10032,plain,
% 5.77/5.73 (succ(succ(X1!59)) = succ(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10031])).
% 5.77/5.73 tff(10033,plain,
% 5.77/5.73 (succ(succ(X1!59)) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10032, 39])).
% 5.77/5.73 tff(10034,plain,
% 5.77/5.73 (succ(succ(succ(X1!59))) = succ(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10033])).
% 5.77/5.73 tff(10035,plain,
% 5.77/5.73 (succ(succ(succ(X1!59))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10034, 53])).
% 5.77/5.73 tff(10036,plain,
% 5.77/5.73 (succ(succ(succ(succ(X1!59)))) = succ(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10035])).
% 5.77/5.73 tff(10037,plain,
% 5.77/5.73 (succ(succ(succ(succ(X1!59)))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[10036, 45])).
% 5.77/5.73 tff(10038,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(X1!59))))) = succ(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10037])).
% 5.77/5.73 tff(10039,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(X1!59))))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10038, 28])).
% 5.77/5.73 tff(10040,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10039])).
% 5.77/5.73 tff(10041,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[10040, 42])).
% 5.77/5.73 tff(10042,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10041])).
% 5.77/5.73 tff(10043,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[10042, 58])).
% 5.77/5.73 tff(10044,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10043])).
% 5.77/5.73 tff(10045,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[10044, 36])).
% 5.77/5.73 tff(10046,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10045])).
% 5.77/5.73 tff(10047,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[10046, 48])).
% 5.77/5.73 tff(10048,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10047])).
% 5.77/5.73 tff(10049,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10048, 14])).
% 5.77/5.73 tff(10050,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10049])).
% 5.77/5.73 tff(10051,plain,
% 5.77/5.73 (NSX1!33 = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[305, 10050, 33])).
% 5.77/5.73 tff(10052,plain,
% 5.77/5.73 (pred(NSX1!33) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10051])).
% 5.77/5.73 tff(10053,plain,
% 5.77/5.73 (pred(NSX1!33) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10052, 16])).
% 5.77/5.73 tff(10054,plain,
% 5.77/5.73 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n4, n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10053, 10029])).
% 5.77/5.73 tff(10055,plain,
% 5.77/5.73 (Y2!56 = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[310, 10054, 673])).
% 5.77/5.73 tff(10056,plain,
% 5.77/5.73 (pred(Y2!56) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10055])).
% 5.77/5.73 tff(10057,plain,
% 5.77/5.73 (pred(Y2!56) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10056, 20])).
% 5.77/5.73 tff(10058,plain,
% 5.77/5.73 (pred(pred(Y2!56)) = pred(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10057])).
% 5.77/5.73 tff(10059,plain,
% 5.77/5.73 (pred(pred(Y2!56)) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10058, 19])).
% 5.77/5.73 tff(10060,plain,
% 5.77/5.73 (pred(pred(pred(Y2!56))) = pred(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10059])).
% 5.77/5.73 tff(10061,plain,
% 5.77/5.73 (pred(pred(pred(Y2!56))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10060, 18])).
% 5.77/5.73 tff(10062,plain,
% 5.77/5.73 (pred(pred(pred(pred(Y2!56)))) = pred(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10061])).
% 5.77/5.73 tff(10063,plain,
% 5.77/5.73 (pred(pred(pred(pred(Y2!56)))) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[10062, 17])).
% 5.77/5.73 tff(10064,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10063])).
% 5.77/5.73 tff(10065,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(Y2!56))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10064, 16])).
% 5.77/5.73 tff(10066,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10065])).
% 5.77/5.73 tff(10067,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[10066, 15])).
% 5.77/5.73 tff(10068,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10067])).
% 5.77/5.73 tff(10069,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[10068, 25])).
% 5.77/5.73 tff(10070,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10069])).
% 5.77/5.73 tff(10071,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[10070, 24])).
% 5.77/5.73 tff(10072,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10071])).
% 5.77/5.73 tff(10073,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[10072, 23])).
% 5.77/5.73 tff(10074,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10073])).
% 5.77/5.73 tff(10075,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10074, 22])).
% 5.77/5.73 tff(10076,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10075])).
% 5.77/5.73 tff(10077,plain,
% 5.77/5.73 (NPY2!30 = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[347, 10076, 21])).
% 5.77/5.73 tff(10078,plain,
% 5.77/5.73 (succ(NPY2!30) = succ(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10077])).
% 5.77/5.73 tff(10079,plain,
% 5.77/5.73 (succ(NPY2!30) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10078, 28])).
% 5.77/5.73 tff(10080,plain,
% 5.77/5.73 (succ(Y2!56) = succ(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10055])).
% 5.77/5.73 tff(10081,plain,
% 5.77/5.73 (succ(Y2!56) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10080, 28])).
% 5.77/5.73 tff(10082,plain,
% 5.77/5.73 (succ(succ(Y2!56)) = succ(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10081])).
% 5.77/5.73 tff(10083,plain,
% 5.77/5.73 (succ(succ(Y2!56)) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[10082, 42])).
% 5.77/5.73 tff(10084,plain,
% 5.77/5.73 (succ(succ(succ(Y2!56))) = succ(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10083])).
% 5.77/5.73 tff(10085,plain,
% 5.77/5.73 (succ(succ(succ(Y2!56))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[10084, 58])).
% 5.77/5.73 tff(10086,plain,
% 5.77/5.73 (succ(succ(succ(succ(Y2!56)))) = succ(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10085])).
% 5.77/5.73 tff(10087,plain,
% 5.77/5.73 (succ(succ(succ(succ(Y2!56)))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[10086, 36])).
% 5.77/5.73 tff(10088,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10087])).
% 5.77/5.73 tff(10089,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(Y2!56))))) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[10088, 48])).
% 5.77/5.73 tff(10090,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10089])).
% 5.77/5.73 tff(10091,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10090, 14])).
% 5.77/5.73 tff(10092,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10091])).
% 5.77/5.73 tff(10093,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[10092, 33])).
% 5.77/5.73 tff(10094,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10093])).
% 5.77/5.73 tff(10095,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10094, 30])).
% 5.77/5.73 tff(10096,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10095])).
% 5.77/5.73 tff(10097,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10096, 39])).
% 5.77/5.73 tff(10098,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10097])).
% 5.77/5.73 tff(10099,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10098, 53])).
% 5.77/5.73 tff(10100,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10099])).
% 5.77/5.73 tff(10101,plain,
% 5.77/5.73 (NSY2!28 = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[370, 10100, 45])).
% 5.77/5.73 tff(10102,plain,
% 5.77/5.73 (pred(NSY2!28) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10101])).
% 5.77/5.73 tff(10103,plain,
% 5.77/5.73 (pred(NSY2!28) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10102, 20])).
% 5.77/5.73 tff(10104,plain,
% 5.77/5.73 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n8, n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10103, 10079])).
% 5.77/5.73 tff(10105,plain,
% 5.77/5.73 (sum(pred(NSY2!28), succ(NPY2!30)) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10104, 27])).
% 5.77/5.73 tff(10106,plain,
% 5.77/5.73 (sum(pred(Y1!58), succ(X1!59)) = sum(n4, n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[9948, 10031])).
% 5.77/5.73 tff(10107,plain,
% 5.77/5.73 (sum(pred(Y1!58), succ(X1!59)) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10106, 12])).
% 5.77/5.73 tff(10108,plain,
% 5.77/5.73 (sum(pred(X1!59), succ(Y1!58)) = sum(n4, n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10005, 9972])).
% 5.77/5.73 tff(10109,plain,
% 5.77/5.73 (sum(pred(X1!59), succ(Y1!58)) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10108, 12])).
% 5.77/5.73 tff(10110,plain,
% 5.77/5.73 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n10, n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10109, 10107])).
% 5.77/5.73 tff(10111,plain,
% 5.77/5.73 (X2!57 = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[209, 10110, 29])).
% 5.77/5.73 tff(10112,plain,
% 5.77/5.73 (pred(X2!57) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10111])).
% 5.77/5.73 tff(10113,plain,
% 5.77/5.73 (pred(X2!57) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10112, 20])).
% 5.77/5.73 tff(10114,plain,
% 5.77/5.73 (pred(pred(X2!57)) = pred(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10113])).
% 5.77/5.73 tff(10115,plain,
% 5.77/5.73 (pred(pred(X2!57)) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10114, 19])).
% 5.77/5.73 tff(10116,plain,
% 5.77/5.73 (pred(pred(pred(X2!57))) = pred(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10115])).
% 5.77/5.73 tff(10117,plain,
% 5.77/5.73 (pred(pred(pred(X2!57))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10116, 18])).
% 5.77/5.73 tff(10118,plain,
% 5.77/5.73 (pred(pred(pred(pred(X2!57)))) = pred(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10117])).
% 5.77/5.73 tff(10119,plain,
% 5.77/5.73 (pred(pred(pred(pred(X2!57)))) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[10118, 17])).
% 5.77/5.73 tff(10120,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(X2!57))))) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10119])).
% 5.77/5.73 tff(10121,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(X2!57))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10120, 16])).
% 5.77/5.73 tff(10122,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10121])).
% 5.77/5.73 tff(10123,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[10122, 15])).
% 5.77/5.73 tff(10124,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10123])).
% 5.77/5.73 tff(10125,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[10124, 25])).
% 5.77/5.73 tff(10126,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10125])).
% 5.77/5.73 tff(10127,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[10126, 24])).
% 5.77/5.73 tff(10128,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10127])).
% 5.77/5.73 tff(10129,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[10128, 23])).
% 5.77/5.73 tff(10130,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10129])).
% 5.77/5.73 tff(10131,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10130, 22])).
% 5.77/5.73 tff(10132,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10131])).
% 5.77/5.73 tff(10133,plain,
% 5.77/5.73 (NPX2!31 = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[395, 10132, 21])).
% 5.77/5.73 tff(10134,plain,
% 5.77/5.73 (succ(NPX2!31) = succ(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10133])).
% 5.77/5.73 tff(10135,plain,
% 5.77/5.73 (succ(NPX2!31) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10134, 28])).
% 5.77/5.73 tff(10136,plain,
% 5.77/5.73 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n10, n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10135, 10105])).
% 5.77/5.73 tff(10137,plain,
% 5.77/5.73 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10136, 69])).
% 5.77/5.73 tff(10138,plain,
% 5.77/5.73 (succ(X2!57) = succ(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10111])).
% 5.77/5.73 tff(10139,plain,
% 5.77/5.73 (succ(X2!57) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10138, 28])).
% 5.77/5.73 tff(10140,plain,
% 5.77/5.73 (succ(succ(X2!57)) = succ(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10139])).
% 5.77/5.73 tff(10141,plain,
% 5.77/5.73 (succ(succ(X2!57)) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[10140, 42])).
% 5.77/5.73 tff(10142,plain,
% 5.77/5.73 (succ(succ(succ(X2!57))) = succ(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10141])).
% 5.77/5.73 tff(10143,plain,
% 5.77/5.73 (succ(succ(succ(X2!57))) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[10142, 58])).
% 5.77/5.73 tff(10144,plain,
% 5.77/5.73 (succ(succ(succ(succ(X2!57)))) = succ(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10143])).
% 5.77/5.73 tff(10145,plain,
% 5.77/5.73 (succ(succ(succ(succ(X2!57)))) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[10144, 36])).
% 5.77/5.73 tff(10146,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(X2!57))))) = succ(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10145])).
% 5.77/5.73 tff(10147,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(X2!57))))) = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[10146, 48])).
% 5.77/5.73 tff(10148,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10147])).
% 5.77/5.73 tff(10149,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10148, 14])).
% 5.77/5.73 tff(10150,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10149])).
% 5.77/5.73 tff(10151,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[10150, 33])).
% 5.77/5.73 tff(10152,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10151])).
% 5.77/5.73 tff(10153,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10152, 30])).
% 5.77/5.73 tff(10154,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10153])).
% 5.77/5.73 tff(10155,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10154, 39])).
% 5.77/5.73 tff(10156,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10155])).
% 5.77/5.73 tff(10157,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10156, 53])).
% 5.77/5.73 tff(10158,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10157])).
% 5.77/5.73 tff(10159,plain,
% 5.77/5.73 (NSX2!29 = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[420, 10158, 45])).
% 5.77/5.73 tff(10160,plain,
% 5.77/5.73 (pred(NSX2!29) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10159])).
% 5.77/5.73 tff(10161,plain,
% 5.77/5.73 (pred(NSX2!29) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10160, 20])).
% 5.77/5.73 tff(10162,plain,
% 5.77/5.73 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n8, n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10161, 10137])).
% 5.77/5.73 tff(10163,plain,
% 5.77/5.73 (Y3!54 = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[425, 10162, 98])).
% 5.77/5.73 tff(10164,plain,
% 5.77/5.73 (pred(Y3!54) = pred(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10163])).
% 5.77/5.73 tff(10165,plain,
% 5.77/5.73 (pred(Y3!54) = n2),
% 5.77/5.73 inference(transitivity,[status(thm)],[10164, 25])).
% 5.77/5.73 tff(10166,plain,
% 5.77/5.73 (pred(pred(Y3!54)) = pred(n2)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10165])).
% 5.77/5.73 tff(10167,plain,
% 5.77/5.73 (pred(pred(Y3!54)) = n1),
% 5.77/5.73 inference(transitivity,[status(thm)],[10166, 24])).
% 5.77/5.73 tff(10168,plain,
% 5.77/5.73 (pred(pred(pred(Y3!54))) = pred(n1)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10167])).
% 5.77/5.73 tff(10169,plain,
% 5.77/5.73 (pred(pred(pred(Y3!54))) = n0),
% 5.77/5.73 inference(transitivity,[status(thm)],[10168, 23])).
% 5.77/5.73 tff(10170,plain,
% 5.77/5.73 (pred(pred(pred(pred(Y3!54)))) = pred(n0)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10169])).
% 5.77/5.73 tff(10171,plain,
% 5.77/5.73 (pred(pred(pred(pred(Y3!54)))) = n10),
% 5.77/5.73 inference(transitivity,[status(thm)],[10170, 22])).
% 5.77/5.73 tff(10172,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n10)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10171])).
% 5.77/5.73 tff(10173,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(Y3!54))))) = n9),
% 5.77/5.73 inference(transitivity,[status(thm)],[10172, 21])).
% 5.77/5.73 tff(10174,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n9)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10173])).
% 5.77/5.73 tff(10175,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n8),
% 5.77/5.73 inference(transitivity,[status(thm)],[10174, 20])).
% 5.77/5.73 tff(10176,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n8)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10175])).
% 5.77/5.73 tff(10177,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10176, 19])).
% 5.77/5.73 tff(10178,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10177])).
% 5.77/5.73 tff(10179,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10178, 18])).
% 5.77/5.73 tff(10180,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10179])).
% 5.77/5.73 tff(10181,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[10180, 17])).
% 5.77/5.73 tff(10182,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10181])).
% 5.77/5.73 tff(10183,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10182, 16])).
% 5.77/5.73 tff(10184,plain,
% 5.77/5.73 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10183])).
% 5.77/5.73 tff(10185,plain,
% 5.77/5.73 (NPY3!26 = n3),
% 5.77/5.73 inference(transitivity,[status(thm)],[462, 10184, 15])).
% 5.77/5.73 tff(10186,plain,
% 5.77/5.73 (succ(NPY3!26) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10185])).
% 5.77/5.73 tff(10187,plain,
% 5.77/5.73 (succ(NPY3!26) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10186, 14])).
% 5.77/5.73 tff(10188,plain,
% 5.77/5.73 (succ(Y3!54) = succ(n3)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10163])).
% 5.77/5.73 tff(10189,plain,
% 5.77/5.73 (succ(Y3!54) = n4),
% 5.77/5.73 inference(transitivity,[status(thm)],[10188, 14])).
% 5.77/5.73 tff(10190,plain,
% 5.77/5.73 (succ(succ(Y3!54)) = succ(n4)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10189])).
% 5.77/5.73 tff(10191,plain,
% 5.77/5.73 (succ(succ(Y3!54)) = n5),
% 5.77/5.73 inference(transitivity,[status(thm)],[10190, 33])).
% 5.77/5.73 tff(10192,plain,
% 5.77/5.73 (succ(succ(succ(Y3!54))) = succ(n5)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10191])).
% 5.77/5.73 tff(10193,plain,
% 5.77/5.73 (succ(succ(succ(Y3!54))) = n6),
% 5.77/5.73 inference(transitivity,[status(thm)],[10192, 30])).
% 5.77/5.73 tff(10194,plain,
% 5.77/5.73 (succ(succ(succ(succ(Y3!54)))) = succ(n6)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10193])).
% 5.77/5.73 tff(10195,plain,
% 5.77/5.73 (succ(succ(succ(succ(Y3!54)))) = n7),
% 5.77/5.73 inference(transitivity,[status(thm)],[10194, 39])).
% 5.77/5.73 tff(10196,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n7)),
% 5.77/5.73 inference(monotonicity,[status(thm)],[10195])).
% 5.77/5.73 tff(10197,plain,
% 5.77/5.73 (succ(succ(succ(succ(succ(Y3!54))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10196, 53])).
% 5.77/5.74 tff(10198,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10197])).
% 5.77/5.74 tff(10199,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10198, 45])).
% 5.77/5.74 tff(10200,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10199])).
% 5.77/5.74 tff(10201,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10200, 28])).
% 5.77/5.74 tff(10202,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10201])).
% 5.77/5.74 tff(10203,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10202, 42])).
% 5.77/5.74 tff(10204,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10203])).
% 5.77/5.74 tff(10205,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10204, 58])).
% 5.77/5.74 tff(10206,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10205])).
% 5.77/5.74 tff(10207,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10206, 36])).
% 5.77/5.74 tff(10208,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10207])).
% 5.77/5.74 tff(10209,plain,
% 5.77/5.74 (NSY3!24 = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[485, 10208, 48])).
% 5.77/5.74 tff(10210,plain,
% 5.77/5.74 (pred(NSY3!24) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10209])).
% 5.77/5.74 tff(10211,plain,
% 5.77/5.74 (pred(NSY3!24) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10210, 25])).
% 5.77/5.74 tff(10212,plain,
% 5.77/5.74 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n2, n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10211, 10187])).
% 5.77/5.74 tff(10213,plain,
% 5.77/5.74 (sum(pred(NSY3!24), succ(NPY3!26)) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10212, 13])).
% 5.77/5.74 tff(10214,plain,
% 5.77/5.74 (sum(pred(Y2!56), succ(X2!57)) = sum(n8, n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10057, 10139])).
% 5.77/5.74 tff(10215,plain,
% 5.77/5.74 (sum(pred(Y2!56), succ(X2!57)) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10214, 27])).
% 5.77/5.74 tff(10216,plain,
% 5.77/5.74 (sum(pred(X2!57), succ(Y2!56)) = sum(n8, n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10113, 10081])).
% 5.77/5.74 tff(10217,plain,
% 5.77/5.74 (sum(pred(X2!57), succ(Y2!56)) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10216, 27])).
% 5.77/5.74 tff(10218,plain,
% 5.77/5.74 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n7, n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10217, 10215])).
% 5.77/5.74 tff(10219,plain,
% 5.77/5.74 (X3!55 = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[323, 10218, 26])).
% 5.77/5.74 tff(10220,plain,
% 5.77/5.74 (pred(X3!55) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10219])).
% 5.77/5.74 tff(10221,plain,
% 5.77/5.74 (pred(X3!55) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10220, 25])).
% 5.77/5.74 tff(10222,plain,
% 5.77/5.74 (pred(pred(X3!55)) = pred(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10221])).
% 5.77/5.74 tff(10223,plain,
% 5.77/5.74 (pred(pred(X3!55)) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10222, 24])).
% 5.77/5.74 tff(10224,plain,
% 5.77/5.74 (pred(pred(pred(X3!55))) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10223])).
% 5.77/5.74 tff(10225,plain,
% 5.77/5.74 (pred(pred(pred(X3!55))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10224, 23])).
% 5.77/5.74 tff(10226,plain,
% 5.77/5.74 (pred(pred(pred(pred(X3!55)))) = pred(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10225])).
% 5.77/5.74 tff(10227,plain,
% 5.77/5.74 (pred(pred(pred(pred(X3!55)))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10226, 22])).
% 5.77/5.74 tff(10228,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X3!55))))) = pred(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10227])).
% 5.77/5.74 tff(10229,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X3!55))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10228, 21])).
% 5.77/5.74 tff(10230,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10229])).
% 5.77/5.74 tff(10231,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10230, 20])).
% 5.77/5.74 tff(10232,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10231])).
% 5.77/5.74 tff(10233,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10232, 19])).
% 5.77/5.74 tff(10234,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10233])).
% 5.77/5.74 tff(10235,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10234, 18])).
% 5.77/5.74 tff(10236,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10235])).
% 5.77/5.74 tff(10237,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10236, 17])).
% 5.77/5.74 tff(10238,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10237])).
% 5.77/5.74 tff(10239,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10238, 16])).
% 5.77/5.74 tff(10240,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10239])).
% 5.77/5.74 tff(10241,plain,
% 5.77/5.74 (NPX3!27 = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[510, 10240, 15])).
% 5.77/5.74 tff(10242,plain,
% 5.77/5.74 (succ(NPX3!27) = succ(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10241])).
% 5.77/5.74 tff(10243,plain,
% 5.77/5.74 (succ(NPX3!27) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10242, 14])).
% 5.77/5.74 tff(10244,plain,
% 5.77/5.74 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n4, n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10243, 10213])).
% 5.77/5.74 tff(10245,plain,
% 5.77/5.74 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10244, 12])).
% 5.77/5.74 tff(10246,plain,
% 5.77/5.74 (succ(X3!55) = succ(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10219])).
% 5.77/5.74 tff(10247,plain,
% 5.77/5.74 (succ(X3!55) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10246, 14])).
% 5.77/5.74 tff(10248,plain,
% 5.77/5.74 (succ(succ(X3!55)) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10247])).
% 5.77/5.74 tff(10249,plain,
% 5.77/5.74 (succ(succ(X3!55)) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10248, 33])).
% 5.77/5.74 tff(10250,plain,
% 5.77/5.74 (succ(succ(succ(X3!55))) = succ(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10249])).
% 5.77/5.74 tff(10251,plain,
% 5.77/5.74 (succ(succ(succ(X3!55))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10250, 30])).
% 5.77/5.74 tff(10252,plain,
% 5.77/5.74 (succ(succ(succ(succ(X3!55)))) = succ(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10251])).
% 5.77/5.74 tff(10253,plain,
% 5.77/5.74 (succ(succ(succ(succ(X3!55)))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10252, 39])).
% 5.77/5.74 tff(10254,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(X3!55))))) = succ(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10253])).
% 5.77/5.74 tff(10255,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(X3!55))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10254, 53])).
% 5.77/5.74 tff(10256,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10255])).
% 5.77/5.74 tff(10257,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10256, 45])).
% 5.77/5.74 tff(10258,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10257])).
% 5.77/5.74 tff(10259,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10258, 28])).
% 5.77/5.74 tff(10260,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10259])).
% 5.77/5.74 tff(10261,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10260, 42])).
% 5.77/5.74 tff(10262,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10261])).
% 5.77/5.74 tff(10263,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10262, 58])).
% 5.77/5.74 tff(10264,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10263])).
% 5.77/5.74 tff(10265,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10264, 36])).
% 5.77/5.74 tff(10266,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10265])).
% 5.77/5.74 tff(10267,plain,
% 5.77/5.74 (NSX3!25 = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[535, 10266, 48])).
% 5.77/5.74 tff(10268,plain,
% 5.77/5.74 (pred(NSX3!25) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10267])).
% 5.77/5.74 tff(10269,plain,
% 5.77/5.74 (pred(NSX3!25) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10268, 25])).
% 5.77/5.74 tff(10270,plain,
% 5.77/5.74 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n2, n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10269, 10245])).
% 5.77/5.74 tff(10271,plain,
% 5.77/5.74 (Y4!52 = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[540, 10270, 327])).
% 5.77/5.74 tff(10272,plain,
% 5.77/5.74 (pred(Y4!52) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10271])).
% 5.77/5.74 tff(10273,plain,
% 5.77/5.74 (pred(Y4!52) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10272, 23])).
% 5.77/5.74 tff(10274,plain,
% 5.77/5.74 (pred(pred(Y4!52)) = pred(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10273])).
% 5.77/5.74 tff(10275,plain,
% 5.77/5.74 (pred(pred(Y4!52)) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10274, 22])).
% 5.77/5.74 tff(10276,plain,
% 5.77/5.74 (pred(pred(pred(Y4!52))) = pred(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10275])).
% 5.77/5.74 tff(10277,plain,
% 5.77/5.74 (pred(pred(pred(Y4!52))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10276, 21])).
% 5.77/5.74 tff(10278,plain,
% 5.77/5.74 (pred(pred(pred(pred(Y4!52)))) = pred(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10277])).
% 5.77/5.74 tff(10279,plain,
% 5.77/5.74 (pred(pred(pred(pred(Y4!52)))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10278, 20])).
% 5.77/5.74 tff(10280,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10279])).
% 5.77/5.74 tff(10281,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(Y4!52))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10280, 19])).
% 5.77/5.74 tff(10282,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10281])).
% 5.77/5.74 tff(10283,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10282, 18])).
% 5.77/5.74 tff(10284,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10283])).
% 5.77/5.74 tff(10285,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10284, 17])).
% 5.77/5.74 tff(10286,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10285])).
% 5.77/5.74 tff(10287,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10286, 16])).
% 5.77/5.74 tff(10288,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10287])).
% 5.77/5.74 tff(10289,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10288, 15])).
% 5.77/5.74 tff(10290,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10289])).
% 5.77/5.74 tff(10291,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10290, 25])).
% 5.77/5.74 tff(10292,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10291])).
% 5.77/5.74 tff(10293,plain,
% 5.77/5.74 (NPY4!22 = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[578, 10292, 24])).
% 5.77/5.74 tff(10294,plain,
% 5.77/5.74 (succ(NPY4!22) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10293])).
% 5.77/5.74 tff(10295,plain,
% 5.77/5.74 (succ(NPY4!22) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10294, 36])).
% 5.77/5.74 tff(10296,plain,
% 5.77/5.74 (succ(Y4!52) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10271])).
% 5.77/5.74 tff(10297,plain,
% 5.77/5.74 (succ(Y4!52) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10296, 36])).
% 5.77/5.74 tff(10298,plain,
% 5.77/5.74 (succ(succ(Y4!52)) = succ(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10297])).
% 5.77/5.74 tff(10299,plain,
% 5.77/5.74 (succ(succ(Y4!52)) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10298, 48])).
% 5.77/5.74 tff(10300,plain,
% 5.77/5.74 (succ(succ(succ(Y4!52))) = succ(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10299])).
% 5.77/5.74 tff(10301,plain,
% 5.77/5.74 (succ(succ(succ(Y4!52))) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10300, 14])).
% 5.77/5.74 tff(10302,plain,
% 5.77/5.74 (succ(succ(succ(succ(Y4!52)))) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10301])).
% 5.77/5.74 tff(10303,plain,
% 5.77/5.74 (succ(succ(succ(succ(Y4!52)))) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10302, 33])).
% 5.77/5.74 tff(10304,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10303])).
% 5.77/5.74 tff(10305,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(Y4!52))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10304, 30])).
% 5.77/5.74 tff(10306,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10305])).
% 5.77/5.74 tff(10307,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10306, 39])).
% 5.77/5.74 tff(10308,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10307])).
% 5.77/5.74 tff(10309,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10308, 53])).
% 5.77/5.74 tff(10310,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10309])).
% 5.77/5.74 tff(10311,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10310, 45])).
% 5.77/5.74 tff(10312,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10311])).
% 5.77/5.74 tff(10313,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10312, 28])).
% 5.77/5.74 tff(10314,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10313])).
% 5.77/5.74 tff(10315,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10314, 42])).
% 5.77/5.74 tff(10316,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10315])).
% 5.77/5.74 tff(10317,plain,
% 5.77/5.74 (NSY4!20 = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[601, 10316, 58])).
% 5.77/5.74 tff(10318,plain,
% 5.77/5.74 (pred(NSY4!20) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10317])).
% 5.77/5.74 tff(10319,plain,
% 5.77/5.74 (pred(NSY4!20) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10318, 23])).
% 5.77/5.74 tff(10320,plain,
% 5.77/5.74 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n0, n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10319, 10295])).
% 5.77/5.74 tff(10321,plain,
% 5.77/5.74 (sum(pred(NSY4!20), succ(NPY4!22)) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10320, 35])).
% 5.77/5.74 tff(10322,plain,
% 5.77/5.74 (sum(pred(Y3!54), succ(X3!55)) = sum(n2, n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10165, 10247])).
% 5.77/5.74 tff(10323,plain,
% 5.77/5.74 (sum(pred(Y3!54), succ(X3!55)) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10322, 13])).
% 5.77/5.74 tff(10324,plain,
% 5.77/5.74 (sum(pred(X3!55), succ(Y3!54)) = sum(n2, n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10221, 10189])).
% 5.77/5.74 tff(10325,plain,
% 5.77/5.74 (sum(pred(X3!55), succ(Y3!54)) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10324, 13])).
% 5.77/5.74 tff(10326,plain,
% 5.77/5.74 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n6, n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10325, 10323])).
% 5.77/5.74 tff(10327,plain,
% 5.77/5.74 (X4!53 = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[438, 10326, 37])).
% 5.77/5.74 tff(10328,plain,
% 5.77/5.74 (pred(X4!53) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10327])).
% 5.77/5.74 tff(10329,plain,
% 5.77/5.74 (pred(X4!53) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10328, 23])).
% 5.77/5.74 tff(10330,plain,
% 5.77/5.74 (pred(pred(X4!53)) = pred(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10329])).
% 5.77/5.74 tff(10331,plain,
% 5.77/5.74 (pred(pred(X4!53)) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10330, 22])).
% 5.77/5.74 tff(10332,plain,
% 5.77/5.74 (pred(pred(pred(X4!53))) = pred(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10331])).
% 5.77/5.74 tff(10333,plain,
% 5.77/5.74 (pred(pred(pred(X4!53))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10332, 21])).
% 5.77/5.74 tff(10334,plain,
% 5.77/5.74 (pred(pred(pred(pred(X4!53)))) = pred(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10333])).
% 5.77/5.74 tff(10335,plain,
% 5.77/5.74 (pred(pred(pred(pred(X4!53)))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10334, 20])).
% 5.77/5.74 tff(10336,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X4!53))))) = pred(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10335])).
% 5.77/5.74 tff(10337,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X4!53))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10336, 19])).
% 5.77/5.74 tff(10338,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10337])).
% 5.77/5.74 tff(10339,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10338, 18])).
% 5.77/5.74 tff(10340,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10339])).
% 5.77/5.74 tff(10341,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10340, 17])).
% 5.77/5.74 tff(10342,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10341])).
% 5.77/5.74 tff(10343,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10342, 16])).
% 5.77/5.74 tff(10344,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10343])).
% 5.77/5.74 tff(10345,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10344, 15])).
% 5.77/5.74 tff(10346,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10345])).
% 5.77/5.74 tff(10347,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10346, 25])).
% 5.77/5.74 tff(10348,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10347])).
% 5.77/5.74 tff(10349,plain,
% 5.77/5.74 (NPX4!23 = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[626, 10348, 24])).
% 5.77/5.74 tff(10350,plain,
% 5.77/5.74 (succ(NPX4!23) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10349])).
% 5.77/5.74 tff(10351,plain,
% 5.77/5.74 (succ(NPX4!23) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10350, 36])).
% 5.77/5.74 tff(10352,plain,
% 5.77/5.74 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n2, n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10351, 10321])).
% 5.77/5.74 tff(10353,plain,
% 5.77/5.74 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10352, 34])).
% 5.77/5.74 tff(10354,plain,
% 5.77/5.74 (succ(X4!53) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10327])).
% 5.77/5.74 tff(10355,plain,
% 5.77/5.74 (succ(X4!53) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10354, 36])).
% 5.77/5.74 tff(10356,plain,
% 5.77/5.74 (succ(succ(X4!53)) = succ(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10355])).
% 5.77/5.74 tff(10357,plain,
% 5.77/5.74 (succ(succ(X4!53)) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10356, 48])).
% 5.77/5.74 tff(10358,plain,
% 5.77/5.74 (succ(succ(succ(X4!53))) = succ(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10357])).
% 5.77/5.74 tff(10359,plain,
% 5.77/5.74 (succ(succ(succ(X4!53))) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10358, 14])).
% 5.77/5.74 tff(10360,plain,
% 5.77/5.74 (succ(succ(succ(succ(X4!53)))) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10359])).
% 5.77/5.74 tff(10361,plain,
% 5.77/5.74 (succ(succ(succ(succ(X4!53)))) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10360, 33])).
% 5.77/5.74 tff(10362,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(X4!53))))) = succ(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10361])).
% 5.77/5.74 tff(10363,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(X4!53))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10362, 30])).
% 5.77/5.74 tff(10364,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10363])).
% 5.77/5.74 tff(10365,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10364, 39])).
% 5.77/5.74 tff(10366,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10365])).
% 5.77/5.74 tff(10367,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10366, 53])).
% 5.77/5.74 tff(10368,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10367])).
% 5.77/5.74 tff(10369,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10368, 45])).
% 5.77/5.74 tff(10370,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10369])).
% 5.77/5.74 tff(10371,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10370, 28])).
% 5.77/5.74 tff(10372,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10371])).
% 5.77/5.74 tff(10373,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10372, 42])).
% 5.77/5.74 tff(10374,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10373])).
% 5.77/5.74 tff(10375,plain,
% 5.77/5.74 (NSX4!21 = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[651, 10374, 58])).
% 5.77/5.74 tff(10376,plain,
% 5.77/5.74 (pred(NSX4!21) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10375])).
% 5.77/5.74 tff(10377,plain,
% 5.77/5.74 (pred(NSX4!21) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10376, 23])).
% 5.77/5.74 tff(10378,plain,
% 5.77/5.74 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n0, n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10377, 10353])).
% 5.77/5.74 tff(10379,plain,
% 5.77/5.74 (Y5!50 = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[656, 10378, 442])).
% 5.77/5.74 tff(10380,plain,
% 5.77/5.74 (pred(Y5!50) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10379])).
% 5.77/5.74 tff(10381,plain,
% 5.77/5.74 (pred(Y5!50) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10380, 15])).
% 5.77/5.74 tff(10382,plain,
% 5.77/5.74 (pred(pred(Y5!50)) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10381])).
% 5.77/5.74 tff(10383,plain,
% 5.77/5.74 (pred(pred(Y5!50)) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10382, 25])).
% 5.77/5.74 tff(10384,plain,
% 5.77/5.74 (pred(pred(pred(Y5!50))) = pred(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10383])).
% 5.77/5.74 tff(10385,plain,
% 5.77/5.74 (pred(pred(pred(Y5!50))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10384, 24])).
% 5.77/5.74 tff(10386,plain,
% 5.77/5.74 (pred(pred(pred(pred(Y5!50)))) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10385])).
% 5.77/5.74 tff(10387,plain,
% 5.77/5.74 (pred(pred(pred(pred(Y5!50)))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10386, 23])).
% 5.77/5.74 tff(10388,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10387])).
% 5.77/5.74 tff(10389,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(Y5!50))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10388, 22])).
% 5.77/5.74 tff(10390,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10389])).
% 5.77/5.74 tff(10391,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10390, 21])).
% 5.77/5.74 tff(10392,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10391])).
% 5.77/5.74 tff(10393,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10392, 20])).
% 5.77/5.74 tff(10394,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10393])).
% 5.77/5.74 tff(10395,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10394, 19])).
% 5.77/5.74 tff(10396,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10395])).
% 5.77/5.74 tff(10397,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10396, 18])).
% 5.77/5.74 tff(10398,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10397])).
% 5.77/5.74 tff(10399,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10398, 17])).
% 5.77/5.74 tff(10400,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10399])).
% 5.77/5.74 tff(10401,plain,
% 5.77/5.74 (NPY5!18 = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[694, 10400, 16])).
% 5.77/5.74 tff(10402,plain,
% 5.77/5.74 (succ(NPY5!18) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10401])).
% 5.77/5.74 tff(10403,plain,
% 5.77/5.74 (succ(NPY5!18) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10402, 33])).
% 5.77/5.74 tff(10404,plain,
% 5.77/5.74 (succ(Y5!50) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10379])).
% 5.77/5.74 tff(10405,plain,
% 5.77/5.74 (succ(Y5!50) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10404, 33])).
% 5.77/5.74 tff(10406,plain,
% 5.77/5.74 (succ(succ(Y5!50)) = succ(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10405])).
% 5.77/5.74 tff(10407,plain,
% 5.77/5.74 (succ(succ(Y5!50)) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10406, 30])).
% 5.77/5.74 tff(10408,plain,
% 5.77/5.74 (succ(succ(succ(Y5!50))) = succ(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10407])).
% 5.77/5.74 tff(10409,plain,
% 5.77/5.74 (succ(succ(succ(Y5!50))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10408, 39])).
% 5.77/5.74 tff(10410,plain,
% 5.77/5.74 (succ(succ(succ(succ(Y5!50)))) = succ(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10409])).
% 5.77/5.74 tff(10411,plain,
% 5.77/5.74 (succ(succ(succ(succ(Y5!50)))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10410, 53])).
% 5.77/5.74 tff(10412,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10411])).
% 5.77/5.74 tff(10413,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(Y5!50))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10412, 45])).
% 5.77/5.74 tff(10414,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10413])).
% 5.77/5.74 tff(10415,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10414, 28])).
% 5.77/5.74 tff(10416,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10415])).
% 5.77/5.74 tff(10417,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10416, 42])).
% 5.77/5.74 tff(10418,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10417])).
% 5.77/5.74 tff(10419,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10418, 58])).
% 5.77/5.74 tff(10420,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10419])).
% 5.77/5.74 tff(10421,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10420, 36])).
% 5.77/5.74 tff(10422,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10421])).
% 5.77/5.74 tff(10423,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10422, 48])).
% 5.77/5.74 tff(10424,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10423])).
% 5.77/5.74 tff(10425,plain,
% 5.77/5.74 (NSY5!16 = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[717, 10424, 14])).
% 5.77/5.74 tff(10426,plain,
% 5.77/5.74 (pred(NSY5!16) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10425])).
% 5.77/5.74 tff(10427,plain,
% 5.77/5.74 (pred(NSY5!16) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10426, 15])).
% 5.77/5.74 tff(10428,plain,
% 5.77/5.74 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n3, n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10427, 10403])).
% 5.77/5.74 tff(10429,plain,
% 5.77/5.74 (sum(pred(NSY5!16), succ(NPY5!18)) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10428, 32])).
% 5.77/5.74 tff(10430,plain,
% 5.77/5.74 (sum(pred(Y4!52), succ(X4!53)) = sum(n0, n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10273, 10355])).
% 5.77/5.74 tff(10431,plain,
% 5.77/5.74 (sum(pred(Y4!52), succ(X4!53)) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10430, 35])).
% 5.77/5.74 tff(10432,plain,
% 5.77/5.74 (sum(pred(X4!53), succ(Y4!52)) = sum(n0, n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10329, 10297])).
% 5.77/5.74 tff(10433,plain,
% 5.77/5.74 (sum(pred(X4!53), succ(Y4!52)) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10432, 35])).
% 5.77/5.74 tff(10434,plain,
% 5.77/5.74 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n2, n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10433, 10431])).
% 5.77/5.74 tff(10435,plain,
% 5.77/5.74 (X5!51 = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[553, 10434, 34])).
% 5.77/5.74 tff(10436,plain,
% 5.77/5.74 (pred(X5!51) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10435])).
% 5.77/5.74 tff(10437,plain,
% 5.77/5.74 (pred(X5!51) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10436, 15])).
% 5.77/5.74 tff(10438,plain,
% 5.77/5.74 (pred(pred(X5!51)) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10437])).
% 5.77/5.74 tff(10439,plain,
% 5.77/5.74 (pred(pred(X5!51)) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10438, 25])).
% 5.77/5.74 tff(10440,plain,
% 5.77/5.74 (pred(pred(pred(X5!51))) = pred(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10439])).
% 5.77/5.74 tff(10441,plain,
% 5.77/5.74 (pred(pred(pred(X5!51))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10440, 24])).
% 5.77/5.74 tff(10442,plain,
% 5.77/5.74 (pred(pred(pred(pred(X5!51)))) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10441])).
% 5.77/5.74 tff(10443,plain,
% 5.77/5.74 (pred(pred(pred(pred(X5!51)))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10442, 23])).
% 5.77/5.74 tff(10444,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X5!51))))) = pred(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10443])).
% 5.77/5.74 tff(10445,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X5!51))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10444, 22])).
% 5.77/5.74 tff(10446,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10445])).
% 5.77/5.74 tff(10447,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10446, 21])).
% 5.77/5.74 tff(10448,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10447])).
% 5.77/5.74 tff(10449,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10448, 20])).
% 5.77/5.74 tff(10450,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10449])).
% 5.77/5.74 tff(10451,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10450, 19])).
% 5.77/5.74 tff(10452,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10451])).
% 5.77/5.74 tff(10453,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10452, 18])).
% 5.77/5.74 tff(10454,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10453])).
% 5.77/5.74 tff(10455,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10454, 17])).
% 5.77/5.74 tff(10456,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10455])).
% 5.77/5.74 tff(10457,plain,
% 5.77/5.74 (NPX5!19 = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[742, 10456, 16])).
% 5.77/5.74 tff(10458,plain,
% 5.77/5.74 (succ(NPX5!19) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10457])).
% 5.77/5.74 tff(10459,plain,
% 5.77/5.74 (succ(NPX5!19) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10458, 33])).
% 5.77/5.74 tff(10460,plain,
% 5.77/5.74 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n5, n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10459, 10429])).
% 5.77/5.74 tff(10461,plain,
% 5.77/5.74 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10460, 558])).
% 5.77/5.74 tff(10462,plain,
% 5.77/5.74 (succ(X5!51) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10435])).
% 5.77/5.74 tff(10463,plain,
% 5.77/5.74 (succ(X5!51) = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[10462, 33])).
% 5.77/5.74 tff(10464,plain,
% 5.77/5.74 (succ(succ(X5!51)) = succ(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10463])).
% 5.77/5.74 tff(10465,plain,
% 5.77/5.74 (succ(succ(X5!51)) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10464, 30])).
% 5.77/5.74 tff(10466,plain,
% 5.77/5.74 (succ(succ(succ(X5!51))) = succ(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10465])).
% 5.77/5.74 tff(10467,plain,
% 5.77/5.74 (succ(succ(succ(X5!51))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10466, 39])).
% 5.77/5.74 tff(10468,plain,
% 5.77/5.74 (succ(succ(succ(succ(X5!51)))) = succ(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10467])).
% 5.77/5.74 tff(10469,plain,
% 5.77/5.74 (succ(succ(succ(succ(X5!51)))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10468, 53])).
% 5.77/5.74 tff(10470,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(X5!51))))) = succ(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10469])).
% 5.77/5.74 tff(10471,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(X5!51))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10470, 45])).
% 5.77/5.74 tff(10472,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10471])).
% 5.77/5.74 tff(10473,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10472, 28])).
% 5.77/5.74 tff(10474,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10473])).
% 5.77/5.74 tff(10475,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10474, 42])).
% 5.77/5.74 tff(10476,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10475])).
% 5.77/5.74 tff(10477,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10476, 58])).
% 5.77/5.74 tff(10478,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10477])).
% 5.77/5.74 tff(10479,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10478, 36])).
% 5.77/5.74 tff(10480,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10479])).
% 5.77/5.74 tff(10481,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10480, 48])).
% 5.77/5.74 tff(10482,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10481])).
% 5.77/5.74 tff(10483,plain,
% 5.77/5.74 (NSX5!17 = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[767, 10482, 14])).
% 5.77/5.74 tff(10484,plain,
% 5.77/5.74 (pred(NSX5!17) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10483])).
% 5.77/5.74 tff(10485,plain,
% 5.77/5.74 (pred(NSX5!17) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10484, 15])).
% 5.77/5.74 tff(10486,plain,
% 5.77/5.74 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n3, n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10485, 10461])).
% 5.77/5.74 tff(10487,plain,
% 5.77/5.74 (Y6!48 = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[772, 10486, 557])).
% 5.77/5.74 tff(10488,plain,
% 5.77/5.74 (pred(Y6!48) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10487])).
% 5.77/5.74 tff(10489,plain,
% 5.77/5.74 (pred(Y6!48) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10488, 16])).
% 5.77/5.74 tff(10490,plain,
% 5.77/5.74 (pred(pred(Y6!48)) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10489])).
% 5.77/5.74 tff(10491,plain,
% 5.77/5.74 (pred(pred(Y6!48)) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10490, 15])).
% 5.77/5.74 tff(10492,plain,
% 5.77/5.74 (pred(pred(pred(Y6!48))) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10491])).
% 5.77/5.74 tff(10493,plain,
% 5.77/5.74 (pred(pred(pred(Y6!48))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10492, 25])).
% 5.77/5.74 tff(10494,plain,
% 5.77/5.74 (pred(pred(pred(pred(Y6!48)))) = pred(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10493])).
% 5.77/5.74 tff(10495,plain,
% 5.77/5.74 (pred(pred(pred(pred(Y6!48)))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10494, 24])).
% 5.77/5.74 tff(10496,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10495])).
% 5.77/5.74 tff(10497,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(Y6!48))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10496, 23])).
% 5.77/5.74 tff(10498,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10497])).
% 5.77/5.74 tff(10499,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10498, 22])).
% 5.77/5.74 tff(10500,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10499])).
% 5.77/5.74 tff(10501,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10500, 21])).
% 5.77/5.74 tff(10502,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10501])).
% 5.77/5.74 tff(10503,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10502, 20])).
% 5.77/5.74 tff(10504,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10503])).
% 5.77/5.74 tff(10505,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10504, 19])).
% 5.77/5.74 tff(10506,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10505])).
% 5.77/5.74 tff(10507,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10506, 18])).
% 5.77/5.74 tff(10508,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10507])).
% 5.77/5.74 tff(10509,plain,
% 5.77/5.74 (NPY6!14 = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[1465, 10508, 17])).
% 5.77/5.74 tff(10510,plain,
% 5.77/5.74 (succ(NPY6!14) = succ(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10509])).
% 5.77/5.74 tff(10511,plain,
% 5.77/5.74 (succ(NPY6!14) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10510, 30])).
% 5.77/5.74 tff(10512,plain,
% 5.77/5.74 (succ(Y6!48) = succ(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10487])).
% 5.77/5.74 tff(10513,plain,
% 5.77/5.74 (succ(Y6!48) = n6),
% 5.77/5.74 inference(transitivity,[status(thm)],[10512, 30])).
% 5.77/5.74 tff(10514,plain,
% 5.77/5.74 (succ(succ(Y6!48)) = succ(n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10513])).
% 5.77/5.74 tff(10515,plain,
% 5.77/5.74 (succ(succ(Y6!48)) = n7),
% 5.77/5.74 inference(transitivity,[status(thm)],[10514, 39])).
% 5.77/5.74 tff(10516,plain,
% 5.77/5.74 (succ(succ(succ(Y6!48))) = succ(n7)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10515])).
% 5.77/5.74 tff(10517,plain,
% 5.77/5.74 (succ(succ(succ(Y6!48))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10516, 53])).
% 5.77/5.74 tff(10518,plain,
% 5.77/5.74 (succ(succ(succ(succ(Y6!48)))) = succ(n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10517])).
% 5.77/5.74 tff(10519,plain,
% 5.77/5.74 (succ(succ(succ(succ(Y6!48)))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10518, 45])).
% 5.77/5.74 tff(10520,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10519])).
% 5.77/5.74 tff(10521,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(Y6!48))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10520, 28])).
% 5.77/5.74 tff(10522,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10521])).
% 5.77/5.74 tff(10523,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10522, 42])).
% 5.77/5.74 tff(10524,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10523])).
% 5.77/5.74 tff(10525,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10524, 58])).
% 5.77/5.74 tff(10526,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10525])).
% 5.77/5.74 tff(10527,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10526, 36])).
% 5.77/5.74 tff(10528,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10527])).
% 5.77/5.74 tff(10529,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10528, 48])).
% 5.77/5.74 tff(10530,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10529])).
% 5.77/5.74 tff(10531,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10530, 14])).
% 5.77/5.74 tff(10532,plain,
% 5.77/5.74 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10531])).
% 5.77/5.74 tff(10533,plain,
% 5.77/5.74 (NSY6!12 = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[1490, 10532, 33])).
% 5.77/5.74 tff(10534,plain,
% 5.77/5.74 (pred(NSY6!12) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10533])).
% 5.77/5.74 tff(10535,plain,
% 5.77/5.74 (pred(NSY6!12) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10534, 16])).
% 5.77/5.74 tff(10536,plain,
% 5.77/5.74 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n4, n6)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10535, 10511])).
% 5.77/5.74 tff(10537,plain,
% 5.77/5.74 (sum(pred(NSY6!12), succ(NPY6!14)) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10536, 12])).
% 5.77/5.74 tff(10538,plain,
% 5.77/5.74 (sum(pred(Y5!50), succ(X5!51)) = sum(n3, n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10381, 10463])).
% 5.77/5.74 tff(10539,plain,
% 5.77/5.74 (sum(pred(Y5!50), succ(X5!51)) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10538, 32])).
% 5.77/5.74 tff(10540,plain,
% 5.77/5.74 (sum(pred(X5!51), succ(Y5!50)) = sum(n3, n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10437, 10405])).
% 5.77/5.74 tff(10541,plain,
% 5.77/5.74 (sum(pred(X5!51), succ(Y5!50)) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10540, 32])).
% 5.77/5.74 tff(10542,plain,
% 5.77/5.74 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n8, n8)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10541, 10539])).
% 5.77/5.74 tff(10543,plain,
% 5.77/5.74 (X6!49 = n5),
% 5.77/5.74 inference(transitivity,[status(thm)],[669, 10542, 31])).
% 5.77/5.74 tff(10544,plain,
% 5.77/5.74 (pred(X6!49) = pred(n5)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10543])).
% 5.77/5.74 tff(10545,plain,
% 5.77/5.74 (pred(X6!49) = n4),
% 5.77/5.74 inference(transitivity,[status(thm)],[10544, 16])).
% 5.77/5.74 tff(10546,plain,
% 5.77/5.74 (pred(pred(X6!49)) = pred(n4)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10545])).
% 5.77/5.74 tff(10547,plain,
% 5.77/5.74 (pred(pred(X6!49)) = n3),
% 5.77/5.74 inference(transitivity,[status(thm)],[10546, 15])).
% 5.77/5.74 tff(10548,plain,
% 5.77/5.74 (pred(pred(pred(X6!49))) = pred(n3)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10547])).
% 5.77/5.74 tff(10549,plain,
% 5.77/5.74 (pred(pred(pred(X6!49))) = n2),
% 5.77/5.74 inference(transitivity,[status(thm)],[10548, 25])).
% 5.77/5.74 tff(10550,plain,
% 5.77/5.74 (pred(pred(pred(pred(X6!49)))) = pred(n2)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10549])).
% 5.77/5.74 tff(10551,plain,
% 5.77/5.74 (pred(pred(pred(pred(X6!49)))) = n1),
% 5.77/5.74 inference(transitivity,[status(thm)],[10550, 24])).
% 5.77/5.74 tff(10552,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X6!49))))) = pred(n1)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10551])).
% 5.77/5.74 tff(10553,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(X6!49))))) = n0),
% 5.77/5.74 inference(transitivity,[status(thm)],[10552, 23])).
% 5.77/5.74 tff(10554,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n0)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10553])).
% 5.77/5.74 tff(10555,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n10),
% 5.77/5.74 inference(transitivity,[status(thm)],[10554, 22])).
% 5.77/5.74 tff(10556,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n10)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10555])).
% 5.77/5.74 tff(10557,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n9),
% 5.77/5.74 inference(transitivity,[status(thm)],[10556, 21])).
% 5.77/5.74 tff(10558,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n9)),
% 5.77/5.74 inference(monotonicity,[status(thm)],[10557])).
% 5.77/5.74 tff(10559,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n8),
% 5.77/5.74 inference(transitivity,[status(thm)],[10558, 20])).
% 5.77/5.74 tff(10560,plain,
% 5.77/5.74 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10559])).
% 5.77/5.75 tff(10561,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10560, 19])).
% 5.77/5.75 tff(10562,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10561])).
% 5.77/5.75 tff(10563,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10562, 18])).
% 5.77/5.75 tff(10564,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10563])).
% 5.77/5.75 tff(10565,plain,
% 5.77/5.75 (NPX6!15 = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[1523, 10564, 17])).
% 5.77/5.75 tff(10566,plain,
% 5.77/5.75 (succ(NPX6!15) = succ(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10565])).
% 5.77/5.75 tff(10567,plain,
% 5.77/5.75 (succ(NPX6!15) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10566, 30])).
% 5.77/5.75 tff(10568,plain,
% 5.77/5.75 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n6, n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10567, 10537])).
% 5.77/5.75 tff(10569,plain,
% 5.77/5.75 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10568, 674])).
% 5.77/5.75 tff(10570,plain,
% 5.77/5.75 (succ(X6!49) = succ(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10543])).
% 5.77/5.75 tff(10571,plain,
% 5.77/5.75 (succ(X6!49) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10570, 30])).
% 5.77/5.75 tff(10572,plain,
% 5.77/5.75 (succ(succ(X6!49)) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10571])).
% 5.77/5.75 tff(10573,plain,
% 5.77/5.75 (succ(succ(X6!49)) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10572, 39])).
% 5.77/5.75 tff(10574,plain,
% 5.77/5.75 (succ(succ(succ(X6!49))) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10573])).
% 5.77/5.75 tff(10575,plain,
% 5.77/5.75 (succ(succ(succ(X6!49))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10574, 53])).
% 5.77/5.75 tff(10576,plain,
% 5.77/5.75 (succ(succ(succ(succ(X6!49)))) = succ(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10575])).
% 5.77/5.75 tff(10577,plain,
% 5.77/5.75 (succ(succ(succ(succ(X6!49)))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10576, 45])).
% 5.77/5.75 tff(10578,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(X6!49))))) = succ(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10577])).
% 5.77/5.75 tff(10579,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(X6!49))))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10578, 28])).
% 5.77/5.75 tff(10580,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10579])).
% 5.77/5.75 tff(10581,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10580, 42])).
% 5.77/5.75 tff(10582,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10581])).
% 5.77/5.75 tff(10583,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10582, 58])).
% 5.77/5.75 tff(10584,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10583])).
% 5.77/5.75 tff(10585,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10584, 36])).
% 5.77/5.75 tff(10586,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10585])).
% 5.77/5.75 tff(10587,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10586, 48])).
% 5.77/5.75 tff(10588,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10587])).
% 5.77/5.75 tff(10589,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10588, 14])).
% 5.77/5.75 tff(10590,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10589])).
% 5.77/5.75 tff(10591,plain,
% 5.77/5.75 (NSX6!13 = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[1550, 10590, 33])).
% 5.77/5.75 tff(10592,plain,
% 5.77/5.75 (pred(NSX6!13) = pred(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10591])).
% 5.77/5.75 tff(10593,plain,
% 5.77/5.75 (pred(NSX6!13) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10592, 16])).
% 5.77/5.75 tff(10594,plain,
% 5.77/5.75 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n4, n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10593, 10569])).
% 5.77/5.75 tff(10595,plain,
% 5.77/5.75 (sum(n4, n5) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.77/5.75 inference(symmetry,[status(thm)],[10594])).
% 5.77/5.75 tff(10596,plain,
% 5.77/5.75 (n9 = sum(n4, n5)),
% 5.77/5.75 inference(symmetry,[status(thm)],[673])).
% 5.77/5.75 tff(10597,plain,
% 5.77/5.75 (sum(pred(Y6!48), succ(X6!49)) = sum(n4, n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10489, 10571])).
% 5.77/5.75 tff(10598,plain,
% 5.77/5.75 (sum(pred(Y6!48), succ(X6!49)) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10597, 12])).
% 5.77/5.75 tff(10599,plain,
% 5.77/5.75 (sum(pred(X6!49), succ(Y6!48)) = sum(n4, n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10545, 10513])).
% 5.77/5.75 tff(10600,plain,
% 5.77/5.75 (sum(pred(X6!49), succ(Y6!48)) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10599, 12])).
% 5.77/5.75 tff(10601,plain,
% 5.77/5.75 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n10, n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10600, 10598])).
% 5.77/5.75 tff(10602,plain,
% 5.77/5.75 (X7!47 = Y7!46),
% 5.77/5.75 inference(transitivity,[status(thm)],[785, 10601, 29, 10596, 10595, 794])).
% 5.77/5.75 tff(10603,plain,
% 5.77/5.75 ($false),
% 5.77/5.75 inference(unit_resolution,[status(thm)],[792, 10602])).
% 5.77/5.75 tff(10604,plain,((~(X0!61 = n8)) | (X7!47 = Y7!46) | (~(Y0!60 = n0))), inference(lemma,lemma(discharge,[]))).
% 5.77/5.75 tff(10605,plain,
% 5.77/5.75 (~(X0!61 = n8)),
% 5.77/5.75 inference(unit_resolution,[status(thm)],[10604, 9225, 792])).
% 5.77/5.75 tff(10606,plain,
% 5.77/5.75 (sum(n10, n0) = n10),
% 5.77/5.75 inference(and_elim,[status(thm)],[9])).
% 5.77/5.75 tff(10607,plain,
% 5.77/5.75 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n10, n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[2362, 9275])).
% 5.77/5.75 tff(10608,plain,
% 5.77/5.75 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10607, 10606])).
% 5.77/5.75 tff(10609,plain,
% 5.77/5.75 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n8, n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[2388, 10608])).
% 5.77/5.75 tff(10610,plain,
% 5.77/5.75 (Y1!58 = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[196, 10609, 27])).
% 5.77/5.75 tff(10611,plain,
% 5.77/5.75 (pred(Y1!58) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10610])).
% 5.77/5.75 tff(10612,plain,
% 5.77/5.75 (pred(Y1!58) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10611, 18])).
% 5.77/5.75 tff(10613,plain,
% 5.77/5.75 (pred(pred(Y1!58)) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10612])).
% 5.77/5.75 tff(10614,plain,
% 5.77/5.75 (pred(pred(Y1!58)) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10613, 17])).
% 5.77/5.75 tff(10615,plain,
% 5.77/5.75 (pred(pred(pred(Y1!58))) = pred(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10614])).
% 5.77/5.75 tff(10616,plain,
% 5.77/5.75 (pred(pred(pred(Y1!58))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10615, 16])).
% 5.77/5.75 tff(10617,plain,
% 5.77/5.75 (pred(pred(pred(pred(Y1!58)))) = pred(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10616])).
% 5.77/5.75 tff(10618,plain,
% 5.77/5.75 (pred(pred(pred(pred(Y1!58)))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10617, 15])).
% 5.77/5.75 tff(10619,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10618])).
% 5.77/5.75 tff(10620,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(Y1!58))))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10619, 25])).
% 5.77/5.75 tff(10621,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10620])).
% 5.77/5.75 tff(10622,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10621, 24])).
% 5.77/5.75 tff(10623,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10622])).
% 5.77/5.75 tff(10624,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10623, 23])).
% 5.77/5.75 tff(10625,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10624])).
% 5.77/5.75 tff(10626,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10625, 22])).
% 5.77/5.75 tff(10627,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10626])).
% 5.77/5.75 tff(10628,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10627, 21])).
% 5.77/5.75 tff(10629,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10628])).
% 5.77/5.75 tff(10630,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10629, 20])).
% 5.77/5.75 tff(10631,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10630])).
% 5.77/5.75 tff(10632,plain,
% 5.77/5.75 (NPY1!34 = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[232, 10631, 19])).
% 5.77/5.75 tff(10633,plain,
% 5.77/5.75 (succ(NPY1!34) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10632])).
% 5.77/5.75 tff(10634,plain,
% 5.77/5.75 (succ(NPY1!34) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10633, 53])).
% 5.77/5.75 tff(10635,plain,
% 5.77/5.75 (succ(Y1!58) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10610])).
% 5.77/5.75 tff(10636,plain,
% 5.77/5.75 (succ(Y1!58) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10635, 53])).
% 5.77/5.75 tff(10637,plain,
% 5.77/5.75 (succ(succ(Y1!58)) = succ(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10636])).
% 5.77/5.75 tff(10638,plain,
% 5.77/5.75 (succ(succ(Y1!58)) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10637, 45])).
% 5.77/5.75 tff(10639,plain,
% 5.77/5.75 (succ(succ(succ(Y1!58))) = succ(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10638])).
% 5.77/5.75 tff(10640,plain,
% 5.77/5.75 (succ(succ(succ(Y1!58))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10639, 28])).
% 5.77/5.75 tff(10641,plain,
% 5.77/5.75 (succ(succ(succ(succ(Y1!58)))) = succ(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10640])).
% 5.77/5.75 tff(10642,plain,
% 5.77/5.75 (succ(succ(succ(succ(Y1!58)))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10641, 42])).
% 5.77/5.75 tff(10643,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10642])).
% 5.77/5.75 tff(10644,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(Y1!58))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10643, 58])).
% 5.77/5.75 tff(10645,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10644])).
% 5.77/5.75 tff(10646,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10645, 36])).
% 5.77/5.75 tff(10647,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10646])).
% 5.77/5.75 tff(10648,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10647, 48])).
% 5.77/5.75 tff(10649,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10648])).
% 5.77/5.75 tff(10650,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10649, 14])).
% 5.77/5.75 tff(10651,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10650])).
% 5.77/5.75 tff(10652,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10651, 33])).
% 5.77/5.75 tff(10653,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10652])).
% 5.77/5.75 tff(10654,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10653, 30])).
% 5.77/5.75 tff(10655,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10654])).
% 5.77/5.75 tff(10656,plain,
% 5.77/5.75 (NSY1!32 = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[255, 10655, 39])).
% 5.77/5.75 tff(10657,plain,
% 5.77/5.75 (pred(NSY1!32) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10656])).
% 5.77/5.75 tff(10658,plain,
% 5.77/5.75 (pred(NSY1!32) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10657, 18])).
% 5.77/5.75 tff(10659,plain,
% 5.77/5.75 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n6, n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10658, 10634])).
% 5.77/5.75 tff(10660,plain,
% 5.77/5.75 (sum(pred(NSY1!32), succ(NPY1!34)) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10659, 52])).
% 5.77/5.75 tff(10661,plain,
% 5.77/5.75 (sum(pred(Y0!60), succ(X0!61)) = sum(n10, n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[9227, 2366])).
% 5.77/5.75 tff(10662,plain,
% 5.77/5.75 (sum(pred(Y0!60), succ(X0!61)) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10661, 29])).
% 5.77/5.75 tff(10663,plain,
% 5.77/5.75 (sum(pred(X0!61), succ(Y0!60)) = sum(n8, n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[2340, 9251])).
% 5.77/5.75 tff(10664,plain,
% 5.77/5.75 (sum(pred(X0!61), succ(Y0!60)) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10663, 1571])).
% 5.77/5.75 tff(10665,plain,
% 5.77/5.75 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n9, n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10664, 10662])).
% 5.77/5.75 tff(10666,plain,
% 5.77/5.75 (X1!59 = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[93, 10665, 54])).
% 5.77/5.75 tff(10667,plain,
% 5.77/5.75 (pred(X1!59) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10666])).
% 5.77/5.75 tff(10668,plain,
% 5.77/5.75 (pred(X1!59) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10667, 18])).
% 5.77/5.75 tff(10669,plain,
% 5.77/5.75 (pred(pred(X1!59)) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10668])).
% 5.77/5.75 tff(10670,plain,
% 5.77/5.75 (pred(pred(X1!59)) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10669, 17])).
% 5.77/5.75 tff(10671,plain,
% 5.77/5.75 (pred(pred(pred(X1!59))) = pred(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10670])).
% 5.77/5.75 tff(10672,plain,
% 5.77/5.75 (pred(pred(pred(X1!59))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10671, 16])).
% 5.77/5.75 tff(10673,plain,
% 5.77/5.75 (pred(pred(pred(pred(X1!59)))) = pred(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10672])).
% 5.77/5.75 tff(10674,plain,
% 5.77/5.75 (pred(pred(pred(pred(X1!59)))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10673, 15])).
% 5.77/5.75 tff(10675,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(X1!59))))) = pred(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10674])).
% 5.77/5.75 tff(10676,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(X1!59))))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10675, 25])).
% 5.77/5.75 tff(10677,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10676])).
% 5.77/5.75 tff(10678,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10677, 24])).
% 5.77/5.75 tff(10679,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10678])).
% 5.77/5.75 tff(10680,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10679, 23])).
% 5.77/5.75 tff(10681,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10680])).
% 5.77/5.75 tff(10682,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10681, 22])).
% 5.77/5.75 tff(10683,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10682])).
% 5.77/5.75 tff(10684,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10683, 21])).
% 5.77/5.75 tff(10685,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10684])).
% 5.77/5.75 tff(10686,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10685, 20])).
% 5.77/5.75 tff(10687,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10686])).
% 5.77/5.75 tff(10688,plain,
% 5.77/5.75 (NPX1!35 = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[280, 10687, 19])).
% 5.77/5.75 tff(10689,plain,
% 5.77/5.75 (succ(NPX1!35) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10688])).
% 5.77/5.75 tff(10690,plain,
% 5.77/5.75 (succ(NPX1!35) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10689, 53])).
% 5.77/5.75 tff(10691,plain,
% 5.77/5.75 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n8, n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10690, 10660])).
% 5.77/5.75 tff(10692,plain,
% 5.77/5.75 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10691, 64])).
% 5.77/5.75 tff(10693,plain,
% 5.77/5.75 (succ(X1!59) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10666])).
% 5.77/5.75 tff(10694,plain,
% 5.77/5.75 (succ(X1!59) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10693, 53])).
% 5.77/5.75 tff(10695,plain,
% 5.77/5.75 (succ(succ(X1!59)) = succ(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10694])).
% 5.77/5.75 tff(10696,plain,
% 5.77/5.75 (succ(succ(X1!59)) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10695, 45])).
% 5.77/5.75 tff(10697,plain,
% 5.77/5.75 (succ(succ(succ(X1!59))) = succ(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10696])).
% 5.77/5.75 tff(10698,plain,
% 5.77/5.75 (succ(succ(succ(X1!59))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10697, 28])).
% 5.77/5.75 tff(10699,plain,
% 5.77/5.75 (succ(succ(succ(succ(X1!59)))) = succ(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10698])).
% 5.77/5.75 tff(10700,plain,
% 5.77/5.75 (succ(succ(succ(succ(X1!59)))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10699, 42])).
% 5.77/5.75 tff(10701,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(X1!59))))) = succ(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10700])).
% 5.77/5.75 tff(10702,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(X1!59))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10701, 58])).
% 5.77/5.75 tff(10703,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10702])).
% 5.77/5.75 tff(10704,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10703, 36])).
% 5.77/5.75 tff(10705,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10704])).
% 5.77/5.75 tff(10706,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10705, 48])).
% 5.77/5.75 tff(10707,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10706])).
% 5.77/5.75 tff(10708,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10707, 14])).
% 5.77/5.75 tff(10709,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10708])).
% 5.77/5.75 tff(10710,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10709, 33])).
% 5.77/5.75 tff(10711,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10710])).
% 5.77/5.75 tff(10712,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10711, 30])).
% 5.77/5.75 tff(10713,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10712])).
% 5.77/5.75 tff(10714,plain,
% 5.77/5.75 (NSX1!33 = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[305, 10713, 39])).
% 5.77/5.75 tff(10715,plain,
% 5.77/5.75 (pred(NSX1!33) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10714])).
% 5.77/5.75 tff(10716,plain,
% 5.77/5.75 (pred(NSX1!33) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10715, 18])).
% 5.77/5.75 tff(10717,plain,
% 5.77/5.75 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n6, n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10716, 10692])).
% 5.77/5.75 tff(10718,plain,
% 5.77/5.75 (Y2!56 = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[310, 10717, 788])).
% 5.77/5.75 tff(10719,plain,
% 5.77/5.75 (pred(Y2!56) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10718])).
% 5.77/5.75 tff(10720,plain,
% 5.77/5.75 (pred(Y2!56) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10719, 17])).
% 5.77/5.75 tff(10721,plain,
% 5.77/5.75 (pred(pred(Y2!56)) = pred(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10720])).
% 5.77/5.75 tff(10722,plain,
% 5.77/5.75 (pred(pred(Y2!56)) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10721, 16])).
% 5.77/5.75 tff(10723,plain,
% 5.77/5.75 (pred(pred(pred(Y2!56))) = pred(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10722])).
% 5.77/5.75 tff(10724,plain,
% 5.77/5.75 (pred(pred(pred(Y2!56))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10723, 15])).
% 5.77/5.75 tff(10725,plain,
% 5.77/5.75 (pred(pred(pred(pred(Y2!56)))) = pred(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10724])).
% 5.77/5.75 tff(10726,plain,
% 5.77/5.75 (pred(pred(pred(pred(Y2!56)))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10725, 25])).
% 5.77/5.75 tff(10727,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10726])).
% 5.77/5.75 tff(10728,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(Y2!56))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10727, 24])).
% 5.77/5.75 tff(10729,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10728])).
% 5.77/5.75 tff(10730,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10729, 23])).
% 5.77/5.75 tff(10731,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10730])).
% 5.77/5.75 tff(10732,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10731, 22])).
% 5.77/5.75 tff(10733,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10732])).
% 5.77/5.75 tff(10734,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10733, 21])).
% 5.77/5.75 tff(10735,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10734])).
% 5.77/5.75 tff(10736,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10735, 20])).
% 5.77/5.75 tff(10737,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10736])).
% 5.77/5.75 tff(10738,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10737, 19])).
% 5.77/5.75 tff(10739,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10738])).
% 5.77/5.75 tff(10740,plain,
% 5.77/5.75 (NPY2!30 = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[347, 10739, 18])).
% 5.77/5.75 tff(10741,plain,
% 5.77/5.75 (succ(NPY2!30) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10740])).
% 5.77/5.75 tff(10742,plain,
% 5.77/5.75 (succ(NPY2!30) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10741, 39])).
% 5.77/5.75 tff(10743,plain,
% 5.77/5.75 (succ(Y2!56) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10718])).
% 5.77/5.75 tff(10744,plain,
% 5.77/5.75 (succ(Y2!56) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10743, 39])).
% 5.77/5.75 tff(10745,plain,
% 5.77/5.75 (succ(succ(Y2!56)) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10744])).
% 5.77/5.75 tff(10746,plain,
% 5.77/5.75 (succ(succ(Y2!56)) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10745, 53])).
% 5.77/5.75 tff(10747,plain,
% 5.77/5.75 (succ(succ(succ(Y2!56))) = succ(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10746])).
% 5.77/5.75 tff(10748,plain,
% 5.77/5.75 (succ(succ(succ(Y2!56))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10747, 45])).
% 5.77/5.75 tff(10749,plain,
% 5.77/5.75 (succ(succ(succ(succ(Y2!56)))) = succ(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10748])).
% 5.77/5.75 tff(10750,plain,
% 5.77/5.75 (succ(succ(succ(succ(Y2!56)))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10749, 28])).
% 5.77/5.75 tff(10751,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10750])).
% 5.77/5.75 tff(10752,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(Y2!56))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10751, 42])).
% 5.77/5.75 tff(10753,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10752])).
% 5.77/5.75 tff(10754,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10753, 58])).
% 5.77/5.75 tff(10755,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10754])).
% 5.77/5.75 tff(10756,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10755, 36])).
% 5.77/5.75 tff(10757,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10756])).
% 5.77/5.75 tff(10758,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10757, 48])).
% 5.77/5.75 tff(10759,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10758])).
% 5.77/5.75 tff(10760,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10759, 14])).
% 5.77/5.75 tff(10761,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10760])).
% 5.77/5.75 tff(10762,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10761, 33])).
% 5.77/5.75 tff(10763,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10762])).
% 5.77/5.75 tff(10764,plain,
% 5.77/5.75 (NSY2!28 = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[370, 10763, 30])).
% 5.77/5.75 tff(10765,plain,
% 5.77/5.75 (pred(NSY2!28) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10764])).
% 5.77/5.75 tff(10766,plain,
% 5.77/5.75 (pred(NSY2!28) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10765, 17])).
% 5.77/5.75 tff(10767,plain,
% 5.77/5.75 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n5, n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10766, 10742])).
% 5.77/5.75 tff(10768,plain,
% 5.77/5.75 (sum(pred(NSY2!28), succ(NPY2!30)) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10767, 50])).
% 5.77/5.75 tff(10769,plain,
% 5.77/5.75 (sum(pred(Y1!58), succ(X1!59)) = sum(n6, n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10612, 10694])).
% 5.77/5.75 tff(10770,plain,
% 5.77/5.75 (sum(pred(Y1!58), succ(X1!59)) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10769, 52])).
% 5.77/5.75 tff(10771,plain,
% 5.77/5.75 (sum(pred(X1!59), succ(Y1!58)) = sum(n6, n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10668, 10636])).
% 5.77/5.75 tff(10772,plain,
% 5.77/5.75 (sum(pred(X1!59), succ(Y1!58)) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10771, 52])).
% 5.77/5.75 tff(10773,plain,
% 5.77/5.75 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n3, n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10772, 10770])).
% 5.77/5.75 tff(10774,plain,
% 5.77/5.75 (X2!57 = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[209, 10773, 51])).
% 5.77/5.75 tff(10775,plain,
% 5.77/5.75 (pred(X2!57) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10774])).
% 5.77/5.75 tff(10776,plain,
% 5.77/5.75 (pred(X2!57) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10775, 17])).
% 5.77/5.75 tff(10777,plain,
% 5.77/5.75 (pred(pred(X2!57)) = pred(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10776])).
% 5.77/5.75 tff(10778,plain,
% 5.77/5.75 (pred(pred(X2!57)) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10777, 16])).
% 5.77/5.75 tff(10779,plain,
% 5.77/5.75 (pred(pred(pred(X2!57))) = pred(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10778])).
% 5.77/5.75 tff(10780,plain,
% 5.77/5.75 (pred(pred(pred(X2!57))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10779, 15])).
% 5.77/5.75 tff(10781,plain,
% 5.77/5.75 (pred(pred(pred(pred(X2!57)))) = pred(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10780])).
% 5.77/5.75 tff(10782,plain,
% 5.77/5.75 (pred(pred(pred(pred(X2!57)))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10781, 25])).
% 5.77/5.75 tff(10783,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(X2!57))))) = pred(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10782])).
% 5.77/5.75 tff(10784,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(X2!57))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10783, 24])).
% 5.77/5.75 tff(10785,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10784])).
% 5.77/5.75 tff(10786,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10785, 23])).
% 5.77/5.75 tff(10787,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10786])).
% 5.77/5.75 tff(10788,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10787, 22])).
% 5.77/5.75 tff(10789,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10788])).
% 5.77/5.75 tff(10790,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10789, 21])).
% 5.77/5.75 tff(10791,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10790])).
% 5.77/5.75 tff(10792,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10791, 20])).
% 5.77/5.75 tff(10793,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10792])).
% 5.77/5.75 tff(10794,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10793, 19])).
% 5.77/5.75 tff(10795,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10794])).
% 5.77/5.75 tff(10796,plain,
% 5.77/5.75 (NPX2!31 = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[395, 10795, 18])).
% 5.77/5.75 tff(10797,plain,
% 5.77/5.75 (succ(NPX2!31) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10796])).
% 5.77/5.75 tff(10798,plain,
% 5.77/5.75 (succ(NPX2!31) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10797, 39])).
% 5.77/5.75 tff(10799,plain,
% 5.77/5.75 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n7, n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10798, 10768])).
% 5.77/5.75 tff(10800,plain,
% 5.77/5.75 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10799, 787])).
% 5.77/5.75 tff(10801,plain,
% 5.77/5.75 (succ(X2!57) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10774])).
% 5.77/5.75 tff(10802,plain,
% 5.77/5.75 (succ(X2!57) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10801, 39])).
% 5.77/5.75 tff(10803,plain,
% 5.77/5.75 (succ(succ(X2!57)) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10802])).
% 5.77/5.75 tff(10804,plain,
% 5.77/5.75 (succ(succ(X2!57)) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10803, 53])).
% 5.77/5.75 tff(10805,plain,
% 5.77/5.75 (succ(succ(succ(X2!57))) = succ(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10804])).
% 5.77/5.75 tff(10806,plain,
% 5.77/5.75 (succ(succ(succ(X2!57))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10805, 45])).
% 5.77/5.75 tff(10807,plain,
% 5.77/5.75 (succ(succ(succ(succ(X2!57)))) = succ(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10806])).
% 5.77/5.75 tff(10808,plain,
% 5.77/5.75 (succ(succ(succ(succ(X2!57)))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10807, 28])).
% 5.77/5.75 tff(10809,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(X2!57))))) = succ(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10808])).
% 5.77/5.75 tff(10810,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(X2!57))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10809, 42])).
% 5.77/5.75 tff(10811,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10810])).
% 5.77/5.75 tff(10812,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10811, 58])).
% 5.77/5.75 tff(10813,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10812])).
% 5.77/5.75 tff(10814,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[10813, 36])).
% 5.77/5.75 tff(10815,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10814])).
% 5.77/5.75 tff(10816,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10815, 48])).
% 5.77/5.75 tff(10817,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10816])).
% 5.77/5.75 tff(10818,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10817, 14])).
% 5.77/5.75 tff(10819,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10818])).
% 5.77/5.75 tff(10820,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10819, 33])).
% 5.77/5.75 tff(10821,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10820])).
% 5.77/5.75 tff(10822,plain,
% 5.77/5.75 (NSX2!29 = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[420, 10821, 30])).
% 5.77/5.75 tff(10823,plain,
% 5.77/5.75 (pred(NSX2!29) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10822])).
% 5.77/5.75 tff(10824,plain,
% 5.77/5.75 (pred(NSX2!29) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10823, 17])).
% 5.77/5.75 tff(10825,plain,
% 5.77/5.75 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n5, n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10824, 10800])).
% 5.77/5.75 tff(10826,plain,
% 5.77/5.75 (Y3!54 = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[425, 10825, 558])).
% 5.77/5.75 tff(10827,plain,
% 5.77/5.75 (pred(Y3!54) = pred(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10826])).
% 5.77/5.75 tff(10828,plain,
% 5.77/5.75 (pred(Y3!54) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10827, 24])).
% 5.77/5.75 tff(10829,plain,
% 5.77/5.75 (pred(pred(Y3!54)) = pred(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10828])).
% 5.77/5.75 tff(10830,plain,
% 5.77/5.75 (pred(pred(Y3!54)) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10829, 23])).
% 5.77/5.75 tff(10831,plain,
% 5.77/5.75 (pred(pred(pred(Y3!54))) = pred(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10830])).
% 5.77/5.75 tff(10832,plain,
% 5.77/5.75 (pred(pred(pred(Y3!54))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10831, 22])).
% 5.77/5.75 tff(10833,plain,
% 5.77/5.75 (pred(pred(pred(pred(Y3!54)))) = pred(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10832])).
% 5.77/5.75 tff(10834,plain,
% 5.77/5.75 (pred(pred(pred(pred(Y3!54)))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10833, 21])).
% 5.77/5.75 tff(10835,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10834])).
% 5.77/5.75 tff(10836,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(Y3!54))))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10835, 20])).
% 5.77/5.75 tff(10837,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10836])).
% 5.77/5.75 tff(10838,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10837, 19])).
% 5.77/5.75 tff(10839,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10838])).
% 5.77/5.75 tff(10840,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10839, 18])).
% 5.77/5.75 tff(10841,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10840])).
% 5.77/5.75 tff(10842,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10841, 17])).
% 5.77/5.75 tff(10843,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10842])).
% 5.77/5.75 tff(10844,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10843, 16])).
% 5.77/5.75 tff(10845,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10844])).
% 5.77/5.75 tff(10846,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10845, 15])).
% 5.77/5.75 tff(10847,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10846])).
% 5.77/5.75 tff(10848,plain,
% 5.77/5.75 (NPY3!26 = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[462, 10847, 25])).
% 5.77/5.75 tff(10849,plain,
% 5.77/5.75 (succ(NPY3!26) = succ(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10848])).
% 5.77/5.75 tff(10850,plain,
% 5.77/5.75 (succ(NPY3!26) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10849, 48])).
% 5.77/5.75 tff(10851,plain,
% 5.77/5.75 (succ(Y3!54) = succ(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10826])).
% 5.77/5.75 tff(10852,plain,
% 5.77/5.75 (succ(Y3!54) = n3),
% 5.77/5.75 inference(transitivity,[status(thm)],[10851, 48])).
% 5.77/5.75 tff(10853,plain,
% 5.77/5.75 (succ(succ(Y3!54)) = succ(n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10852])).
% 5.77/5.75 tff(10854,plain,
% 5.77/5.75 (succ(succ(Y3!54)) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10853, 14])).
% 5.77/5.75 tff(10855,plain,
% 5.77/5.75 (succ(succ(succ(Y3!54))) = succ(n4)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10854])).
% 5.77/5.75 tff(10856,plain,
% 5.77/5.75 (succ(succ(succ(Y3!54))) = n5),
% 5.77/5.75 inference(transitivity,[status(thm)],[10855, 33])).
% 5.77/5.75 tff(10857,plain,
% 5.77/5.75 (succ(succ(succ(succ(Y3!54)))) = succ(n5)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10856])).
% 5.77/5.75 tff(10858,plain,
% 5.77/5.75 (succ(succ(succ(succ(Y3!54)))) = n6),
% 5.77/5.75 inference(transitivity,[status(thm)],[10857, 30])).
% 5.77/5.75 tff(10859,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n6)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10858])).
% 5.77/5.75 tff(10860,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(Y3!54))))) = n7),
% 5.77/5.75 inference(transitivity,[status(thm)],[10859, 39])).
% 5.77/5.75 tff(10861,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10860])).
% 5.77/5.75 tff(10862,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n8),
% 5.77/5.75 inference(transitivity,[status(thm)],[10861, 53])).
% 5.77/5.75 tff(10863,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n8)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10862])).
% 5.77/5.75 tff(10864,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10863, 45])).
% 5.77/5.75 tff(10865,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n9)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10864])).
% 5.77/5.75 tff(10866,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10865, 28])).
% 5.77/5.75 tff(10867,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10866])).
% 5.77/5.75 tff(10868,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10867, 42])).
% 5.77/5.75 tff(10869,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10868])).
% 5.77/5.75 tff(10870,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10869, 58])).
% 5.77/5.75 tff(10871,plain,
% 5.77/5.75 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10870])).
% 5.77/5.75 tff(10872,plain,
% 5.77/5.75 (NSY3!24 = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[485, 10871, 36])).
% 5.77/5.75 tff(10873,plain,
% 5.77/5.75 (pred(NSY3!24) = pred(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10872])).
% 5.77/5.75 tff(10874,plain,
% 5.77/5.75 (pred(NSY3!24) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10873, 24])).
% 5.77/5.75 tff(10875,plain,
% 5.77/5.75 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n1, n3)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10874, 10850])).
% 5.77/5.75 tff(10876,plain,
% 5.77/5.75 (sum(pred(NSY3!24), succ(NPY3!26)) = n4),
% 5.77/5.75 inference(transitivity,[status(thm)],[10875, 47])).
% 5.77/5.75 tff(10877,plain,
% 5.77/5.75 (sum(pred(Y2!56), succ(X2!57)) = sum(n5, n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10720, 10802])).
% 5.77/5.75 tff(10878,plain,
% 5.77/5.75 (sum(pred(Y2!56), succ(X2!57)) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10877, 50])).
% 5.77/5.75 tff(10879,plain,
% 5.77/5.75 (sum(pred(X2!57), succ(Y2!56)) = sum(n5, n7)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10776, 10744])).
% 5.77/5.75 tff(10880,plain,
% 5.77/5.75 (sum(pred(X2!57), succ(Y2!56)) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10879, 50])).
% 5.77/5.75 tff(10881,plain,
% 5.77/5.75 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n1, n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10880, 10878])).
% 5.77/5.75 tff(10882,plain,
% 5.77/5.75 (X3!55 = n2),
% 5.77/5.75 inference(transitivity,[status(thm)],[323, 10881, 49])).
% 5.77/5.75 tff(10883,plain,
% 5.77/5.75 (pred(X3!55) = pred(n2)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10882])).
% 5.77/5.75 tff(10884,plain,
% 5.77/5.75 (pred(X3!55) = n1),
% 5.77/5.75 inference(transitivity,[status(thm)],[10883, 24])).
% 5.77/5.75 tff(10885,plain,
% 5.77/5.75 (pred(pred(X3!55)) = pred(n1)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10884])).
% 5.77/5.75 tff(10886,plain,
% 5.77/5.75 (pred(pred(X3!55)) = n0),
% 5.77/5.75 inference(transitivity,[status(thm)],[10885, 23])).
% 5.77/5.75 tff(10887,plain,
% 5.77/5.75 (pred(pred(pred(X3!55))) = pred(n0)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10886])).
% 5.77/5.75 tff(10888,plain,
% 5.77/5.75 (pred(pred(pred(X3!55))) = n10),
% 5.77/5.75 inference(transitivity,[status(thm)],[10887, 22])).
% 5.77/5.75 tff(10889,plain,
% 5.77/5.75 (pred(pred(pred(pred(X3!55)))) = pred(n10)),
% 5.77/5.75 inference(monotonicity,[status(thm)],[10888])).
% 5.77/5.75 tff(10890,plain,
% 5.77/5.75 (pred(pred(pred(pred(X3!55)))) = n9),
% 5.77/5.75 inference(transitivity,[status(thm)],[10889, 21])).
% 5.77/5.75 tff(10891,plain,
% 5.77/5.75 (pred(pred(pred(pred(pred(X3!55))))) = pred(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10890])).
% 5.77/5.76 tff(10892,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(X3!55))))) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[10891, 20])).
% 5.77/5.76 tff(10893,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10892])).
% 5.77/5.76 tff(10894,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[10893, 19])).
% 5.77/5.76 tff(10895,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10894])).
% 5.77/5.76 tff(10896,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[10895, 18])).
% 5.77/5.76 tff(10897,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10896])).
% 5.77/5.76 tff(10898,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[10897, 17])).
% 5.77/5.76 tff(10899,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10898])).
% 5.77/5.76 tff(10900,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[10899, 16])).
% 5.77/5.76 tff(10901,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10900])).
% 5.77/5.76 tff(10902,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[10901, 15])).
% 5.77/5.76 tff(10903,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10902])).
% 5.77/5.76 tff(10904,plain,
% 5.77/5.76 (NPX3!27 = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[510, 10903, 25])).
% 5.77/5.76 tff(10905,plain,
% 5.77/5.76 (succ(NPX3!27) = succ(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10904])).
% 5.77/5.76 tff(10906,plain,
% 5.77/5.76 (succ(NPX3!27) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[10905, 48])).
% 5.77/5.76 tff(10907,plain,
% 5.77/5.76 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n3, n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10906, 10876])).
% 5.77/5.76 tff(10908,plain,
% 5.77/5.76 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[10907, 786])).
% 5.77/5.76 tff(10909,plain,
% 5.77/5.76 (succ(X3!55) = succ(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10882])).
% 5.77/5.76 tff(10910,plain,
% 5.77/5.76 (succ(X3!55) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[10909, 48])).
% 5.77/5.76 tff(10911,plain,
% 5.77/5.76 (succ(succ(X3!55)) = succ(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10910])).
% 5.77/5.76 tff(10912,plain,
% 5.77/5.76 (succ(succ(X3!55)) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[10911, 14])).
% 5.77/5.76 tff(10913,plain,
% 5.77/5.76 (succ(succ(succ(X3!55))) = succ(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10912])).
% 5.77/5.76 tff(10914,plain,
% 5.77/5.76 (succ(succ(succ(X3!55))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[10913, 33])).
% 5.77/5.76 tff(10915,plain,
% 5.77/5.76 (succ(succ(succ(succ(X3!55)))) = succ(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10914])).
% 5.77/5.76 tff(10916,plain,
% 5.77/5.76 (succ(succ(succ(succ(X3!55)))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[10915, 30])).
% 5.77/5.76 tff(10917,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(X3!55))))) = succ(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10916])).
% 5.77/5.76 tff(10918,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(X3!55))))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[10917, 39])).
% 5.77/5.76 tff(10919,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10918])).
% 5.77/5.76 tff(10920,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[10919, 53])).
% 5.77/5.76 tff(10921,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10920])).
% 5.77/5.76 tff(10922,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[10921, 45])).
% 5.77/5.76 tff(10923,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10922])).
% 5.77/5.76 tff(10924,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[10923, 28])).
% 5.77/5.76 tff(10925,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10924])).
% 5.77/5.76 tff(10926,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[10925, 42])).
% 5.77/5.76 tff(10927,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10926])).
% 5.77/5.76 tff(10928,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[10927, 58])).
% 5.77/5.76 tff(10929,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10928])).
% 5.77/5.76 tff(10930,plain,
% 5.77/5.76 (NSX3!25 = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[535, 10929, 36])).
% 5.77/5.76 tff(10931,plain,
% 5.77/5.76 (pred(NSX3!25) = pred(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10930])).
% 5.77/5.76 tff(10932,plain,
% 5.77/5.76 (pred(NSX3!25) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[10931, 24])).
% 5.77/5.76 tff(10933,plain,
% 5.77/5.76 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n1, n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10932, 10908])).
% 5.77/5.76 tff(10934,plain,
% 5.77/5.76 (Y4!52 = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[540, 10933, 791])).
% 5.77/5.76 tff(10935,plain,
% 5.77/5.76 (pred(Y4!52) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10934])).
% 5.77/5.76 tff(10936,plain,
% 5.77/5.76 (pred(Y4!52) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[10935, 19])).
% 5.77/5.76 tff(10937,plain,
% 5.77/5.76 (pred(pred(Y4!52)) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10936])).
% 5.77/5.76 tff(10938,plain,
% 5.77/5.76 (pred(pred(Y4!52)) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[10937, 18])).
% 5.77/5.76 tff(10939,plain,
% 5.77/5.76 (pred(pred(pred(Y4!52))) = pred(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10938])).
% 5.77/5.76 tff(10940,plain,
% 5.77/5.76 (pred(pred(pred(Y4!52))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[10939, 17])).
% 5.77/5.76 tff(10941,plain,
% 5.77/5.76 (pred(pred(pred(pred(Y4!52)))) = pred(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10940])).
% 5.77/5.76 tff(10942,plain,
% 5.77/5.76 (pred(pred(pred(pred(Y4!52)))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[10941, 16])).
% 5.77/5.76 tff(10943,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10942])).
% 5.77/5.76 tff(10944,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(Y4!52))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[10943, 15])).
% 5.77/5.76 tff(10945,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10944])).
% 5.77/5.76 tff(10946,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[10945, 25])).
% 5.77/5.76 tff(10947,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10946])).
% 5.77/5.76 tff(10948,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[10947, 24])).
% 5.77/5.76 tff(10949,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10948])).
% 5.77/5.76 tff(10950,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[10949, 23])).
% 5.77/5.76 tff(10951,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10950])).
% 5.77/5.76 tff(10952,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[10951, 22])).
% 5.77/5.76 tff(10953,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10952])).
% 5.77/5.76 tff(10954,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[10953, 21])).
% 5.77/5.76 tff(10955,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10954])).
% 5.77/5.76 tff(10956,plain,
% 5.77/5.76 (NPY4!22 = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[578, 10955, 20])).
% 5.77/5.76 tff(10957,plain,
% 5.77/5.76 (succ(NPY4!22) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10956])).
% 5.77/5.76 tff(10958,plain,
% 5.77/5.76 (succ(NPY4!22) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[10957, 45])).
% 5.77/5.76 tff(10959,plain,
% 5.77/5.76 (succ(Y4!52) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10934])).
% 5.77/5.76 tff(10960,plain,
% 5.77/5.76 (succ(Y4!52) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[10959, 45])).
% 5.77/5.76 tff(10961,plain,
% 5.77/5.76 (succ(succ(Y4!52)) = succ(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10960])).
% 5.77/5.76 tff(10962,plain,
% 5.77/5.76 (succ(succ(Y4!52)) = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[10961, 28])).
% 5.77/5.76 tff(10963,plain,
% 5.77/5.76 (succ(succ(succ(Y4!52))) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10962])).
% 5.77/5.76 tff(10964,plain,
% 5.77/5.76 (succ(succ(succ(Y4!52))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[10963, 42])).
% 5.77/5.76 tff(10965,plain,
% 5.77/5.76 (succ(succ(succ(succ(Y4!52)))) = succ(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10964])).
% 5.77/5.76 tff(10966,plain,
% 5.77/5.76 (succ(succ(succ(succ(Y4!52)))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[10965, 58])).
% 5.77/5.76 tff(10967,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10966])).
% 5.77/5.76 tff(10968,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(Y4!52))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[10967, 36])).
% 5.77/5.76 tff(10969,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10968])).
% 5.77/5.76 tff(10970,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[10969, 48])).
% 5.77/5.76 tff(10971,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10970])).
% 5.77/5.76 tff(10972,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[10971, 14])).
% 5.77/5.76 tff(10973,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10972])).
% 5.77/5.76 tff(10974,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[10973, 33])).
% 5.77/5.76 tff(10975,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10974])).
% 5.77/5.76 tff(10976,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[10975, 30])).
% 5.77/5.76 tff(10977,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10976])).
% 5.77/5.76 tff(10978,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[10977, 39])).
% 5.77/5.76 tff(10979,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10978])).
% 5.77/5.76 tff(10980,plain,
% 5.77/5.76 (NSY4!20 = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[601, 10979, 53])).
% 5.77/5.76 tff(10981,plain,
% 5.77/5.76 (pred(NSY4!20) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10980])).
% 5.77/5.76 tff(10982,plain,
% 5.77/5.76 (pred(NSY4!20) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[10981, 19])).
% 5.77/5.76 tff(10983,plain,
% 5.77/5.76 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n7, n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10982, 10958])).
% 5.77/5.76 tff(10984,plain,
% 5.77/5.76 (sum(pred(NSY4!20), succ(NPY4!22)) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[10983, 44])).
% 5.77/5.76 tff(10985,plain,
% 5.77/5.76 (sum(pred(Y3!54), succ(X3!55)) = sum(n1, n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10828, 10910])).
% 5.77/5.76 tff(10986,plain,
% 5.77/5.76 (sum(pred(Y3!54), succ(X3!55)) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[10985, 47])).
% 5.77/5.76 tff(10987,plain,
% 5.77/5.76 (sum(pred(X3!55), succ(Y3!54)) = sum(n1, n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10884, 10852])).
% 5.77/5.76 tff(10988,plain,
% 5.77/5.76 (sum(pred(X3!55), succ(Y3!54)) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[10987, 47])).
% 5.77/5.76 tff(10989,plain,
% 5.77/5.76 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n4, n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10988, 10986])).
% 5.77/5.76 tff(10990,plain,
% 5.77/5.76 (X4!53 = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[438, 10989, 46])).
% 5.77/5.76 tff(10991,plain,
% 5.77/5.76 (pred(X4!53) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10990])).
% 5.77/5.76 tff(10992,plain,
% 5.77/5.76 (pred(X4!53) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[10991, 19])).
% 5.77/5.76 tff(10993,plain,
% 5.77/5.76 (pred(pred(X4!53)) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10992])).
% 5.77/5.76 tff(10994,plain,
% 5.77/5.76 (pred(pred(X4!53)) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[10993, 18])).
% 5.77/5.76 tff(10995,plain,
% 5.77/5.76 (pred(pred(pred(X4!53))) = pred(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10994])).
% 5.77/5.76 tff(10996,plain,
% 5.77/5.76 (pred(pred(pred(X4!53))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[10995, 17])).
% 5.77/5.76 tff(10997,plain,
% 5.77/5.76 (pred(pred(pred(pred(X4!53)))) = pred(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10996])).
% 5.77/5.76 tff(10998,plain,
% 5.77/5.76 (pred(pred(pred(pred(X4!53)))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[10997, 16])).
% 5.77/5.76 tff(10999,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(X4!53))))) = pred(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10998])).
% 5.77/5.76 tff(11000,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(X4!53))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[10999, 15])).
% 5.77/5.76 tff(11001,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11000])).
% 5.77/5.76 tff(11002,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11001, 25])).
% 5.77/5.76 tff(11003,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11002])).
% 5.77/5.76 tff(11004,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11003, 24])).
% 5.77/5.76 tff(11005,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11004])).
% 5.77/5.76 tff(11006,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11005, 23])).
% 5.77/5.76 tff(11007,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11006])).
% 5.77/5.76 tff(11008,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[11007, 22])).
% 5.77/5.76 tff(11009,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11008])).
% 5.77/5.76 tff(11010,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11009, 21])).
% 5.77/5.76 tff(11011,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11010])).
% 5.77/5.76 tff(11012,plain,
% 5.77/5.76 (NPX4!23 = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[626, 11011, 20])).
% 5.77/5.76 tff(11013,plain,
% 5.77/5.76 (succ(NPX4!23) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11012])).
% 5.77/5.76 tff(11014,plain,
% 5.77/5.76 (succ(NPX4!23) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11013, 45])).
% 5.77/5.76 tff(11015,plain,
% 5.77/5.76 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n9, n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11014, 10984])).
% 5.77/5.76 tff(11016,plain,
% 5.77/5.76 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11015, 790])).
% 5.77/5.76 tff(11017,plain,
% 5.77/5.76 (succ(X4!53) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10990])).
% 5.77/5.76 tff(11018,plain,
% 5.77/5.76 (succ(X4!53) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11017, 45])).
% 5.77/5.76 tff(11019,plain,
% 5.77/5.76 (succ(succ(X4!53)) = succ(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11018])).
% 5.77/5.76 tff(11020,plain,
% 5.77/5.76 (succ(succ(X4!53)) = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[11019, 28])).
% 5.77/5.76 tff(11021,plain,
% 5.77/5.76 (succ(succ(succ(X4!53))) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11020])).
% 5.77/5.76 tff(11022,plain,
% 5.77/5.76 (succ(succ(succ(X4!53))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11021, 42])).
% 5.77/5.76 tff(11023,plain,
% 5.77/5.76 (succ(succ(succ(succ(X4!53)))) = succ(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11022])).
% 5.77/5.76 tff(11024,plain,
% 5.77/5.76 (succ(succ(succ(succ(X4!53)))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11023, 58])).
% 5.77/5.76 tff(11025,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(X4!53))))) = succ(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11024])).
% 5.77/5.76 tff(11026,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(X4!53))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11025, 36])).
% 5.77/5.76 tff(11027,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11026])).
% 5.77/5.76 tff(11028,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11027, 48])).
% 5.77/5.76 tff(11029,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11028])).
% 5.77/5.76 tff(11030,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11029, 14])).
% 5.77/5.76 tff(11031,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11030])).
% 5.77/5.76 tff(11032,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11031, 33])).
% 5.77/5.76 tff(11033,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11032])).
% 5.77/5.76 tff(11034,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11033, 30])).
% 5.77/5.76 tff(11035,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11034])).
% 5.77/5.76 tff(11036,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[11035, 39])).
% 5.77/5.76 tff(11037,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11036])).
% 5.77/5.76 tff(11038,plain,
% 5.77/5.76 (NSX4!21 = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[651, 11037, 53])).
% 5.77/5.76 tff(11039,plain,
% 5.77/5.76 (pred(NSX4!21) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11038])).
% 5.77/5.76 tff(11040,plain,
% 5.77/5.76 (pred(NSX4!21) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[11039, 19])).
% 5.77/5.76 tff(11041,plain,
% 5.77/5.76 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n7, n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11040, 11016])).
% 5.77/5.76 tff(11042,plain,
% 5.77/5.76 (Y5!50 = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[656, 11041, 789])).
% 5.77/5.76 tff(11043,plain,
% 5.77/5.76 (pred(Y5!50) = pred(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11042])).
% 5.77/5.76 tff(11044,plain,
% 5.77/5.76 (pred(Y5!50) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11043, 21])).
% 5.77/5.76 tff(11045,plain,
% 5.77/5.76 (pred(pred(Y5!50)) = pred(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11044])).
% 5.77/5.76 tff(11046,plain,
% 5.77/5.76 (pred(pred(Y5!50)) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[11045, 20])).
% 5.77/5.76 tff(11047,plain,
% 5.77/5.76 (pred(pred(pred(Y5!50))) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11046])).
% 5.77/5.76 tff(11048,plain,
% 5.77/5.76 (pred(pred(pred(Y5!50))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[11047, 19])).
% 5.77/5.76 tff(11049,plain,
% 5.77/5.76 (pred(pred(pred(pred(Y5!50)))) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11048])).
% 5.77/5.76 tff(11050,plain,
% 5.77/5.76 (pred(pred(pred(pred(Y5!50)))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11049, 18])).
% 5.77/5.76 tff(11051,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11050])).
% 5.77/5.76 tff(11052,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(Y5!50))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11051, 17])).
% 5.77/5.76 tff(11053,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11052])).
% 5.77/5.76 tff(11054,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11053, 16])).
% 5.77/5.76 tff(11055,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11054])).
% 5.77/5.76 tff(11056,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11055, 15])).
% 5.77/5.76 tff(11057,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11056])).
% 5.77/5.76 tff(11058,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11057, 25])).
% 5.77/5.76 tff(11059,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11058])).
% 5.77/5.76 tff(11060,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11059, 24])).
% 5.77/5.76 tff(11061,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11060])).
% 5.77/5.76 tff(11062,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11061, 23])).
% 5.77/5.76 tff(11063,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11062])).
% 5.77/5.76 tff(11064,plain,
% 5.77/5.76 (NPY5!18 = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[694, 11063, 22])).
% 5.77/5.76 tff(11065,plain,
% 5.77/5.76 (succ(NPY5!18) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11064])).
% 5.77/5.76 tff(11066,plain,
% 5.77/5.76 (succ(NPY5!18) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11065, 42])).
% 5.77/5.76 tff(11067,plain,
% 5.77/5.76 (succ(Y5!50) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11042])).
% 5.77/5.76 tff(11068,plain,
% 5.77/5.76 (succ(Y5!50) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11067, 42])).
% 5.77/5.76 tff(11069,plain,
% 5.77/5.76 (succ(succ(Y5!50)) = succ(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11068])).
% 5.77/5.76 tff(11070,plain,
% 5.77/5.76 (succ(succ(Y5!50)) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11069, 58])).
% 5.77/5.76 tff(11071,plain,
% 5.77/5.76 (succ(succ(succ(Y5!50))) = succ(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11070])).
% 5.77/5.76 tff(11072,plain,
% 5.77/5.76 (succ(succ(succ(Y5!50))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11071, 36])).
% 5.77/5.76 tff(11073,plain,
% 5.77/5.76 (succ(succ(succ(succ(Y5!50)))) = succ(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11072])).
% 5.77/5.76 tff(11074,plain,
% 5.77/5.76 (succ(succ(succ(succ(Y5!50)))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11073, 48])).
% 5.77/5.76 tff(11075,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11074])).
% 5.77/5.76 tff(11076,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(Y5!50))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11075, 14])).
% 5.77/5.76 tff(11077,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11076])).
% 5.77/5.76 tff(11078,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11077, 33])).
% 5.77/5.76 tff(11079,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11078])).
% 5.77/5.76 tff(11080,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11079, 30])).
% 5.77/5.76 tff(11081,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11080])).
% 5.77/5.76 tff(11082,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[11081, 39])).
% 5.77/5.76 tff(11083,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11082])).
% 5.77/5.76 tff(11084,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[11083, 53])).
% 5.77/5.76 tff(11085,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11084])).
% 5.77/5.76 tff(11086,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11085, 45])).
% 5.77/5.76 tff(11087,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11086])).
% 5.77/5.76 tff(11088,plain,
% 5.77/5.76 (NSY5!16 = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[717, 11087, 28])).
% 5.77/5.76 tff(11089,plain,
% 5.77/5.76 (pred(NSY5!16) = pred(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11088])).
% 5.77/5.76 tff(11090,plain,
% 5.77/5.76 (pred(NSY5!16) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11089, 21])).
% 5.77/5.76 tff(11091,plain,
% 5.77/5.76 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n9, n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11090, 11066])).
% 5.77/5.76 tff(11092,plain,
% 5.77/5.76 (sum(pred(NSY5!16), succ(NPY5!18)) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11091, 41])).
% 5.77/5.76 tff(11093,plain,
% 5.77/5.76 (sum(pred(Y4!52), succ(X4!53)) = sum(n7, n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10936, 11018])).
% 5.77/5.76 tff(11094,plain,
% 5.77/5.76 (sum(pred(Y4!52), succ(X4!53)) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11093, 44])).
% 5.77/5.76 tff(11095,plain,
% 5.77/5.76 (sum(pred(X4!53), succ(Y4!52)) = sum(n7, n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[10992, 10960])).
% 5.77/5.76 tff(11096,plain,
% 5.77/5.76 (sum(pred(X4!53), succ(Y4!52)) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11095, 44])).
% 5.77/5.76 tff(11097,plain,
% 5.77/5.76 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n5, n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11096, 11094])).
% 5.77/5.76 tff(11098,plain,
% 5.77/5.76 (X5!51 = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[553, 11097, 43])).
% 5.77/5.76 tff(11099,plain,
% 5.77/5.76 (pred(X5!51) = pred(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11098])).
% 5.77/5.76 tff(11100,plain,
% 5.77/5.76 (pred(X5!51) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11099, 21])).
% 5.77/5.76 tff(11101,plain,
% 5.77/5.76 (pred(pred(X5!51)) = pred(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11100])).
% 5.77/5.76 tff(11102,plain,
% 5.77/5.76 (pred(pred(X5!51)) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[11101, 20])).
% 5.77/5.76 tff(11103,plain,
% 5.77/5.76 (pred(pred(pred(X5!51))) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11102])).
% 5.77/5.76 tff(11104,plain,
% 5.77/5.76 (pred(pred(pred(X5!51))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[11103, 19])).
% 5.77/5.76 tff(11105,plain,
% 5.77/5.76 (pred(pred(pred(pred(X5!51)))) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11104])).
% 5.77/5.76 tff(11106,plain,
% 5.77/5.76 (pred(pred(pred(pred(X5!51)))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11105, 18])).
% 5.77/5.76 tff(11107,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(X5!51))))) = pred(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11106])).
% 5.77/5.76 tff(11108,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(X5!51))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11107, 17])).
% 5.77/5.76 tff(11109,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11108])).
% 5.77/5.76 tff(11110,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11109, 16])).
% 5.77/5.76 tff(11111,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11110])).
% 5.77/5.76 tff(11112,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11111, 15])).
% 5.77/5.76 tff(11113,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11112])).
% 5.77/5.76 tff(11114,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11113, 25])).
% 5.77/5.76 tff(11115,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11114])).
% 5.77/5.76 tff(11116,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11115, 24])).
% 5.77/5.76 tff(11117,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11116])).
% 5.77/5.76 tff(11118,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11117, 23])).
% 5.77/5.76 tff(11119,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11118])).
% 5.77/5.76 tff(11120,plain,
% 5.77/5.76 (NPX5!19 = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[742, 11119, 22])).
% 5.77/5.76 tff(11121,plain,
% 5.77/5.76 (succ(NPX5!19) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11120])).
% 5.77/5.76 tff(11122,plain,
% 5.77/5.76 (succ(NPX5!19) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11121, 42])).
% 5.77/5.76 tff(11123,plain,
% 5.77/5.76 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n0, n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11122, 11092])).
% 5.77/5.76 tff(11124,plain,
% 5.77/5.76 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11123, 40])).
% 5.77/5.76 tff(11125,plain,
% 5.77/5.76 (succ(X5!51) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11098])).
% 5.77/5.76 tff(11126,plain,
% 5.77/5.76 (succ(X5!51) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11125, 42])).
% 5.77/5.76 tff(11127,plain,
% 5.77/5.76 (succ(succ(X5!51)) = succ(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11126])).
% 5.77/5.76 tff(11128,plain,
% 5.77/5.76 (succ(succ(X5!51)) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11127, 58])).
% 5.77/5.76 tff(11129,plain,
% 5.77/5.76 (succ(succ(succ(X5!51))) = succ(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11128])).
% 5.77/5.76 tff(11130,plain,
% 5.77/5.76 (succ(succ(succ(X5!51))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11129, 36])).
% 5.77/5.76 tff(11131,plain,
% 5.77/5.76 (succ(succ(succ(succ(X5!51)))) = succ(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11130])).
% 5.77/5.76 tff(11132,plain,
% 5.77/5.76 (succ(succ(succ(succ(X5!51)))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11131, 48])).
% 5.77/5.76 tff(11133,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(X5!51))))) = succ(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11132])).
% 5.77/5.76 tff(11134,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(X5!51))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11133, 14])).
% 5.77/5.76 tff(11135,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11134])).
% 5.77/5.76 tff(11136,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11135, 33])).
% 5.77/5.76 tff(11137,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11136])).
% 5.77/5.76 tff(11138,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11137, 30])).
% 5.77/5.76 tff(11139,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11138])).
% 5.77/5.76 tff(11140,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[11139, 39])).
% 5.77/5.76 tff(11141,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11140])).
% 5.77/5.76 tff(11142,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[11141, 53])).
% 5.77/5.76 tff(11143,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11142])).
% 5.77/5.76 tff(11144,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11143, 45])).
% 5.77/5.76 tff(11145,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11144])).
% 5.77/5.76 tff(11146,plain,
% 5.77/5.76 (NSX5!17 = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[767, 11145, 28])).
% 5.77/5.76 tff(11147,plain,
% 5.77/5.76 (pred(NSX5!17) = pred(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11146])).
% 5.77/5.76 tff(11148,plain,
% 5.77/5.76 (pred(NSX5!17) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11147, 21])).
% 5.77/5.76 tff(11149,plain,
% 5.77/5.76 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n9, n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11148, 11124])).
% 5.77/5.76 tff(11150,plain,
% 5.77/5.76 (Y6!48 = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[772, 11149, 54])).
% 5.77/5.76 tff(11151,plain,
% 5.77/5.76 (pred(Y6!48) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11150])).
% 5.77/5.76 tff(11152,plain,
% 5.77/5.76 (pred(Y6!48) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11151, 18])).
% 5.77/5.76 tff(11153,plain,
% 5.77/5.76 (pred(pred(Y6!48)) = pred(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11152])).
% 5.77/5.76 tff(11154,plain,
% 5.77/5.76 (pred(pred(Y6!48)) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11153, 17])).
% 5.77/5.76 tff(11155,plain,
% 5.77/5.76 (pred(pred(pred(Y6!48))) = pred(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11154])).
% 5.77/5.76 tff(11156,plain,
% 5.77/5.76 (pred(pred(pred(Y6!48))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11155, 16])).
% 5.77/5.76 tff(11157,plain,
% 5.77/5.76 (pred(pred(pred(pred(Y6!48)))) = pred(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11156])).
% 5.77/5.76 tff(11158,plain,
% 5.77/5.76 (pred(pred(pred(pred(Y6!48)))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11157, 15])).
% 5.77/5.76 tff(11159,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11158])).
% 5.77/5.76 tff(11160,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(Y6!48))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11159, 25])).
% 5.77/5.76 tff(11161,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11160])).
% 5.77/5.76 tff(11162,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11161, 24])).
% 5.77/5.76 tff(11163,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11162])).
% 5.77/5.76 tff(11164,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11163, 23])).
% 5.77/5.76 tff(11165,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11164])).
% 5.77/5.76 tff(11166,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[11165, 22])).
% 5.77/5.76 tff(11167,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11166])).
% 5.77/5.76 tff(11168,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11167, 21])).
% 5.77/5.76 tff(11169,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11168])).
% 5.77/5.76 tff(11170,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[11169, 20])).
% 5.77/5.76 tff(11171,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11170])).
% 5.77/5.76 tff(11172,plain,
% 5.77/5.76 (NPY6!14 = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[1465, 11171, 19])).
% 5.77/5.76 tff(11173,plain,
% 5.77/5.76 (succ(NPY6!14) = succ(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11172])).
% 5.77/5.76 tff(11174,plain,
% 5.77/5.76 (succ(NPY6!14) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[11173, 53])).
% 5.77/5.76 tff(11175,plain,
% 5.77/5.76 (succ(Y6!48) = succ(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11150])).
% 5.77/5.76 tff(11176,plain,
% 5.77/5.76 (succ(Y6!48) = n8),
% 5.77/5.76 inference(transitivity,[status(thm)],[11175, 53])).
% 5.77/5.76 tff(11177,plain,
% 5.77/5.76 (succ(succ(Y6!48)) = succ(n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11176])).
% 5.77/5.76 tff(11178,plain,
% 5.77/5.76 (succ(succ(Y6!48)) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11177, 45])).
% 5.77/5.76 tff(11179,plain,
% 5.77/5.76 (succ(succ(succ(Y6!48))) = succ(n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11178])).
% 5.77/5.76 tff(11180,plain,
% 5.77/5.76 (succ(succ(succ(Y6!48))) = n10),
% 5.77/5.76 inference(transitivity,[status(thm)],[11179, 28])).
% 5.77/5.76 tff(11181,plain,
% 5.77/5.76 (succ(succ(succ(succ(Y6!48)))) = succ(n10)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11180])).
% 5.77/5.76 tff(11182,plain,
% 5.77/5.76 (succ(succ(succ(succ(Y6!48)))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11181, 42])).
% 5.77/5.76 tff(11183,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11182])).
% 5.77/5.76 tff(11184,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(Y6!48))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11183, 58])).
% 5.77/5.76 tff(11185,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11184])).
% 5.77/5.76 tff(11186,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11185, 36])).
% 5.77/5.76 tff(11187,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11186])).
% 5.77/5.76 tff(11188,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11187, 48])).
% 5.77/5.76 tff(11189,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11188])).
% 5.77/5.76 tff(11190,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11189, 14])).
% 5.77/5.76 tff(11191,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11190])).
% 5.77/5.76 tff(11192,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11191, 33])).
% 5.77/5.76 tff(11193,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11192])).
% 5.77/5.76 tff(11194,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11193, 30])).
% 5.77/5.76 tff(11195,plain,
% 5.77/5.76 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11194])).
% 5.77/5.76 tff(11196,plain,
% 5.77/5.76 (NSY6!12 = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[1490, 11195, 39])).
% 5.77/5.76 tff(11197,plain,
% 5.77/5.76 (pred(NSY6!12) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11196])).
% 5.77/5.76 tff(11198,plain,
% 5.77/5.76 (pred(NSY6!12) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11197, 18])).
% 5.77/5.76 tff(11199,plain,
% 5.77/5.76 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n6, n8)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11198, 11174])).
% 5.77/5.76 tff(11200,plain,
% 5.77/5.76 (sum(pred(NSY6!12), succ(NPY6!14)) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11199, 52])).
% 5.77/5.76 tff(11201,plain,
% 5.77/5.76 (sum(pred(Y5!50), succ(X5!51)) = sum(n9, n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11044, 11126])).
% 5.77/5.76 tff(11202,plain,
% 5.77/5.76 (sum(pred(Y5!50), succ(X5!51)) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11201, 41])).
% 5.77/5.76 tff(11203,plain,
% 5.77/5.76 (sum(pred(X5!51), succ(Y5!50)) = sum(n9, n0)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11100, 11068])).
% 5.77/5.76 tff(11204,plain,
% 5.77/5.76 (sum(pred(X5!51), succ(Y5!50)) = n9),
% 5.77/5.76 inference(transitivity,[status(thm)],[11203, 41])).
% 5.77/5.76 tff(11205,plain,
% 5.77/5.76 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n9, n9)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11204, 11202])).
% 5.77/5.76 tff(11206,plain,
% 5.77/5.76 (X6!49 = n7),
% 5.77/5.76 inference(transitivity,[status(thm)],[669, 11205, 54])).
% 5.77/5.76 tff(11207,plain,
% 5.77/5.76 (pred(X6!49) = pred(n7)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11206])).
% 5.77/5.76 tff(11208,plain,
% 5.77/5.76 (pred(X6!49) = n6),
% 5.77/5.76 inference(transitivity,[status(thm)],[11207, 18])).
% 5.77/5.76 tff(11209,plain,
% 5.77/5.76 (pred(pred(X6!49)) = pred(n6)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11208])).
% 5.77/5.76 tff(11210,plain,
% 5.77/5.76 (pred(pred(X6!49)) = n5),
% 5.77/5.76 inference(transitivity,[status(thm)],[11209, 17])).
% 5.77/5.76 tff(11211,plain,
% 5.77/5.76 (pred(pred(pred(X6!49))) = pred(n5)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11210])).
% 5.77/5.76 tff(11212,plain,
% 5.77/5.76 (pred(pred(pred(X6!49))) = n4),
% 5.77/5.76 inference(transitivity,[status(thm)],[11211, 16])).
% 5.77/5.76 tff(11213,plain,
% 5.77/5.76 (pred(pred(pred(pred(X6!49)))) = pred(n4)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11212])).
% 5.77/5.76 tff(11214,plain,
% 5.77/5.76 (pred(pred(pred(pred(X6!49)))) = n3),
% 5.77/5.76 inference(transitivity,[status(thm)],[11213, 15])).
% 5.77/5.76 tff(11215,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(X6!49))))) = pred(n3)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11214])).
% 5.77/5.76 tff(11216,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(X6!49))))) = n2),
% 5.77/5.76 inference(transitivity,[status(thm)],[11215, 25])).
% 5.77/5.76 tff(11217,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n2)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11216])).
% 5.77/5.76 tff(11218,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n1),
% 5.77/5.76 inference(transitivity,[status(thm)],[11217, 24])).
% 5.77/5.76 tff(11219,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n1)),
% 5.77/5.76 inference(monotonicity,[status(thm)],[11218])).
% 5.77/5.76 tff(11220,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n0),
% 5.77/5.76 inference(transitivity,[status(thm)],[11219, 23])).
% 5.77/5.76 tff(11221,plain,
% 5.77/5.76 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11220])).
% 5.77/5.77 tff(11222,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11221, 22])).
% 5.77/5.77 tff(11223,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11222])).
% 5.77/5.77 tff(11224,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11223, 21])).
% 5.77/5.77 tff(11225,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11224])).
% 5.77/5.77 tff(11226,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11225, 20])).
% 5.77/5.77 tff(11227,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11226])).
% 5.77/5.77 tff(11228,plain,
% 5.77/5.77 (NPX6!15 = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[1523, 11227, 19])).
% 5.77/5.77 tff(11229,plain,
% 5.77/5.77 (succ(NPX6!15) = succ(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11228])).
% 5.77/5.77 tff(11230,plain,
% 5.77/5.77 (succ(NPX6!15) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11229, 53])).
% 5.77/5.77 tff(11231,plain,
% 5.77/5.77 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n8, n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11230, 11200])).
% 5.77/5.77 tff(11232,plain,
% 5.77/5.77 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11231, 64])).
% 5.77/5.77 tff(11233,plain,
% 5.77/5.77 (succ(X6!49) = succ(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11206])).
% 5.77/5.77 tff(11234,plain,
% 5.77/5.77 (succ(X6!49) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11233, 53])).
% 5.77/5.77 tff(11235,plain,
% 5.77/5.77 (succ(succ(X6!49)) = succ(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11234])).
% 5.77/5.77 tff(11236,plain,
% 5.77/5.77 (succ(succ(X6!49)) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11235, 45])).
% 5.77/5.77 tff(11237,plain,
% 5.77/5.77 (succ(succ(succ(X6!49))) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11236])).
% 5.77/5.77 tff(11238,plain,
% 5.77/5.77 (succ(succ(succ(X6!49))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11237, 28])).
% 5.77/5.77 tff(11239,plain,
% 5.77/5.77 (succ(succ(succ(succ(X6!49)))) = succ(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11238])).
% 5.77/5.77 tff(11240,plain,
% 5.77/5.77 (succ(succ(succ(succ(X6!49)))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11239, 42])).
% 5.77/5.77 tff(11241,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(X6!49))))) = succ(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11240])).
% 5.77/5.77 tff(11242,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(X6!49))))) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11241, 58])).
% 5.77/5.77 tff(11243,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11242])).
% 5.77/5.77 tff(11244,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11243, 36])).
% 5.77/5.77 tff(11245,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11244])).
% 5.77/5.77 tff(11246,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11245, 48])).
% 5.77/5.77 tff(11247,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11246])).
% 5.77/5.77 tff(11248,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11247, 14])).
% 5.77/5.77 tff(11249,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11248])).
% 5.77/5.77 tff(11250,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11249, 33])).
% 5.77/5.77 tff(11251,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11250])).
% 5.77/5.77 tff(11252,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11251, 30])).
% 5.77/5.77 tff(11253,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11252])).
% 5.77/5.77 tff(11254,plain,
% 5.77/5.77 (NSX6!13 = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[1550, 11253, 39])).
% 5.77/5.77 tff(11255,plain,
% 5.77/5.77 (pred(NSX6!13) = pred(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11254])).
% 5.77/5.77 tff(11256,plain,
% 5.77/5.77 (pred(NSX6!13) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11255, 18])).
% 5.77/5.77 tff(11257,plain,
% 5.77/5.77 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n6, n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11256, 11232])).
% 5.77/5.77 tff(11258,plain,
% 5.77/5.77 (sum(n6, n0) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.77/5.77 inference(symmetry,[status(thm)],[11257])).
% 5.77/5.77 tff(11259,plain,
% 5.77/5.77 (n6 = sum(n6, n0)),
% 5.77/5.77 inference(symmetry,[status(thm)],[788])).
% 5.77/5.77 tff(11260,plain,
% 5.77/5.77 (sum(pred(Y6!48), succ(X6!49)) = sum(n6, n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11152, 11234])).
% 5.77/5.77 tff(11261,plain,
% 5.77/5.77 (sum(pred(Y6!48), succ(X6!49)) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11260, 52])).
% 5.77/5.77 tff(11262,plain,
% 5.77/5.77 (sum(pred(X6!49), succ(Y6!48)) = sum(n6, n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11208, 11176])).
% 5.77/5.77 tff(11263,plain,
% 5.77/5.77 (sum(pred(X6!49), succ(Y6!48)) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11262, 52])).
% 5.77/5.77 tff(11264,plain,
% 5.77/5.77 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n3, n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11263, 11261])).
% 5.77/5.77 tff(11265,plain,
% 5.77/5.77 (X7!47 = Y7!46),
% 5.77/5.77 inference(transitivity,[status(thm)],[785, 11264, 51, 11259, 11258, 794])).
% 5.77/5.77 tff(11266,plain,
% 5.77/5.77 ($false),
% 5.77/5.77 inference(unit_resolution,[status(thm)],[792, 11265])).
% 5.77/5.77 tff(11267,plain,((~(X0!61 = n9)) | (X7!47 = Y7!46) | (~(Y0!60 = n0))), inference(lemma,lemma(discharge,[]))).
% 5.77/5.77 tff(11268,plain,
% 5.77/5.77 (~(X0!61 = n9)),
% 5.77/5.77 inference(unit_resolution,[status(thm)],[11267, 9225, 792])).
% 5.77/5.77 tff(11269,plain,
% 5.77/5.77 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n0, n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[3792, 9275])).
% 5.77/5.77 tff(11270,plain,
% 5.77/5.77 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11269, 59])).
% 5.77/5.77 tff(11271,plain,
% 5.77/5.77 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n9, n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[3818, 11270])).
% 5.77/5.77 tff(11272,plain,
% 5.77/5.77 (Y1!58 = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[196, 11271, 41])).
% 5.77/5.77 tff(11273,plain,
% 5.77/5.77 (pred(Y1!58) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11272])).
% 5.77/5.77 tff(11274,plain,
% 5.77/5.77 (pred(Y1!58) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11273, 20])).
% 5.77/5.77 tff(11275,plain,
% 5.77/5.77 (pred(pred(Y1!58)) = pred(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11274])).
% 5.77/5.77 tff(11276,plain,
% 5.77/5.77 (pred(pred(Y1!58)) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11275, 19])).
% 5.77/5.77 tff(11277,plain,
% 5.77/5.77 (pred(pred(pred(Y1!58))) = pred(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11276])).
% 5.77/5.77 tff(11278,plain,
% 5.77/5.77 (pred(pred(pred(Y1!58))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11277, 18])).
% 5.77/5.77 tff(11279,plain,
% 5.77/5.77 (pred(pred(pred(pred(Y1!58)))) = pred(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11278])).
% 5.77/5.77 tff(11280,plain,
% 5.77/5.77 (pred(pred(pred(pred(Y1!58)))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11279, 17])).
% 5.77/5.77 tff(11281,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11280])).
% 5.77/5.77 tff(11282,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(Y1!58))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11281, 16])).
% 5.77/5.77 tff(11283,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11282])).
% 5.77/5.77 tff(11284,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11283, 15])).
% 5.77/5.77 tff(11285,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11284])).
% 5.77/5.77 tff(11286,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11285, 25])).
% 5.77/5.77 tff(11287,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11286])).
% 5.77/5.77 tff(11288,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11287, 24])).
% 5.77/5.77 tff(11289,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11288])).
% 5.77/5.77 tff(11290,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11289, 23])).
% 5.77/5.77 tff(11291,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11290])).
% 5.77/5.77 tff(11292,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11291, 22])).
% 5.77/5.77 tff(11293,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11292])).
% 5.77/5.77 tff(11294,plain,
% 5.77/5.77 (NPY1!34 = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[232, 11293, 21])).
% 5.77/5.77 tff(11295,plain,
% 5.77/5.77 (succ(NPY1!34) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11294])).
% 5.77/5.77 tff(11296,plain,
% 5.77/5.77 (succ(NPY1!34) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11295, 28])).
% 5.77/5.77 tff(11297,plain,
% 5.77/5.77 (succ(Y1!58) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11272])).
% 5.77/5.77 tff(11298,plain,
% 5.77/5.77 (succ(Y1!58) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11297, 28])).
% 5.77/5.77 tff(11299,plain,
% 5.77/5.77 (succ(succ(Y1!58)) = succ(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11298])).
% 5.77/5.77 tff(11300,plain,
% 5.77/5.77 (succ(succ(Y1!58)) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11299, 42])).
% 5.77/5.77 tff(11301,plain,
% 5.77/5.77 (succ(succ(succ(Y1!58))) = succ(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11300])).
% 5.77/5.77 tff(11302,plain,
% 5.77/5.77 (succ(succ(succ(Y1!58))) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11301, 58])).
% 5.77/5.77 tff(11303,plain,
% 5.77/5.77 (succ(succ(succ(succ(Y1!58)))) = succ(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11302])).
% 5.77/5.77 tff(11304,plain,
% 5.77/5.77 (succ(succ(succ(succ(Y1!58)))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11303, 36])).
% 5.77/5.77 tff(11305,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11304])).
% 5.77/5.77 tff(11306,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(Y1!58))))) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11305, 48])).
% 5.77/5.77 tff(11307,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11306])).
% 5.77/5.77 tff(11308,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11307, 14])).
% 5.77/5.77 tff(11309,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11308])).
% 5.77/5.77 tff(11310,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11309, 33])).
% 5.77/5.77 tff(11311,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11310])).
% 5.77/5.77 tff(11312,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11311, 30])).
% 5.77/5.77 tff(11313,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11312])).
% 5.77/5.77 tff(11314,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11313, 39])).
% 5.77/5.77 tff(11315,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11314])).
% 5.77/5.77 tff(11316,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11315, 53])).
% 5.77/5.77 tff(11317,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11316])).
% 5.77/5.77 tff(11318,plain,
% 5.77/5.77 (NSY1!32 = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[255, 11317, 45])).
% 5.77/5.77 tff(11319,plain,
% 5.77/5.77 (pred(NSY1!32) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11318])).
% 5.77/5.77 tff(11320,plain,
% 5.77/5.77 (pred(NSY1!32) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11319, 20])).
% 5.77/5.77 tff(11321,plain,
% 5.77/5.77 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n8, n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11320, 11296])).
% 5.77/5.77 tff(11322,plain,
% 5.77/5.77 (sum(pred(NSY1!32), succ(NPY1!34)) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11321, 27])).
% 5.77/5.77 tff(11323,plain,
% 5.77/5.77 (sum(pred(Y0!60), succ(X0!61)) = sum(n10, n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[9227, 3796])).
% 5.77/5.77 tff(11324,plain,
% 5.77/5.77 (sum(pred(Y0!60), succ(X0!61)) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11323, 10606])).
% 5.77/5.77 tff(11325,plain,
% 5.77/5.77 (sum(pred(X0!61), succ(Y0!60)) = sum(n9, n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[3770, 9251])).
% 5.77/5.77 tff(11326,plain,
% 5.77/5.77 (sum(pred(X0!61), succ(Y0!60)) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11325, 4481])).
% 5.77/5.77 tff(11327,plain,
% 5.77/5.77 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n10, n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11326, 11324])).
% 5.77/5.77 tff(11328,plain,
% 5.77/5.77 (X1!59 = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[93, 11327, 29])).
% 5.77/5.77 tff(11329,plain,
% 5.77/5.77 (pred(X1!59) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11328])).
% 5.77/5.77 tff(11330,plain,
% 5.77/5.77 (pred(X1!59) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11329, 20])).
% 5.77/5.77 tff(11331,plain,
% 5.77/5.77 (pred(pred(X1!59)) = pred(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11330])).
% 5.77/5.77 tff(11332,plain,
% 5.77/5.77 (pred(pred(X1!59)) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11331, 19])).
% 5.77/5.77 tff(11333,plain,
% 5.77/5.77 (pred(pred(pred(X1!59))) = pred(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11332])).
% 5.77/5.77 tff(11334,plain,
% 5.77/5.77 (pred(pred(pred(X1!59))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11333, 18])).
% 5.77/5.77 tff(11335,plain,
% 5.77/5.77 (pred(pred(pred(pred(X1!59)))) = pred(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11334])).
% 5.77/5.77 tff(11336,plain,
% 5.77/5.77 (pred(pred(pred(pred(X1!59)))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11335, 17])).
% 5.77/5.77 tff(11337,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(X1!59))))) = pred(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11336])).
% 5.77/5.77 tff(11338,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(X1!59))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11337, 16])).
% 5.77/5.77 tff(11339,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11338])).
% 5.77/5.77 tff(11340,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11339, 15])).
% 5.77/5.77 tff(11341,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11340])).
% 5.77/5.77 tff(11342,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11341, 25])).
% 5.77/5.77 tff(11343,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11342])).
% 5.77/5.77 tff(11344,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11343, 24])).
% 5.77/5.77 tff(11345,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11344])).
% 5.77/5.77 tff(11346,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11345, 23])).
% 5.77/5.77 tff(11347,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11346])).
% 5.77/5.77 tff(11348,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11347, 22])).
% 5.77/5.77 tff(11349,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11348])).
% 5.77/5.77 tff(11350,plain,
% 5.77/5.77 (NPX1!35 = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[280, 11349, 21])).
% 5.77/5.77 tff(11351,plain,
% 5.77/5.77 (succ(NPX1!35) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11350])).
% 5.77/5.77 tff(11352,plain,
% 5.77/5.77 (succ(NPX1!35) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11351, 28])).
% 5.77/5.77 tff(11353,plain,
% 5.77/5.77 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n10, n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11352, 11322])).
% 5.77/5.77 tff(11354,plain,
% 5.77/5.77 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11353, 69])).
% 5.77/5.77 tff(11355,plain,
% 5.77/5.77 (succ(X1!59) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11328])).
% 5.77/5.77 tff(11356,plain,
% 5.77/5.77 (succ(X1!59) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11355, 28])).
% 5.77/5.77 tff(11357,plain,
% 5.77/5.77 (succ(succ(X1!59)) = succ(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11356])).
% 5.77/5.77 tff(11358,plain,
% 5.77/5.77 (succ(succ(X1!59)) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11357, 42])).
% 5.77/5.77 tff(11359,plain,
% 5.77/5.77 (succ(succ(succ(X1!59))) = succ(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11358])).
% 5.77/5.77 tff(11360,plain,
% 5.77/5.77 (succ(succ(succ(X1!59))) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11359, 58])).
% 5.77/5.77 tff(11361,plain,
% 5.77/5.77 (succ(succ(succ(succ(X1!59)))) = succ(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11360])).
% 5.77/5.77 tff(11362,plain,
% 5.77/5.77 (succ(succ(succ(succ(X1!59)))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11361, 36])).
% 5.77/5.77 tff(11363,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(X1!59))))) = succ(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11362])).
% 5.77/5.77 tff(11364,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(X1!59))))) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11363, 48])).
% 5.77/5.77 tff(11365,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11364])).
% 5.77/5.77 tff(11366,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11365, 14])).
% 5.77/5.77 tff(11367,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11366])).
% 5.77/5.77 tff(11368,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11367, 33])).
% 5.77/5.77 tff(11369,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11368])).
% 5.77/5.77 tff(11370,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11369, 30])).
% 5.77/5.77 tff(11371,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11370])).
% 5.77/5.77 tff(11372,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11371, 39])).
% 5.77/5.77 tff(11373,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11372])).
% 5.77/5.77 tff(11374,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11373, 53])).
% 5.77/5.77 tff(11375,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11374])).
% 5.77/5.77 tff(11376,plain,
% 5.77/5.77 (NSX1!33 = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[305, 11375, 45])).
% 5.77/5.77 tff(11377,plain,
% 5.77/5.77 (pred(NSX1!33) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11376])).
% 5.77/5.77 tff(11378,plain,
% 5.77/5.77 (pred(NSX1!33) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11377, 20])).
% 5.77/5.77 tff(11379,plain,
% 5.77/5.77 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n8, n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11378, 11354])).
% 5.77/5.77 tff(11380,plain,
% 5.77/5.77 (Y2!56 = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[310, 11379, 98])).
% 5.77/5.77 tff(11381,plain,
% 5.77/5.77 (pred(Y2!56) = pred(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11380])).
% 5.77/5.77 tff(11382,plain,
% 5.77/5.77 (pred(Y2!56) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11381, 25])).
% 5.77/5.77 tff(11383,plain,
% 5.77/5.77 (pred(pred(Y2!56)) = pred(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11382])).
% 5.77/5.77 tff(11384,plain,
% 5.77/5.77 (pred(pred(Y2!56)) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11383, 24])).
% 5.77/5.77 tff(11385,plain,
% 5.77/5.77 (pred(pred(pred(Y2!56))) = pred(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11384])).
% 5.77/5.77 tff(11386,plain,
% 5.77/5.77 (pred(pred(pred(Y2!56))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11385, 23])).
% 5.77/5.77 tff(11387,plain,
% 5.77/5.77 (pred(pred(pred(pred(Y2!56)))) = pred(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11386])).
% 5.77/5.77 tff(11388,plain,
% 5.77/5.77 (pred(pred(pred(pred(Y2!56)))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11387, 22])).
% 5.77/5.77 tff(11389,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11388])).
% 5.77/5.77 tff(11390,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(Y2!56))))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11389, 21])).
% 5.77/5.77 tff(11391,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11390])).
% 5.77/5.77 tff(11392,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11391, 20])).
% 5.77/5.77 tff(11393,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11392])).
% 5.77/5.77 tff(11394,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11393, 19])).
% 5.77/5.77 tff(11395,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11394])).
% 5.77/5.77 tff(11396,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11395, 18])).
% 5.77/5.77 tff(11397,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11396])).
% 5.77/5.77 tff(11398,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11397, 17])).
% 5.77/5.77 tff(11399,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11398])).
% 5.77/5.77 tff(11400,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11399, 16])).
% 5.77/5.77 tff(11401,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11400])).
% 5.77/5.77 tff(11402,plain,
% 5.77/5.77 (NPY2!30 = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[347, 11401, 15])).
% 5.77/5.77 tff(11403,plain,
% 5.77/5.77 (succ(NPY2!30) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11402])).
% 5.77/5.77 tff(11404,plain,
% 5.77/5.77 (succ(NPY2!30) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11403, 14])).
% 5.77/5.77 tff(11405,plain,
% 5.77/5.77 (succ(Y2!56) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11380])).
% 5.77/5.77 tff(11406,plain,
% 5.77/5.77 (succ(Y2!56) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11405, 14])).
% 5.77/5.77 tff(11407,plain,
% 5.77/5.77 (succ(succ(Y2!56)) = succ(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11406])).
% 5.77/5.77 tff(11408,plain,
% 5.77/5.77 (succ(succ(Y2!56)) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11407, 33])).
% 5.77/5.77 tff(11409,plain,
% 5.77/5.77 (succ(succ(succ(Y2!56))) = succ(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11408])).
% 5.77/5.77 tff(11410,plain,
% 5.77/5.77 (succ(succ(succ(Y2!56))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11409, 30])).
% 5.77/5.77 tff(11411,plain,
% 5.77/5.77 (succ(succ(succ(succ(Y2!56)))) = succ(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11410])).
% 5.77/5.77 tff(11412,plain,
% 5.77/5.77 (succ(succ(succ(succ(Y2!56)))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11411, 39])).
% 5.77/5.77 tff(11413,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11412])).
% 5.77/5.77 tff(11414,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(Y2!56))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11413, 53])).
% 5.77/5.77 tff(11415,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11414])).
% 5.77/5.77 tff(11416,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11415, 45])).
% 5.77/5.77 tff(11417,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11416])).
% 5.77/5.77 tff(11418,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11417, 28])).
% 5.77/5.77 tff(11419,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11418])).
% 5.77/5.77 tff(11420,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11419, 42])).
% 5.77/5.77 tff(11421,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11420])).
% 5.77/5.77 tff(11422,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11421, 58])).
% 5.77/5.77 tff(11423,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11422])).
% 5.77/5.77 tff(11424,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11423, 36])).
% 5.77/5.77 tff(11425,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11424])).
% 5.77/5.77 tff(11426,plain,
% 5.77/5.77 (NSY2!28 = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[370, 11425, 48])).
% 5.77/5.77 tff(11427,plain,
% 5.77/5.77 (pred(NSY2!28) = pred(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11426])).
% 5.77/5.77 tff(11428,plain,
% 5.77/5.77 (pred(NSY2!28) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11427, 25])).
% 5.77/5.77 tff(11429,plain,
% 5.77/5.77 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n2, n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11428, 11404])).
% 5.77/5.77 tff(11430,plain,
% 5.77/5.77 (sum(pred(NSY2!28), succ(NPY2!30)) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11429, 13])).
% 5.77/5.77 tff(11431,plain,
% 5.77/5.77 (sum(pred(Y1!58), succ(X1!59)) = sum(n8, n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11274, 11356])).
% 5.77/5.77 tff(11432,plain,
% 5.77/5.77 (sum(pred(Y1!58), succ(X1!59)) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11431, 27])).
% 5.77/5.77 tff(11433,plain,
% 5.77/5.77 (sum(pred(X1!59), succ(Y1!58)) = sum(n8, n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11330, 11298])).
% 5.77/5.77 tff(11434,plain,
% 5.77/5.77 (sum(pred(X1!59), succ(Y1!58)) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11433, 27])).
% 5.77/5.77 tff(11435,plain,
% 5.77/5.77 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n7, n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11434, 11432])).
% 5.77/5.77 tff(11436,plain,
% 5.77/5.77 (X2!57 = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[209, 11435, 26])).
% 5.77/5.77 tff(11437,plain,
% 5.77/5.77 (pred(X2!57) = pred(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11436])).
% 5.77/5.77 tff(11438,plain,
% 5.77/5.77 (pred(X2!57) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11437, 25])).
% 5.77/5.77 tff(11439,plain,
% 5.77/5.77 (pred(pred(X2!57)) = pred(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11438])).
% 5.77/5.77 tff(11440,plain,
% 5.77/5.77 (pred(pred(X2!57)) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11439, 24])).
% 5.77/5.77 tff(11441,plain,
% 5.77/5.77 (pred(pred(pred(X2!57))) = pred(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11440])).
% 5.77/5.77 tff(11442,plain,
% 5.77/5.77 (pred(pred(pred(X2!57))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11441, 23])).
% 5.77/5.77 tff(11443,plain,
% 5.77/5.77 (pred(pred(pred(pred(X2!57)))) = pred(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11442])).
% 5.77/5.77 tff(11444,plain,
% 5.77/5.77 (pred(pred(pred(pred(X2!57)))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11443, 22])).
% 5.77/5.77 tff(11445,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(X2!57))))) = pred(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11444])).
% 5.77/5.77 tff(11446,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(X2!57))))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11445, 21])).
% 5.77/5.77 tff(11447,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11446])).
% 5.77/5.77 tff(11448,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11447, 20])).
% 5.77/5.77 tff(11449,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11448])).
% 5.77/5.77 tff(11450,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11449, 19])).
% 5.77/5.77 tff(11451,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11450])).
% 5.77/5.77 tff(11452,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11451, 18])).
% 5.77/5.77 tff(11453,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11452])).
% 5.77/5.77 tff(11454,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11453, 17])).
% 5.77/5.77 tff(11455,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11454])).
% 5.77/5.77 tff(11456,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11455, 16])).
% 5.77/5.77 tff(11457,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11456])).
% 5.77/5.77 tff(11458,plain,
% 5.77/5.77 (NPX2!31 = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[395, 11457, 15])).
% 5.77/5.77 tff(11459,plain,
% 5.77/5.77 (succ(NPX2!31) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11458])).
% 5.77/5.77 tff(11460,plain,
% 5.77/5.77 (succ(NPX2!31) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11459, 14])).
% 5.77/5.77 tff(11461,plain,
% 5.77/5.77 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n4, n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11460, 11430])).
% 5.77/5.77 tff(11462,plain,
% 5.77/5.77 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11461, 12])).
% 5.77/5.77 tff(11463,plain,
% 5.77/5.77 (succ(X2!57) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11436])).
% 5.77/5.77 tff(11464,plain,
% 5.77/5.77 (succ(X2!57) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11463, 14])).
% 5.77/5.77 tff(11465,plain,
% 5.77/5.77 (succ(succ(X2!57)) = succ(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11464])).
% 5.77/5.77 tff(11466,plain,
% 5.77/5.77 (succ(succ(X2!57)) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11465, 33])).
% 5.77/5.77 tff(11467,plain,
% 5.77/5.77 (succ(succ(succ(X2!57))) = succ(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11466])).
% 5.77/5.77 tff(11468,plain,
% 5.77/5.77 (succ(succ(succ(X2!57))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11467, 30])).
% 5.77/5.77 tff(11469,plain,
% 5.77/5.77 (succ(succ(succ(succ(X2!57)))) = succ(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11468])).
% 5.77/5.77 tff(11470,plain,
% 5.77/5.77 (succ(succ(succ(succ(X2!57)))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11469, 39])).
% 5.77/5.77 tff(11471,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(X2!57))))) = succ(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11470])).
% 5.77/5.77 tff(11472,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(X2!57))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11471, 53])).
% 5.77/5.77 tff(11473,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11472])).
% 5.77/5.77 tff(11474,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11473, 45])).
% 5.77/5.77 tff(11475,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11474])).
% 5.77/5.77 tff(11476,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11475, 28])).
% 5.77/5.77 tff(11477,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11476])).
% 5.77/5.77 tff(11478,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11477, 42])).
% 5.77/5.77 tff(11479,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11478])).
% 5.77/5.77 tff(11480,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[11479, 58])).
% 5.77/5.77 tff(11481,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11480])).
% 5.77/5.77 tff(11482,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11481, 36])).
% 5.77/5.77 tff(11483,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11482])).
% 5.77/5.77 tff(11484,plain,
% 5.77/5.77 (NSX2!29 = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[420, 11483, 48])).
% 5.77/5.77 tff(11485,plain,
% 5.77/5.77 (pred(NSX2!29) = pred(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11484])).
% 5.77/5.77 tff(11486,plain,
% 5.77/5.77 (pred(NSX2!29) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11485, 25])).
% 5.77/5.77 tff(11487,plain,
% 5.77/5.77 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n2, n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11486, 11462])).
% 5.77/5.77 tff(11488,plain,
% 5.77/5.77 (Y3!54 = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[425, 11487, 327])).
% 5.77/5.77 tff(11489,plain,
% 5.77/5.77 (pred(Y3!54) = pred(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11488])).
% 5.77/5.77 tff(11490,plain,
% 5.77/5.77 (pred(Y3!54) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11489, 23])).
% 5.77/5.77 tff(11491,plain,
% 5.77/5.77 (pred(pred(Y3!54)) = pred(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11490])).
% 5.77/5.77 tff(11492,plain,
% 5.77/5.77 (pred(pred(Y3!54)) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11491, 22])).
% 5.77/5.77 tff(11493,plain,
% 5.77/5.77 (pred(pred(pred(Y3!54))) = pred(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11492])).
% 5.77/5.77 tff(11494,plain,
% 5.77/5.77 (pred(pred(pred(Y3!54))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11493, 21])).
% 5.77/5.77 tff(11495,plain,
% 5.77/5.77 (pred(pred(pred(pred(Y3!54)))) = pred(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11494])).
% 5.77/5.77 tff(11496,plain,
% 5.77/5.77 (pred(pred(pred(pred(Y3!54)))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11495, 20])).
% 5.77/5.77 tff(11497,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11496])).
% 5.77/5.77 tff(11498,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(Y3!54))))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11497, 19])).
% 5.77/5.77 tff(11499,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11498])).
% 5.77/5.77 tff(11500,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11499, 18])).
% 5.77/5.77 tff(11501,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11500])).
% 5.77/5.77 tff(11502,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11501, 17])).
% 5.77/5.77 tff(11503,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11502])).
% 5.77/5.77 tff(11504,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11503, 16])).
% 5.77/5.77 tff(11505,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11504])).
% 5.77/5.77 tff(11506,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11505, 15])).
% 5.77/5.77 tff(11507,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11506])).
% 5.77/5.77 tff(11508,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11507, 25])).
% 5.77/5.77 tff(11509,plain,
% 5.77/5.77 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11508])).
% 5.77/5.77 tff(11510,plain,
% 5.77/5.77 (NPY3!26 = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[462, 11509, 24])).
% 5.77/5.77 tff(11511,plain,
% 5.77/5.77 (succ(NPY3!26) = succ(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11510])).
% 5.77/5.77 tff(11512,plain,
% 5.77/5.77 (succ(NPY3!26) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11511, 36])).
% 5.77/5.77 tff(11513,plain,
% 5.77/5.77 (succ(Y3!54) = succ(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11488])).
% 5.77/5.77 tff(11514,plain,
% 5.77/5.77 (succ(Y3!54) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11513, 36])).
% 5.77/5.77 tff(11515,plain,
% 5.77/5.77 (succ(succ(Y3!54)) = succ(n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11514])).
% 5.77/5.77 tff(11516,plain,
% 5.77/5.77 (succ(succ(Y3!54)) = n3),
% 5.77/5.77 inference(transitivity,[status(thm)],[11515, 48])).
% 5.77/5.77 tff(11517,plain,
% 5.77/5.77 (succ(succ(succ(Y3!54))) = succ(n3)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11516])).
% 5.77/5.77 tff(11518,plain,
% 5.77/5.77 (succ(succ(succ(Y3!54))) = n4),
% 5.77/5.77 inference(transitivity,[status(thm)],[11517, 14])).
% 5.77/5.77 tff(11519,plain,
% 5.77/5.77 (succ(succ(succ(succ(Y3!54)))) = succ(n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11518])).
% 5.77/5.77 tff(11520,plain,
% 5.77/5.77 (succ(succ(succ(succ(Y3!54)))) = n5),
% 5.77/5.77 inference(transitivity,[status(thm)],[11519, 33])).
% 5.77/5.77 tff(11521,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n5)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11520])).
% 5.77/5.77 tff(11522,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(Y3!54))))) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11521, 30])).
% 5.77/5.77 tff(11523,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11522])).
% 5.77/5.77 tff(11524,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n7),
% 5.77/5.77 inference(transitivity,[status(thm)],[11523, 39])).
% 5.77/5.77 tff(11525,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n7)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11524])).
% 5.77/5.77 tff(11526,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n8),
% 5.77/5.77 inference(transitivity,[status(thm)],[11525, 53])).
% 5.77/5.77 tff(11527,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n8)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11526])).
% 5.77/5.77 tff(11528,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11527, 45])).
% 5.77/5.77 tff(11529,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n9)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11528])).
% 5.77/5.77 tff(11530,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11529, 28])).
% 5.77/5.77 tff(11531,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11530])).
% 5.77/5.77 tff(11532,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11531, 42])).
% 5.77/5.77 tff(11533,plain,
% 5.77/5.77 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11532])).
% 5.77/5.77 tff(11534,plain,
% 5.77/5.77 (NSY3!24 = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[485, 11533, 58])).
% 5.77/5.77 tff(11535,plain,
% 5.77/5.77 (pred(NSY3!24) = pred(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11534])).
% 5.77/5.77 tff(11536,plain,
% 5.77/5.77 (pred(NSY3!24) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11535, 23])).
% 5.77/5.77 tff(11537,plain,
% 5.77/5.77 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n0, n2)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11536, 11512])).
% 5.77/5.77 tff(11538,plain,
% 5.77/5.77 (sum(pred(NSY3!24), succ(NPY3!26)) = n2),
% 5.77/5.77 inference(transitivity,[status(thm)],[11537, 35])).
% 5.77/5.77 tff(11539,plain,
% 5.77/5.77 (sum(pred(Y2!56), succ(X2!57)) = sum(n2, n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11382, 11464])).
% 5.77/5.77 tff(11540,plain,
% 5.77/5.77 (sum(pred(Y2!56), succ(X2!57)) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11539, 13])).
% 5.77/5.77 tff(11541,plain,
% 5.77/5.77 (sum(pred(X2!57), succ(Y2!56)) = sum(n2, n4)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11438, 11406])).
% 5.77/5.77 tff(11542,plain,
% 5.77/5.77 (sum(pred(X2!57), succ(Y2!56)) = n6),
% 5.77/5.77 inference(transitivity,[status(thm)],[11541, 13])).
% 5.77/5.77 tff(11543,plain,
% 5.77/5.77 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n6, n6)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11542, 11540])).
% 5.77/5.77 tff(11544,plain,
% 5.77/5.77 (X3!55 = n1),
% 5.77/5.77 inference(transitivity,[status(thm)],[323, 11543, 37])).
% 5.77/5.77 tff(11545,plain,
% 5.77/5.77 (pred(X3!55) = pred(n1)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11544])).
% 5.77/5.77 tff(11546,plain,
% 5.77/5.77 (pred(X3!55) = n0),
% 5.77/5.77 inference(transitivity,[status(thm)],[11545, 23])).
% 5.77/5.77 tff(11547,plain,
% 5.77/5.77 (pred(pred(X3!55)) = pred(n0)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11546])).
% 5.77/5.77 tff(11548,plain,
% 5.77/5.77 (pred(pred(X3!55)) = n10),
% 5.77/5.77 inference(transitivity,[status(thm)],[11547, 22])).
% 5.77/5.77 tff(11549,plain,
% 5.77/5.77 (pred(pred(pred(X3!55))) = pred(n10)),
% 5.77/5.77 inference(monotonicity,[status(thm)],[11548])).
% 5.77/5.77 tff(11550,plain,
% 5.77/5.77 (pred(pred(pred(X3!55))) = n9),
% 5.77/5.77 inference(transitivity,[status(thm)],[11549, 21])).
% 5.77/5.77 tff(11551,plain,
% 5.77/5.77 (pred(pred(pred(pred(X3!55)))) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11550])).
% 5.77/5.78 tff(11552,plain,
% 5.77/5.78 (pred(pred(pred(pred(X3!55)))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11551, 20])).
% 5.77/5.78 tff(11553,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X3!55))))) = pred(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11552])).
% 5.77/5.78 tff(11554,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X3!55))))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11553, 19])).
% 5.77/5.78 tff(11555,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11554])).
% 5.77/5.78 tff(11556,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11555, 18])).
% 5.77/5.78 tff(11557,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11556])).
% 5.77/5.78 tff(11558,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11557, 17])).
% 5.77/5.78 tff(11559,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11558])).
% 5.77/5.78 tff(11560,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11559, 16])).
% 5.77/5.78 tff(11561,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11560])).
% 5.77/5.78 tff(11562,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11561, 15])).
% 5.77/5.78 tff(11563,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11562])).
% 5.77/5.78 tff(11564,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11563, 25])).
% 5.77/5.78 tff(11565,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11564])).
% 5.77/5.78 tff(11566,plain,
% 5.77/5.78 (NPX3!27 = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[510, 11565, 24])).
% 5.77/5.78 tff(11567,plain,
% 5.77/5.78 (succ(NPX3!27) = succ(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11566])).
% 5.77/5.78 tff(11568,plain,
% 5.77/5.78 (succ(NPX3!27) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11567, 36])).
% 5.77/5.78 tff(11569,plain,
% 5.77/5.78 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n2, n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11568, 11538])).
% 5.77/5.78 tff(11570,plain,
% 5.77/5.78 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11569, 34])).
% 5.77/5.78 tff(11571,plain,
% 5.77/5.78 (succ(X3!55) = succ(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11544])).
% 5.77/5.78 tff(11572,plain,
% 5.77/5.78 (succ(X3!55) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11571, 36])).
% 5.77/5.78 tff(11573,plain,
% 5.77/5.78 (succ(succ(X3!55)) = succ(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11572])).
% 5.77/5.78 tff(11574,plain,
% 5.77/5.78 (succ(succ(X3!55)) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11573, 48])).
% 5.77/5.78 tff(11575,plain,
% 5.77/5.78 (succ(succ(succ(X3!55))) = succ(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11574])).
% 5.77/5.78 tff(11576,plain,
% 5.77/5.78 (succ(succ(succ(X3!55))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11575, 14])).
% 5.77/5.78 tff(11577,plain,
% 5.77/5.78 (succ(succ(succ(succ(X3!55)))) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11576])).
% 5.77/5.78 tff(11578,plain,
% 5.77/5.78 (succ(succ(succ(succ(X3!55)))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11577, 33])).
% 5.77/5.78 tff(11579,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(X3!55))))) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11578])).
% 5.77/5.78 tff(11580,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(X3!55))))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11579, 30])).
% 5.77/5.78 tff(11581,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11580])).
% 5.77/5.78 tff(11582,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11581, 39])).
% 5.77/5.78 tff(11583,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11582])).
% 5.77/5.78 tff(11584,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11583, 53])).
% 5.77/5.78 tff(11585,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11584])).
% 5.77/5.78 tff(11586,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11585, 45])).
% 5.77/5.78 tff(11587,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11586])).
% 5.77/5.78 tff(11588,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11587, 28])).
% 5.77/5.78 tff(11589,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11588])).
% 5.77/5.78 tff(11590,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11589, 42])).
% 5.77/5.78 tff(11591,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11590])).
% 5.77/5.78 tff(11592,plain,
% 5.77/5.78 (NSX3!25 = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[535, 11591, 58])).
% 5.77/5.78 tff(11593,plain,
% 5.77/5.78 (pred(NSX3!25) = pred(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11592])).
% 5.77/5.78 tff(11594,plain,
% 5.77/5.78 (pred(NSX3!25) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11593, 23])).
% 5.77/5.78 tff(11595,plain,
% 5.77/5.78 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n0, n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11594, 11570])).
% 5.77/5.78 tff(11596,plain,
% 5.77/5.78 (Y4!52 = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[540, 11595, 442])).
% 5.77/5.78 tff(11597,plain,
% 5.77/5.78 (pred(Y4!52) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11596])).
% 5.77/5.78 tff(11598,plain,
% 5.77/5.78 (pred(Y4!52) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11597, 15])).
% 5.77/5.78 tff(11599,plain,
% 5.77/5.78 (pred(pred(Y4!52)) = pred(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11598])).
% 5.77/5.78 tff(11600,plain,
% 5.77/5.78 (pred(pred(Y4!52)) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11599, 25])).
% 5.77/5.78 tff(11601,plain,
% 5.77/5.78 (pred(pred(pred(Y4!52))) = pred(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11600])).
% 5.77/5.78 tff(11602,plain,
% 5.77/5.78 (pred(pred(pred(Y4!52))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11601, 24])).
% 5.77/5.78 tff(11603,plain,
% 5.77/5.78 (pred(pred(pred(pred(Y4!52)))) = pred(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11602])).
% 5.77/5.78 tff(11604,plain,
% 5.77/5.78 (pred(pred(pred(pred(Y4!52)))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11603, 23])).
% 5.77/5.78 tff(11605,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11604])).
% 5.77/5.78 tff(11606,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(Y4!52))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11605, 22])).
% 5.77/5.78 tff(11607,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11606])).
% 5.77/5.78 tff(11608,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11607, 21])).
% 5.77/5.78 tff(11609,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11608])).
% 5.77/5.78 tff(11610,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11609, 20])).
% 5.77/5.78 tff(11611,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11610])).
% 5.77/5.78 tff(11612,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11611, 19])).
% 5.77/5.78 tff(11613,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11612])).
% 5.77/5.78 tff(11614,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11613, 18])).
% 5.77/5.78 tff(11615,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11614])).
% 5.77/5.78 tff(11616,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11615, 17])).
% 5.77/5.78 tff(11617,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11616])).
% 5.77/5.78 tff(11618,plain,
% 5.77/5.78 (NPY4!22 = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[578, 11617, 16])).
% 5.77/5.78 tff(11619,plain,
% 5.77/5.78 (succ(NPY4!22) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11618])).
% 5.77/5.78 tff(11620,plain,
% 5.77/5.78 (succ(NPY4!22) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11619, 33])).
% 5.77/5.78 tff(11621,plain,
% 5.77/5.78 (succ(Y4!52) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11596])).
% 5.77/5.78 tff(11622,plain,
% 5.77/5.78 (succ(Y4!52) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11621, 33])).
% 5.77/5.78 tff(11623,plain,
% 5.77/5.78 (succ(succ(Y4!52)) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11622])).
% 5.77/5.78 tff(11624,plain,
% 5.77/5.78 (succ(succ(Y4!52)) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11623, 30])).
% 5.77/5.78 tff(11625,plain,
% 5.77/5.78 (succ(succ(succ(Y4!52))) = succ(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11624])).
% 5.77/5.78 tff(11626,plain,
% 5.77/5.78 (succ(succ(succ(Y4!52))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11625, 39])).
% 5.77/5.78 tff(11627,plain,
% 5.77/5.78 (succ(succ(succ(succ(Y4!52)))) = succ(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11626])).
% 5.77/5.78 tff(11628,plain,
% 5.77/5.78 (succ(succ(succ(succ(Y4!52)))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11627, 53])).
% 5.77/5.78 tff(11629,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11628])).
% 5.77/5.78 tff(11630,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(Y4!52))))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11629, 45])).
% 5.77/5.78 tff(11631,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11630])).
% 5.77/5.78 tff(11632,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11631, 28])).
% 5.77/5.78 tff(11633,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11632])).
% 5.77/5.78 tff(11634,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11633, 42])).
% 5.77/5.78 tff(11635,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11634])).
% 5.77/5.78 tff(11636,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11635, 58])).
% 5.77/5.78 tff(11637,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11636])).
% 5.77/5.78 tff(11638,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11637, 36])).
% 5.77/5.78 tff(11639,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11638])).
% 5.77/5.78 tff(11640,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11639, 48])).
% 5.77/5.78 tff(11641,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11640])).
% 5.77/5.78 tff(11642,plain,
% 5.77/5.78 (NSY4!20 = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[601, 11641, 14])).
% 5.77/5.78 tff(11643,plain,
% 5.77/5.78 (pred(NSY4!20) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11642])).
% 5.77/5.78 tff(11644,plain,
% 5.77/5.78 (pred(NSY4!20) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11643, 15])).
% 5.77/5.78 tff(11645,plain,
% 5.77/5.78 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n3, n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11644, 11620])).
% 5.77/5.78 tff(11646,plain,
% 5.77/5.78 (sum(pred(NSY4!20), succ(NPY4!22)) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11645, 32])).
% 5.77/5.78 tff(11647,plain,
% 5.77/5.78 (sum(pred(Y3!54), succ(X3!55)) = sum(n0, n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11490, 11572])).
% 5.77/5.78 tff(11648,plain,
% 5.77/5.78 (sum(pred(Y3!54), succ(X3!55)) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11647, 35])).
% 5.77/5.78 tff(11649,plain,
% 5.77/5.78 (sum(pred(X3!55), succ(Y3!54)) = sum(n0, n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11546, 11514])).
% 5.77/5.78 tff(11650,plain,
% 5.77/5.78 (sum(pred(X3!55), succ(Y3!54)) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11649, 35])).
% 5.77/5.78 tff(11651,plain,
% 5.77/5.78 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n2, n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11650, 11648])).
% 5.77/5.78 tff(11652,plain,
% 5.77/5.78 (X4!53 = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[438, 11651, 34])).
% 5.77/5.78 tff(11653,plain,
% 5.77/5.78 (pred(X4!53) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11652])).
% 5.77/5.78 tff(11654,plain,
% 5.77/5.78 (pred(X4!53) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11653, 15])).
% 5.77/5.78 tff(11655,plain,
% 5.77/5.78 (pred(pred(X4!53)) = pred(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11654])).
% 5.77/5.78 tff(11656,plain,
% 5.77/5.78 (pred(pred(X4!53)) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11655, 25])).
% 5.77/5.78 tff(11657,plain,
% 5.77/5.78 (pred(pred(pred(X4!53))) = pred(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11656])).
% 5.77/5.78 tff(11658,plain,
% 5.77/5.78 (pred(pred(pred(X4!53))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11657, 24])).
% 5.77/5.78 tff(11659,plain,
% 5.77/5.78 (pred(pred(pred(pred(X4!53)))) = pred(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11658])).
% 5.77/5.78 tff(11660,plain,
% 5.77/5.78 (pred(pred(pred(pred(X4!53)))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11659, 23])).
% 5.77/5.78 tff(11661,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X4!53))))) = pred(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11660])).
% 5.77/5.78 tff(11662,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X4!53))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11661, 22])).
% 5.77/5.78 tff(11663,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11662])).
% 5.77/5.78 tff(11664,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11663, 21])).
% 5.77/5.78 tff(11665,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11664])).
% 5.77/5.78 tff(11666,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11665, 20])).
% 5.77/5.78 tff(11667,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11666])).
% 5.77/5.78 tff(11668,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11667, 19])).
% 5.77/5.78 tff(11669,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11668])).
% 5.77/5.78 tff(11670,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11669, 18])).
% 5.77/5.78 tff(11671,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11670])).
% 5.77/5.78 tff(11672,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11671, 17])).
% 5.77/5.78 tff(11673,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11672])).
% 5.77/5.78 tff(11674,plain,
% 5.77/5.78 (NPX4!23 = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[626, 11673, 16])).
% 5.77/5.78 tff(11675,plain,
% 5.77/5.78 (succ(NPX4!23) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11674])).
% 5.77/5.78 tff(11676,plain,
% 5.77/5.78 (succ(NPX4!23) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11675, 33])).
% 5.77/5.78 tff(11677,plain,
% 5.77/5.78 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n5, n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11676, 11646])).
% 5.77/5.78 tff(11678,plain,
% 5.77/5.78 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11677, 558])).
% 5.77/5.78 tff(11679,plain,
% 5.77/5.78 (succ(X4!53) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11652])).
% 5.77/5.78 tff(11680,plain,
% 5.77/5.78 (succ(X4!53) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11679, 33])).
% 5.77/5.78 tff(11681,plain,
% 5.77/5.78 (succ(succ(X4!53)) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11680])).
% 5.77/5.78 tff(11682,plain,
% 5.77/5.78 (succ(succ(X4!53)) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11681, 30])).
% 5.77/5.78 tff(11683,plain,
% 5.77/5.78 (succ(succ(succ(X4!53))) = succ(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11682])).
% 5.77/5.78 tff(11684,plain,
% 5.77/5.78 (succ(succ(succ(X4!53))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11683, 39])).
% 5.77/5.78 tff(11685,plain,
% 5.77/5.78 (succ(succ(succ(succ(X4!53)))) = succ(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11684])).
% 5.77/5.78 tff(11686,plain,
% 5.77/5.78 (succ(succ(succ(succ(X4!53)))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11685, 53])).
% 5.77/5.78 tff(11687,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(X4!53))))) = succ(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11686])).
% 5.77/5.78 tff(11688,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(X4!53))))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11687, 45])).
% 5.77/5.78 tff(11689,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11688])).
% 5.77/5.78 tff(11690,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11689, 28])).
% 5.77/5.78 tff(11691,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11690])).
% 5.77/5.78 tff(11692,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11691, 42])).
% 5.77/5.78 tff(11693,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11692])).
% 5.77/5.78 tff(11694,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11693, 58])).
% 5.77/5.78 tff(11695,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11694])).
% 5.77/5.78 tff(11696,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11695, 36])).
% 5.77/5.78 tff(11697,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11696])).
% 5.77/5.78 tff(11698,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11697, 48])).
% 5.77/5.78 tff(11699,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11698])).
% 5.77/5.78 tff(11700,plain,
% 5.77/5.78 (NSX4!21 = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[651, 11699, 14])).
% 5.77/5.78 tff(11701,plain,
% 5.77/5.78 (pred(NSX4!21) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11700])).
% 5.77/5.78 tff(11702,plain,
% 5.77/5.78 (pred(NSX4!21) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11701, 15])).
% 5.77/5.78 tff(11703,plain,
% 5.77/5.78 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n3, n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11702, 11678])).
% 5.77/5.78 tff(11704,plain,
% 5.77/5.78 (Y5!50 = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[656, 11703, 557])).
% 5.77/5.78 tff(11705,plain,
% 5.77/5.78 (pred(Y5!50) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11704])).
% 5.77/5.78 tff(11706,plain,
% 5.77/5.78 (pred(Y5!50) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11705, 16])).
% 5.77/5.78 tff(11707,plain,
% 5.77/5.78 (pred(pred(Y5!50)) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11706])).
% 5.77/5.78 tff(11708,plain,
% 5.77/5.78 (pred(pred(Y5!50)) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11707, 15])).
% 5.77/5.78 tff(11709,plain,
% 5.77/5.78 (pred(pred(pred(Y5!50))) = pred(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11708])).
% 5.77/5.78 tff(11710,plain,
% 5.77/5.78 (pred(pred(pred(Y5!50))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11709, 25])).
% 5.77/5.78 tff(11711,plain,
% 5.77/5.78 (pred(pred(pred(pred(Y5!50)))) = pred(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11710])).
% 5.77/5.78 tff(11712,plain,
% 5.77/5.78 (pred(pred(pred(pred(Y5!50)))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11711, 24])).
% 5.77/5.78 tff(11713,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11712])).
% 5.77/5.78 tff(11714,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(Y5!50))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11713, 23])).
% 5.77/5.78 tff(11715,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11714])).
% 5.77/5.78 tff(11716,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11715, 22])).
% 5.77/5.78 tff(11717,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11716])).
% 5.77/5.78 tff(11718,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11717, 21])).
% 5.77/5.78 tff(11719,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11718])).
% 5.77/5.78 tff(11720,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11719, 20])).
% 5.77/5.78 tff(11721,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11720])).
% 5.77/5.78 tff(11722,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11721, 19])).
% 5.77/5.78 tff(11723,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11722])).
% 5.77/5.78 tff(11724,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11723, 18])).
% 5.77/5.78 tff(11725,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11724])).
% 5.77/5.78 tff(11726,plain,
% 5.77/5.78 (NPY5!18 = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[694, 11725, 17])).
% 5.77/5.78 tff(11727,plain,
% 5.77/5.78 (succ(NPY5!18) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11726])).
% 5.77/5.78 tff(11728,plain,
% 5.77/5.78 (succ(NPY5!18) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11727, 30])).
% 5.77/5.78 tff(11729,plain,
% 5.77/5.78 (succ(Y5!50) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11704])).
% 5.77/5.78 tff(11730,plain,
% 5.77/5.78 (succ(Y5!50) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11729, 30])).
% 5.77/5.78 tff(11731,plain,
% 5.77/5.78 (succ(succ(Y5!50)) = succ(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11730])).
% 5.77/5.78 tff(11732,plain,
% 5.77/5.78 (succ(succ(Y5!50)) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11731, 39])).
% 5.77/5.78 tff(11733,plain,
% 5.77/5.78 (succ(succ(succ(Y5!50))) = succ(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11732])).
% 5.77/5.78 tff(11734,plain,
% 5.77/5.78 (succ(succ(succ(Y5!50))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11733, 53])).
% 5.77/5.78 tff(11735,plain,
% 5.77/5.78 (succ(succ(succ(succ(Y5!50)))) = succ(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11734])).
% 5.77/5.78 tff(11736,plain,
% 5.77/5.78 (succ(succ(succ(succ(Y5!50)))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11735, 45])).
% 5.77/5.78 tff(11737,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11736])).
% 5.77/5.78 tff(11738,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(Y5!50))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11737, 28])).
% 5.77/5.78 tff(11739,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11738])).
% 5.77/5.78 tff(11740,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11739, 42])).
% 5.77/5.78 tff(11741,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11740])).
% 5.77/5.78 tff(11742,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11741, 58])).
% 5.77/5.78 tff(11743,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11742])).
% 5.77/5.78 tff(11744,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11743, 36])).
% 5.77/5.78 tff(11745,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11744])).
% 5.77/5.78 tff(11746,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11745, 48])).
% 5.77/5.78 tff(11747,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11746])).
% 5.77/5.78 tff(11748,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11747, 14])).
% 5.77/5.78 tff(11749,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11748])).
% 5.77/5.78 tff(11750,plain,
% 5.77/5.78 (NSY5!16 = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[717, 11749, 33])).
% 5.77/5.78 tff(11751,plain,
% 5.77/5.78 (pred(NSY5!16) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11750])).
% 5.77/5.78 tff(11752,plain,
% 5.77/5.78 (pred(NSY5!16) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11751, 16])).
% 5.77/5.78 tff(11753,plain,
% 5.77/5.78 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n4, n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11752, 11728])).
% 5.77/5.78 tff(11754,plain,
% 5.77/5.78 (sum(pred(NSY5!16), succ(NPY5!18)) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11753, 12])).
% 5.77/5.78 tff(11755,plain,
% 5.77/5.78 (sum(pred(Y4!52), succ(X4!53)) = sum(n3, n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11598, 11680])).
% 5.77/5.78 tff(11756,plain,
% 5.77/5.78 (sum(pred(Y4!52), succ(X4!53)) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11755, 32])).
% 5.77/5.78 tff(11757,plain,
% 5.77/5.78 (sum(pred(X4!53), succ(Y4!52)) = sum(n3, n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11654, 11622])).
% 5.77/5.78 tff(11758,plain,
% 5.77/5.78 (sum(pred(X4!53), succ(Y4!52)) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11757, 32])).
% 5.77/5.78 tff(11759,plain,
% 5.77/5.78 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n8, n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11758, 11756])).
% 5.77/5.78 tff(11760,plain,
% 5.77/5.78 (X5!51 = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[553, 11759, 31])).
% 5.77/5.78 tff(11761,plain,
% 5.77/5.78 (pred(X5!51) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11760])).
% 5.77/5.78 tff(11762,plain,
% 5.77/5.78 (pred(X5!51) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11761, 16])).
% 5.77/5.78 tff(11763,plain,
% 5.77/5.78 (pred(pred(X5!51)) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11762])).
% 5.77/5.78 tff(11764,plain,
% 5.77/5.78 (pred(pred(X5!51)) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11763, 15])).
% 5.77/5.78 tff(11765,plain,
% 5.77/5.78 (pred(pred(pred(X5!51))) = pred(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11764])).
% 5.77/5.78 tff(11766,plain,
% 5.77/5.78 (pred(pred(pred(X5!51))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11765, 25])).
% 5.77/5.78 tff(11767,plain,
% 5.77/5.78 (pred(pred(pred(pred(X5!51)))) = pred(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11766])).
% 5.77/5.78 tff(11768,plain,
% 5.77/5.78 (pred(pred(pred(pred(X5!51)))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11767, 24])).
% 5.77/5.78 tff(11769,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X5!51))))) = pred(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11768])).
% 5.77/5.78 tff(11770,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X5!51))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11769, 23])).
% 5.77/5.78 tff(11771,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11770])).
% 5.77/5.78 tff(11772,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11771, 22])).
% 5.77/5.78 tff(11773,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11772])).
% 5.77/5.78 tff(11774,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11773, 21])).
% 5.77/5.78 tff(11775,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11774])).
% 5.77/5.78 tff(11776,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11775, 20])).
% 5.77/5.78 tff(11777,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11776])).
% 5.77/5.78 tff(11778,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11777, 19])).
% 5.77/5.78 tff(11779,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11778])).
% 5.77/5.78 tff(11780,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11779, 18])).
% 5.77/5.78 tff(11781,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11780])).
% 5.77/5.78 tff(11782,plain,
% 5.77/5.78 (NPX5!19 = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[742, 11781, 17])).
% 5.77/5.78 tff(11783,plain,
% 5.77/5.78 (succ(NPX5!19) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11782])).
% 5.77/5.78 tff(11784,plain,
% 5.77/5.78 (succ(NPX5!19) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11783, 30])).
% 5.77/5.78 tff(11785,plain,
% 5.77/5.78 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n6, n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11784, 11754])).
% 5.77/5.78 tff(11786,plain,
% 5.77/5.78 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11785, 674])).
% 5.77/5.78 tff(11787,plain,
% 5.77/5.78 (succ(X5!51) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11760])).
% 5.77/5.78 tff(11788,plain,
% 5.77/5.78 (succ(X5!51) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11787, 30])).
% 5.77/5.78 tff(11789,plain,
% 5.77/5.78 (succ(succ(X5!51)) = succ(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11788])).
% 5.77/5.78 tff(11790,plain,
% 5.77/5.78 (succ(succ(X5!51)) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11789, 39])).
% 5.77/5.78 tff(11791,plain,
% 5.77/5.78 (succ(succ(succ(X5!51))) = succ(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11790])).
% 5.77/5.78 tff(11792,plain,
% 5.77/5.78 (succ(succ(succ(X5!51))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11791, 53])).
% 5.77/5.78 tff(11793,plain,
% 5.77/5.78 (succ(succ(succ(succ(X5!51)))) = succ(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11792])).
% 5.77/5.78 tff(11794,plain,
% 5.77/5.78 (succ(succ(succ(succ(X5!51)))) = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[11793, 45])).
% 5.77/5.78 tff(11795,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(X5!51))))) = succ(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11794])).
% 5.77/5.78 tff(11796,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(X5!51))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11795, 28])).
% 5.77/5.78 tff(11797,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11796])).
% 5.77/5.78 tff(11798,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11797, 42])).
% 5.77/5.78 tff(11799,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11798])).
% 5.77/5.78 tff(11800,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11799, 58])).
% 5.77/5.78 tff(11801,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11800])).
% 5.77/5.78 tff(11802,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11801, 36])).
% 5.77/5.78 tff(11803,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11802])).
% 5.77/5.78 tff(11804,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11803, 48])).
% 5.77/5.78 tff(11805,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11804])).
% 5.77/5.78 tff(11806,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11805, 14])).
% 5.77/5.78 tff(11807,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11806])).
% 5.77/5.78 tff(11808,plain,
% 5.77/5.78 (NSX5!17 = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[767, 11807, 33])).
% 5.77/5.78 tff(11809,plain,
% 5.77/5.78 (pred(NSX5!17) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11808])).
% 5.77/5.78 tff(11810,plain,
% 5.77/5.78 (pred(NSX5!17) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11809, 16])).
% 5.77/5.78 tff(11811,plain,
% 5.77/5.78 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n4, n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11810, 11786])).
% 5.77/5.78 tff(11812,plain,
% 5.77/5.78 (Y6!48 = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[772, 11811, 673])).
% 5.77/5.78 tff(11813,plain,
% 5.77/5.78 (pred(Y6!48) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11812])).
% 5.77/5.78 tff(11814,plain,
% 5.77/5.78 (pred(Y6!48) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11813, 20])).
% 5.77/5.78 tff(11815,plain,
% 5.77/5.78 (pred(pred(Y6!48)) = pred(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11814])).
% 5.77/5.78 tff(11816,plain,
% 5.77/5.78 (pred(pred(Y6!48)) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11815, 19])).
% 5.77/5.78 tff(11817,plain,
% 5.77/5.78 (pred(pred(pred(Y6!48))) = pred(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11816])).
% 5.77/5.78 tff(11818,plain,
% 5.77/5.78 (pred(pred(pred(Y6!48))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11817, 18])).
% 5.77/5.78 tff(11819,plain,
% 5.77/5.78 (pred(pred(pred(pred(Y6!48)))) = pred(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11818])).
% 5.77/5.78 tff(11820,plain,
% 5.77/5.78 (pred(pred(pred(pred(Y6!48)))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11819, 17])).
% 5.77/5.78 tff(11821,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11820])).
% 5.77/5.78 tff(11822,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(Y6!48))))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11821, 16])).
% 5.77/5.78 tff(11823,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11822])).
% 5.77/5.78 tff(11824,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11823, 15])).
% 5.77/5.78 tff(11825,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11824])).
% 5.77/5.78 tff(11826,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11825, 25])).
% 5.77/5.78 tff(11827,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11826])).
% 5.77/5.78 tff(11828,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11827, 24])).
% 5.77/5.78 tff(11829,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11828])).
% 5.77/5.78 tff(11830,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11829, 23])).
% 5.77/5.78 tff(11831,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11830])).
% 5.77/5.78 tff(11832,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11831, 22])).
% 5.77/5.78 tff(11833,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11832])).
% 5.77/5.78 tff(11834,plain,
% 5.77/5.78 (NPY6!14 = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[1465, 11833, 21])).
% 5.77/5.78 tff(11835,plain,
% 5.77/5.78 (succ(NPY6!14) = succ(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11834])).
% 5.77/5.78 tff(11836,plain,
% 5.77/5.78 (succ(NPY6!14) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11835, 28])).
% 5.77/5.78 tff(11837,plain,
% 5.77/5.78 (succ(Y6!48) = succ(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11812])).
% 5.77/5.78 tff(11838,plain,
% 5.77/5.78 (succ(Y6!48) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11837, 28])).
% 5.77/5.78 tff(11839,plain,
% 5.77/5.78 (succ(succ(Y6!48)) = succ(n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11838])).
% 5.77/5.78 tff(11840,plain,
% 5.77/5.78 (succ(succ(Y6!48)) = n0),
% 5.77/5.78 inference(transitivity,[status(thm)],[11839, 42])).
% 5.77/5.78 tff(11841,plain,
% 5.77/5.78 (succ(succ(succ(Y6!48))) = succ(n0)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11840])).
% 5.77/5.78 tff(11842,plain,
% 5.77/5.78 (succ(succ(succ(Y6!48))) = n1),
% 5.77/5.78 inference(transitivity,[status(thm)],[11841, 58])).
% 5.77/5.78 tff(11843,plain,
% 5.77/5.78 (succ(succ(succ(succ(Y6!48)))) = succ(n1)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11842])).
% 5.77/5.78 tff(11844,plain,
% 5.77/5.78 (succ(succ(succ(succ(Y6!48)))) = n2),
% 5.77/5.78 inference(transitivity,[status(thm)],[11843, 36])).
% 5.77/5.78 tff(11845,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n2)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11844])).
% 5.77/5.78 tff(11846,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(Y6!48))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11845, 48])).
% 5.77/5.78 tff(11847,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11846])).
% 5.77/5.78 tff(11848,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11847, 14])).
% 5.77/5.78 tff(11849,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11848])).
% 5.77/5.78 tff(11850,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11849, 33])).
% 5.77/5.78 tff(11851,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11850])).
% 5.77/5.78 tff(11852,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11851, 30])).
% 5.77/5.78 tff(11853,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11852])).
% 5.77/5.78 tff(11854,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11853, 39])).
% 5.77/5.78 tff(11855,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11854])).
% 5.77/5.78 tff(11856,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11855, 53])).
% 5.77/5.78 tff(11857,plain,
% 5.77/5.78 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11856])).
% 5.77/5.78 tff(11858,plain,
% 5.77/5.78 (NSY6!12 = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[1490, 11857, 45])).
% 5.77/5.78 tff(11859,plain,
% 5.77/5.78 (pred(NSY6!12) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11858])).
% 5.77/5.78 tff(11860,plain,
% 5.77/5.78 (pred(NSY6!12) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11859, 20])).
% 5.77/5.78 tff(11861,plain,
% 5.77/5.78 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n8, n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11860, 11836])).
% 5.77/5.78 tff(11862,plain,
% 5.77/5.78 (sum(pred(NSY6!12), succ(NPY6!14)) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11861, 27])).
% 5.77/5.78 tff(11863,plain,
% 5.77/5.78 (sum(pred(Y5!50), succ(X5!51)) = sum(n4, n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11706, 11788])).
% 5.77/5.78 tff(11864,plain,
% 5.77/5.78 (sum(pred(Y5!50), succ(X5!51)) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11863, 12])).
% 5.77/5.78 tff(11865,plain,
% 5.77/5.78 (sum(pred(X5!51), succ(Y5!50)) = sum(n4, n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11762, 11730])).
% 5.77/5.78 tff(11866,plain,
% 5.77/5.78 (sum(pred(X5!51), succ(Y5!50)) = n10),
% 5.77/5.78 inference(transitivity,[status(thm)],[11865, 12])).
% 5.77/5.78 tff(11867,plain,
% 5.77/5.78 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n10, n10)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11866, 11864])).
% 5.77/5.78 tff(11868,plain,
% 5.77/5.78 (X6!49 = n9),
% 5.77/5.78 inference(transitivity,[status(thm)],[669, 11867, 29])).
% 5.77/5.78 tff(11869,plain,
% 5.77/5.78 (pred(X6!49) = pred(n9)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11868])).
% 5.77/5.78 tff(11870,plain,
% 5.77/5.78 (pred(X6!49) = n8),
% 5.77/5.78 inference(transitivity,[status(thm)],[11869, 20])).
% 5.77/5.78 tff(11871,plain,
% 5.77/5.78 (pred(pred(X6!49)) = pred(n8)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11870])).
% 5.77/5.78 tff(11872,plain,
% 5.77/5.78 (pred(pred(X6!49)) = n7),
% 5.77/5.78 inference(transitivity,[status(thm)],[11871, 19])).
% 5.77/5.78 tff(11873,plain,
% 5.77/5.78 (pred(pred(pred(X6!49))) = pred(n7)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11872])).
% 5.77/5.78 tff(11874,plain,
% 5.77/5.78 (pred(pred(pred(X6!49))) = n6),
% 5.77/5.78 inference(transitivity,[status(thm)],[11873, 18])).
% 5.77/5.78 tff(11875,plain,
% 5.77/5.78 (pred(pred(pred(pred(X6!49)))) = pred(n6)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11874])).
% 5.77/5.78 tff(11876,plain,
% 5.77/5.78 (pred(pred(pred(pred(X6!49)))) = n5),
% 5.77/5.78 inference(transitivity,[status(thm)],[11875, 17])).
% 5.77/5.78 tff(11877,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X6!49))))) = pred(n5)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11876])).
% 5.77/5.78 tff(11878,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(X6!49))))) = n4),
% 5.77/5.78 inference(transitivity,[status(thm)],[11877, 16])).
% 5.77/5.78 tff(11879,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n4)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11878])).
% 5.77/5.78 tff(11880,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n3),
% 5.77/5.78 inference(transitivity,[status(thm)],[11879, 15])).
% 5.77/5.78 tff(11881,plain,
% 5.77/5.78 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n3)),
% 5.77/5.78 inference(monotonicity,[status(thm)],[11880])).
% 5.77/5.79 tff(11882,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n2),
% 5.77/5.79 inference(transitivity,[status(thm)],[11881, 25])).
% 5.77/5.79 tff(11883,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n2)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11882])).
% 5.77/5.79 tff(11884,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n1),
% 5.77/5.79 inference(transitivity,[status(thm)],[11883, 24])).
% 5.77/5.79 tff(11885,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n1)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11884])).
% 5.77/5.79 tff(11886,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n0),
% 5.77/5.79 inference(transitivity,[status(thm)],[11885, 23])).
% 5.77/5.79 tff(11887,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n0)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11886])).
% 5.77/5.79 tff(11888,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n10),
% 5.77/5.79 inference(transitivity,[status(thm)],[11887, 22])).
% 5.77/5.79 tff(11889,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n10)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11888])).
% 5.77/5.79 tff(11890,plain,
% 5.77/5.79 (NPX6!15 = n9),
% 5.77/5.79 inference(transitivity,[status(thm)],[1523, 11889, 21])).
% 5.77/5.79 tff(11891,plain,
% 5.77/5.79 (succ(NPX6!15) = succ(n9)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11890])).
% 5.77/5.79 tff(11892,plain,
% 5.77/5.79 (succ(NPX6!15) = n10),
% 5.77/5.79 inference(transitivity,[status(thm)],[11891, 28])).
% 5.77/5.79 tff(11893,plain,
% 5.77/5.79 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n10, n7)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11892, 11862])).
% 5.77/5.79 tff(11894,plain,
% 5.77/5.79 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n6),
% 5.77/5.79 inference(transitivity,[status(thm)],[11893, 69])).
% 5.77/5.79 tff(11895,plain,
% 5.77/5.79 (succ(X6!49) = succ(n9)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11868])).
% 5.77/5.79 tff(11896,plain,
% 5.77/5.79 (succ(X6!49) = n10),
% 5.77/5.79 inference(transitivity,[status(thm)],[11895, 28])).
% 5.77/5.79 tff(11897,plain,
% 5.77/5.79 (succ(succ(X6!49)) = succ(n10)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11896])).
% 5.77/5.79 tff(11898,plain,
% 5.77/5.79 (succ(succ(X6!49)) = n0),
% 5.77/5.79 inference(transitivity,[status(thm)],[11897, 42])).
% 5.77/5.79 tff(11899,plain,
% 5.77/5.79 (succ(succ(succ(X6!49))) = succ(n0)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11898])).
% 5.77/5.79 tff(11900,plain,
% 5.77/5.79 (succ(succ(succ(X6!49))) = n1),
% 5.77/5.79 inference(transitivity,[status(thm)],[11899, 58])).
% 5.77/5.79 tff(11901,plain,
% 5.77/5.79 (succ(succ(succ(succ(X6!49)))) = succ(n1)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11900])).
% 5.77/5.79 tff(11902,plain,
% 5.77/5.79 (succ(succ(succ(succ(X6!49)))) = n2),
% 5.77/5.79 inference(transitivity,[status(thm)],[11901, 36])).
% 5.77/5.79 tff(11903,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(X6!49))))) = succ(n2)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11902])).
% 5.77/5.79 tff(11904,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(X6!49))))) = n3),
% 5.77/5.79 inference(transitivity,[status(thm)],[11903, 48])).
% 5.77/5.79 tff(11905,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n3)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11904])).
% 5.77/5.79 tff(11906,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n4),
% 5.77/5.79 inference(transitivity,[status(thm)],[11905, 14])).
% 5.77/5.79 tff(11907,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n4)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11906])).
% 5.77/5.79 tff(11908,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n5),
% 5.77/5.79 inference(transitivity,[status(thm)],[11907, 33])).
% 5.77/5.79 tff(11909,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n5)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11908])).
% 5.77/5.79 tff(11910,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n6),
% 5.77/5.79 inference(transitivity,[status(thm)],[11909, 30])).
% 5.77/5.79 tff(11911,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n6)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11910])).
% 5.77/5.79 tff(11912,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n7),
% 5.77/5.79 inference(transitivity,[status(thm)],[11911, 39])).
% 5.77/5.79 tff(11913,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n7)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11912])).
% 5.77/5.79 tff(11914,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n8),
% 5.77/5.79 inference(transitivity,[status(thm)],[11913, 53])).
% 5.77/5.79 tff(11915,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n8)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11914])).
% 5.77/5.79 tff(11916,plain,
% 5.77/5.79 (NSX6!13 = n9),
% 5.77/5.79 inference(transitivity,[status(thm)],[1550, 11915, 45])).
% 5.77/5.79 tff(11917,plain,
% 5.77/5.79 (pred(NSX6!13) = pred(n9)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11916])).
% 5.77/5.79 tff(11918,plain,
% 5.77/5.79 (pred(NSX6!13) = n8),
% 5.77/5.79 inference(transitivity,[status(thm)],[11917, 20])).
% 5.77/5.79 tff(11919,plain,
% 5.77/5.79 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n8, n6)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11918, 11894])).
% 5.77/5.79 tff(11920,plain,
% 5.77/5.79 (sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.77/5.79 inference(symmetry,[status(thm)],[11919])).
% 5.77/5.79 tff(11921,plain,
% 5.77/5.79 (sum(pred(Y6!48), succ(X6!49)) = sum(n8, n10)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11814, 11896])).
% 5.77/5.79 tff(11922,plain,
% 5.77/5.79 (sum(pred(Y6!48), succ(X6!49)) = n7),
% 5.77/5.79 inference(transitivity,[status(thm)],[11921, 27])).
% 5.77/5.79 tff(11923,plain,
% 5.77/5.79 (sum(pred(X6!49), succ(Y6!48)) = sum(n8, n10)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11870, 11838])).
% 5.77/5.79 tff(11924,plain,
% 5.77/5.79 (sum(pred(X6!49), succ(Y6!48)) = n7),
% 5.77/5.79 inference(transitivity,[status(thm)],[11923, 27])).
% 5.77/5.79 tff(11925,plain,
% 5.77/5.79 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n7, n7)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11924, 11922])).
% 5.77/5.79 tff(11926,plain,
% 5.77/5.79 (X7!47 = Y7!46),
% 5.77/5.79 inference(transitivity,[status(thm)],[785, 11925, 26, 1556, 11920, 794])).
% 5.77/5.79 tff(11927,plain,
% 5.77/5.79 ($false),
% 5.77/5.79 inference(unit_resolution,[status(thm)],[792, 11926])).
% 5.77/5.79 tff(11928,plain,((~(X0!61 = n10)) | (X7!47 = Y7!46) | (~(Y0!60 = n0))), inference(lemma,lemma(discharge,[]))).
% 5.77/5.79 tff(11929,plain,
% 5.77/5.79 (~(X0!61 = n10)),
% 5.77/5.79 inference(unit_resolution,[status(thm)],[11928, 9225, 792])).
% 5.77/5.79 tff(11930,assumption,(X0!61 = n4), introduced(assumption)).
% 5.77/5.79 tff(11931,plain,
% 5.77/5.79 (pred(X0!61) = pred(n4)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11930])).
% 5.77/5.79 tff(11932,plain,
% 5.77/5.79 (pred(X0!61) = n3),
% 5.77/5.79 inference(transitivity,[status(thm)],[11931, 15])).
% 5.77/5.79 tff(11933,plain,
% 5.77/5.79 (pred(pred(X0!61)) = pred(n3)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11932])).
% 5.77/5.79 tff(11934,plain,
% 5.77/5.79 (pred(pred(X0!61)) = n2),
% 5.77/5.79 inference(transitivity,[status(thm)],[11933, 25])).
% 5.77/5.79 tff(11935,plain,
% 5.77/5.79 (pred(pred(pred(X0!61))) = pred(n2)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11934])).
% 5.77/5.79 tff(11936,plain,
% 5.77/5.79 (pred(pred(pred(X0!61))) = n1),
% 5.77/5.79 inference(transitivity,[status(thm)],[11935, 24])).
% 5.77/5.79 tff(11937,plain,
% 5.77/5.79 (pred(pred(pred(pred(X0!61)))) = pred(n1)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11936])).
% 5.77/5.79 tff(11938,plain,
% 5.77/5.79 (pred(pred(pred(pred(X0!61)))) = n0),
% 5.77/5.79 inference(transitivity,[status(thm)],[11937, 23])).
% 5.77/5.79 tff(11939,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(X0!61))))) = pred(n0)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11938])).
% 5.77/5.79 tff(11940,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(X0!61))))) = n10),
% 5.77/5.79 inference(transitivity,[status(thm)],[11939, 22])).
% 5.77/5.79 tff(11941,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n10)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11940])).
% 5.77/5.79 tff(11942,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n9),
% 5.77/5.79 inference(transitivity,[status(thm)],[11941, 21])).
% 5.77/5.79 tff(11943,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n9)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11942])).
% 5.77/5.79 tff(11944,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n8),
% 5.77/5.79 inference(transitivity,[status(thm)],[11943, 20])).
% 5.77/5.79 tff(11945,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n8)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11944])).
% 5.77/5.79 tff(11946,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n7),
% 5.77/5.79 inference(transitivity,[status(thm)],[11945, 19])).
% 5.77/5.79 tff(11947,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n7)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11946])).
% 5.77/5.79 tff(11948,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n6),
% 5.77/5.79 inference(transitivity,[status(thm)],[11947, 18])).
% 5.77/5.79 tff(11949,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n6)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11948])).
% 5.77/5.79 tff(11950,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n5),
% 5.77/5.79 inference(transitivity,[status(thm)],[11949, 17])).
% 5.77/5.79 tff(11951,plain,
% 5.77/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n5)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11950])).
% 5.77/5.79 tff(11952,plain,
% 5.77/5.79 (NPX0!39 = n4),
% 5.77/5.79 inference(transitivity,[status(thm)],[166, 11951, 16])).
% 5.77/5.79 tff(11953,plain,
% 5.77/5.79 (succ(NPX0!39) = succ(n4)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11952])).
% 5.77/5.79 tff(11954,plain,
% 5.77/5.79 (succ(NPX0!39) = n5),
% 5.77/5.79 inference(transitivity,[status(thm)],[11953, 33])).
% 5.77/5.79 tff(11955,plain,
% 5.77/5.79 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n5, n8)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11954, 847])).
% 5.77/5.79 tff(11956,plain,
% 5.77/5.79 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n2),
% 5.77/5.79 inference(transitivity,[status(thm)],[11955, 558])).
% 5.77/5.79 tff(11957,plain,
% 5.77/5.79 (succ(X0!61) = succ(n4)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11930])).
% 5.77/5.79 tff(11958,plain,
% 5.77/5.79 (succ(X0!61) = n5),
% 5.77/5.79 inference(transitivity,[status(thm)],[11957, 33])).
% 5.77/5.79 tff(11959,plain,
% 5.77/5.79 (succ(succ(X0!61)) = succ(n5)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11958])).
% 5.77/5.79 tff(11960,plain,
% 5.77/5.79 (succ(succ(X0!61)) = n6),
% 5.77/5.79 inference(transitivity,[status(thm)],[11959, 30])).
% 5.77/5.79 tff(11961,plain,
% 5.77/5.79 (succ(succ(succ(X0!61))) = succ(n6)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11960])).
% 5.77/5.79 tff(11962,plain,
% 5.77/5.79 (succ(succ(succ(X0!61))) = n7),
% 5.77/5.79 inference(transitivity,[status(thm)],[11961, 39])).
% 5.77/5.79 tff(11963,plain,
% 5.77/5.79 (succ(succ(succ(succ(X0!61)))) = succ(n7)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11962])).
% 5.77/5.79 tff(11964,plain,
% 5.77/5.79 (succ(succ(succ(succ(X0!61)))) = n8),
% 5.77/5.79 inference(transitivity,[status(thm)],[11963, 53])).
% 5.77/5.79 tff(11965,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(X0!61))))) = succ(n8)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11964])).
% 5.77/5.79 tff(11966,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(X0!61))))) = n9),
% 5.77/5.79 inference(transitivity,[status(thm)],[11965, 45])).
% 5.77/5.79 tff(11967,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n9)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11966])).
% 5.77/5.79 tff(11968,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n10),
% 5.77/5.79 inference(transitivity,[status(thm)],[11967, 28])).
% 5.77/5.79 tff(11969,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n10)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11968])).
% 5.77/5.79 tff(11970,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n0),
% 5.77/5.79 inference(transitivity,[status(thm)],[11969, 42])).
% 5.77/5.79 tff(11971,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n0)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11970])).
% 5.77/5.79 tff(11972,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n1),
% 5.77/5.79 inference(transitivity,[status(thm)],[11971, 58])).
% 5.77/5.79 tff(11973,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n1)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11972])).
% 5.77/5.79 tff(11974,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n2),
% 5.77/5.79 inference(transitivity,[status(thm)],[11973, 36])).
% 5.77/5.79 tff(11975,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n2)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11974])).
% 5.77/5.79 tff(11976,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n3),
% 5.77/5.79 inference(transitivity,[status(thm)],[11975, 48])).
% 5.77/5.79 tff(11977,plain,
% 5.77/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n3)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11976])).
% 5.77/5.79 tff(11978,plain,
% 5.77/5.79 (NSX0!37 = n4),
% 5.77/5.79 inference(transitivity,[status(thm)],[191, 11977, 14])).
% 5.77/5.79 tff(11979,plain,
% 5.77/5.79 (pred(NSX0!37) = pred(n4)),
% 5.77/5.79 inference(monotonicity,[status(thm)],[11978])).
% 5.85/5.79 tff(11980,plain,
% 5.85/5.79 (pred(NSX0!37) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[11979, 15])).
% 5.85/5.79 tff(11981,plain,
% 5.85/5.79 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n3, n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11980, 11956])).
% 5.85/5.79 tff(11982,plain,
% 5.85/5.79 (Y1!58 = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[196, 11981, 557])).
% 5.85/5.79 tff(11983,plain,
% 5.85/5.79 (pred(Y1!58) = pred(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11982])).
% 5.85/5.79 tff(11984,plain,
% 5.85/5.79 (pred(Y1!58) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[11983, 16])).
% 5.85/5.79 tff(11985,plain,
% 5.85/5.79 (pred(pred(Y1!58)) = pred(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11984])).
% 5.85/5.79 tff(11986,plain,
% 5.85/5.79 (pred(pred(Y1!58)) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[11985, 15])).
% 5.85/5.79 tff(11987,plain,
% 5.85/5.79 (pred(pred(pred(Y1!58))) = pred(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11986])).
% 5.85/5.79 tff(11988,plain,
% 5.85/5.79 (pred(pred(pred(Y1!58))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[11987, 25])).
% 5.85/5.79 tff(11989,plain,
% 5.85/5.79 (pred(pred(pred(pred(Y1!58)))) = pred(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11988])).
% 5.85/5.79 tff(11990,plain,
% 5.85/5.79 (pred(pred(pred(pred(Y1!58)))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[11989, 24])).
% 5.85/5.79 tff(11991,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11990])).
% 5.85/5.79 tff(11992,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(Y1!58))))) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[11991, 23])).
% 5.85/5.79 tff(11993,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11992])).
% 5.85/5.79 tff(11994,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[11993, 22])).
% 5.85/5.79 tff(11995,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11994])).
% 5.85/5.79 tff(11996,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[11995, 21])).
% 5.85/5.79 tff(11997,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11996])).
% 5.85/5.79 tff(11998,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[11997, 20])).
% 5.85/5.79 tff(11999,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11998])).
% 5.85/5.79 tff(12000,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[11999, 19])).
% 5.85/5.79 tff(12001,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12000])).
% 5.85/5.79 tff(12002,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12001, 18])).
% 5.85/5.79 tff(12003,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12002])).
% 5.85/5.79 tff(12004,plain,
% 5.85/5.79 (NPY1!34 = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[232, 12003, 17])).
% 5.85/5.79 tff(12005,plain,
% 5.85/5.79 (succ(NPY1!34) = succ(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12004])).
% 5.85/5.79 tff(12006,plain,
% 5.85/5.79 (succ(NPY1!34) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12005, 30])).
% 5.85/5.79 tff(12007,plain,
% 5.85/5.79 (succ(Y1!58) = succ(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11982])).
% 5.85/5.79 tff(12008,plain,
% 5.85/5.79 (succ(Y1!58) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12007, 30])).
% 5.85/5.79 tff(12009,plain,
% 5.85/5.79 (succ(succ(Y1!58)) = succ(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12008])).
% 5.85/5.79 tff(12010,plain,
% 5.85/5.79 (succ(succ(Y1!58)) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12009, 39])).
% 5.85/5.79 tff(12011,plain,
% 5.85/5.79 (succ(succ(succ(Y1!58))) = succ(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12010])).
% 5.85/5.79 tff(12012,plain,
% 5.85/5.79 (succ(succ(succ(Y1!58))) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12011, 53])).
% 5.85/5.79 tff(12013,plain,
% 5.85/5.79 (succ(succ(succ(succ(Y1!58)))) = succ(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12012])).
% 5.85/5.79 tff(12014,plain,
% 5.85/5.79 (succ(succ(succ(succ(Y1!58)))) = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[12013, 45])).
% 5.85/5.79 tff(12015,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12014])).
% 5.85/5.79 tff(12016,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(Y1!58))))) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12015, 28])).
% 5.85/5.79 tff(12017,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12016])).
% 5.85/5.79 tff(12018,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12017, 42])).
% 5.85/5.79 tff(12019,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12018])).
% 5.85/5.79 tff(12020,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12019, 58])).
% 5.85/5.79 tff(12021,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12020])).
% 5.85/5.79 tff(12022,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12021, 36])).
% 5.85/5.79 tff(12023,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12022])).
% 5.85/5.79 tff(12024,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[12023, 48])).
% 5.85/5.79 tff(12025,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12024])).
% 5.85/5.79 tff(12026,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12025, 14])).
% 5.85/5.79 tff(12027,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12026])).
% 5.85/5.79 tff(12028,plain,
% 5.85/5.79 (NSY1!32 = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[255, 12027, 33])).
% 5.85/5.79 tff(12029,plain,
% 5.85/5.79 (pred(NSY1!32) = pred(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12028])).
% 5.85/5.79 tff(12030,plain,
% 5.85/5.79 (pred(NSY1!32) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12029, 16])).
% 5.85/5.79 tff(12031,plain,
% 5.85/5.79 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n4, n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12030, 12006])).
% 5.85/5.79 tff(12032,plain,
% 5.85/5.79 (sum(pred(NSY1!32), succ(NPY1!34)) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12031, 12])).
% 5.85/5.79 tff(12033,plain,
% 5.85/5.79 (sum(pred(Y0!60), succ(X0!61)) = sum(n3, n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[799, 11958])).
% 5.85/5.79 tff(12034,plain,
% 5.85/5.79 (sum(pred(Y0!60), succ(X0!61)) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12033, 32])).
% 5.85/5.79 tff(12035,plain,
% 5.85/5.79 (sum(pred(X0!61), succ(Y0!60)) = sum(n3, n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11932, 823])).
% 5.85/5.79 tff(12036,plain,
% 5.85/5.79 (sum(pred(X0!61), succ(Y0!60)) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12035, 32])).
% 5.85/5.79 tff(12037,plain,
% 5.85/5.79 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n8, n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12036, 12034])).
% 5.85/5.79 tff(12038,plain,
% 5.85/5.79 (X1!59 = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[93, 12037, 31])).
% 5.85/5.79 tff(12039,plain,
% 5.85/5.79 (pred(X1!59) = pred(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12038])).
% 5.85/5.79 tff(12040,plain,
% 5.85/5.79 (pred(X1!59) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12039, 16])).
% 5.85/5.79 tff(12041,plain,
% 5.85/5.79 (pred(pred(X1!59)) = pred(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12040])).
% 5.85/5.79 tff(12042,plain,
% 5.85/5.79 (pred(pred(X1!59)) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[12041, 15])).
% 5.85/5.79 tff(12043,plain,
% 5.85/5.79 (pred(pred(pred(X1!59))) = pred(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12042])).
% 5.85/5.79 tff(12044,plain,
% 5.85/5.79 (pred(pred(pred(X1!59))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12043, 25])).
% 5.85/5.79 tff(12045,plain,
% 5.85/5.79 (pred(pred(pred(pred(X1!59)))) = pred(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12044])).
% 5.85/5.79 tff(12046,plain,
% 5.85/5.79 (pred(pred(pred(pred(X1!59)))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12045, 24])).
% 5.85/5.79 tff(12047,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(X1!59))))) = pred(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12046])).
% 5.85/5.79 tff(12048,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(X1!59))))) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12047, 23])).
% 5.85/5.79 tff(12049,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12048])).
% 5.85/5.79 tff(12050,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12049, 22])).
% 5.85/5.79 tff(12051,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12050])).
% 5.85/5.79 tff(12052,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[12051, 21])).
% 5.85/5.79 tff(12053,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12052])).
% 5.85/5.79 tff(12054,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12053, 20])).
% 5.85/5.79 tff(12055,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12054])).
% 5.85/5.79 tff(12056,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12055, 19])).
% 5.85/5.79 tff(12057,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12056])).
% 5.85/5.79 tff(12058,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12057, 18])).
% 5.85/5.79 tff(12059,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12058])).
% 5.85/5.79 tff(12060,plain,
% 5.85/5.79 (NPX1!35 = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[280, 12059, 17])).
% 5.85/5.79 tff(12061,plain,
% 5.85/5.79 (succ(NPX1!35) = succ(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12060])).
% 5.85/5.79 tff(12062,plain,
% 5.85/5.79 (succ(NPX1!35) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12061, 30])).
% 5.85/5.79 tff(12063,plain,
% 5.85/5.79 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n6, n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12062, 12032])).
% 5.85/5.79 tff(12064,plain,
% 5.85/5.79 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[12063, 674])).
% 5.85/5.79 tff(12065,plain,
% 5.85/5.79 (succ(X1!59) = succ(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12038])).
% 5.85/5.79 tff(12066,plain,
% 5.85/5.79 (succ(X1!59) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12065, 30])).
% 5.85/5.79 tff(12067,plain,
% 5.85/5.79 (succ(succ(X1!59)) = succ(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12066])).
% 5.85/5.79 tff(12068,plain,
% 5.85/5.79 (succ(succ(X1!59)) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12067, 39])).
% 5.85/5.79 tff(12069,plain,
% 5.85/5.79 (succ(succ(succ(X1!59))) = succ(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12068])).
% 5.85/5.79 tff(12070,plain,
% 5.85/5.79 (succ(succ(succ(X1!59))) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12069, 53])).
% 5.85/5.79 tff(12071,plain,
% 5.85/5.79 (succ(succ(succ(succ(X1!59)))) = succ(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12070])).
% 5.85/5.79 tff(12072,plain,
% 5.85/5.79 (succ(succ(succ(succ(X1!59)))) = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[12071, 45])).
% 5.85/5.79 tff(12073,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(X1!59))))) = succ(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12072])).
% 5.85/5.79 tff(12074,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(X1!59))))) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12073, 28])).
% 5.85/5.79 tff(12075,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12074])).
% 5.85/5.79 tff(12076,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12075, 42])).
% 5.85/5.79 tff(12077,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12076])).
% 5.85/5.79 tff(12078,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12077, 58])).
% 5.85/5.79 tff(12079,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12078])).
% 5.85/5.79 tff(12080,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12079, 36])).
% 5.85/5.79 tff(12081,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12080])).
% 5.85/5.79 tff(12082,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[12081, 48])).
% 5.85/5.79 tff(12083,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12082])).
% 5.85/5.79 tff(12084,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12083, 14])).
% 5.85/5.79 tff(12085,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12084])).
% 5.85/5.79 tff(12086,plain,
% 5.85/5.79 (NSX1!33 = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[305, 12085, 33])).
% 5.85/5.79 tff(12087,plain,
% 5.85/5.79 (pred(NSX1!33) = pred(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12086])).
% 5.85/5.79 tff(12088,plain,
% 5.85/5.79 (pred(NSX1!33) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12087, 16])).
% 5.85/5.79 tff(12089,plain,
% 5.85/5.79 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n4, n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12088, 12064])).
% 5.85/5.79 tff(12090,plain,
% 5.85/5.79 (Y2!56 = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[310, 12089, 673])).
% 5.85/5.79 tff(12091,plain,
% 5.85/5.79 (pred(Y2!56) = pred(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12090])).
% 5.85/5.79 tff(12092,plain,
% 5.85/5.79 (pred(Y2!56) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12091, 20])).
% 5.85/5.79 tff(12093,plain,
% 5.85/5.79 (pred(pred(Y2!56)) = pred(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12092])).
% 5.85/5.79 tff(12094,plain,
% 5.85/5.79 (pred(pred(Y2!56)) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12093, 19])).
% 5.85/5.79 tff(12095,plain,
% 5.85/5.79 (pred(pred(pred(Y2!56))) = pred(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12094])).
% 5.85/5.79 tff(12096,plain,
% 5.85/5.79 (pred(pred(pred(Y2!56))) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12095, 18])).
% 5.85/5.79 tff(12097,plain,
% 5.85/5.79 (pred(pred(pred(pred(Y2!56)))) = pred(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12096])).
% 5.85/5.79 tff(12098,plain,
% 5.85/5.79 (pred(pred(pred(pred(Y2!56)))) = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[12097, 17])).
% 5.85/5.79 tff(12099,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12098])).
% 5.85/5.79 tff(12100,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(Y2!56))))) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12099, 16])).
% 5.85/5.79 tff(12101,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12100])).
% 5.85/5.79 tff(12102,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[12101, 15])).
% 5.85/5.79 tff(12103,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12102])).
% 5.85/5.79 tff(12104,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12103, 25])).
% 5.85/5.79 tff(12105,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12104])).
% 5.85/5.79 tff(12106,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12105, 24])).
% 5.85/5.79 tff(12107,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12106])).
% 5.85/5.79 tff(12108,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12107, 23])).
% 5.85/5.79 tff(12109,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12108])).
% 5.85/5.79 tff(12110,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12109, 22])).
% 5.85/5.79 tff(12111,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12110])).
% 5.85/5.79 tff(12112,plain,
% 5.85/5.79 (NPY2!30 = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[347, 12111, 21])).
% 5.85/5.79 tff(12113,plain,
% 5.85/5.79 (succ(NPY2!30) = succ(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12112])).
% 5.85/5.79 tff(12114,plain,
% 5.85/5.79 (succ(NPY2!30) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12113, 28])).
% 5.85/5.79 tff(12115,plain,
% 5.85/5.79 (succ(Y2!56) = succ(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12090])).
% 5.85/5.79 tff(12116,plain,
% 5.85/5.79 (succ(Y2!56) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12115, 28])).
% 5.85/5.79 tff(12117,plain,
% 5.85/5.79 (succ(succ(Y2!56)) = succ(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12116])).
% 5.85/5.79 tff(12118,plain,
% 5.85/5.79 (succ(succ(Y2!56)) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12117, 42])).
% 5.85/5.79 tff(12119,plain,
% 5.85/5.79 (succ(succ(succ(Y2!56))) = succ(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12118])).
% 5.85/5.79 tff(12120,plain,
% 5.85/5.79 (succ(succ(succ(Y2!56))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12119, 58])).
% 5.85/5.79 tff(12121,plain,
% 5.85/5.79 (succ(succ(succ(succ(Y2!56)))) = succ(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12120])).
% 5.85/5.79 tff(12122,plain,
% 5.85/5.79 (succ(succ(succ(succ(Y2!56)))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12121, 36])).
% 5.85/5.79 tff(12123,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12122])).
% 5.85/5.79 tff(12124,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(Y2!56))))) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[12123, 48])).
% 5.85/5.79 tff(12125,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12124])).
% 5.85/5.79 tff(12126,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12125, 14])).
% 5.85/5.79 tff(12127,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12126])).
% 5.85/5.79 tff(12128,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[12127, 33])).
% 5.85/5.79 tff(12129,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12128])).
% 5.85/5.79 tff(12130,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12129, 30])).
% 5.85/5.79 tff(12131,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12130])).
% 5.85/5.79 tff(12132,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12131, 39])).
% 5.85/5.79 tff(12133,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12132])).
% 5.85/5.79 tff(12134,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12133, 53])).
% 5.85/5.79 tff(12135,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12134])).
% 5.85/5.79 tff(12136,plain,
% 5.85/5.79 (NSY2!28 = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[370, 12135, 45])).
% 5.85/5.79 tff(12137,plain,
% 5.85/5.79 (pred(NSY2!28) = pred(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12136])).
% 5.85/5.79 tff(12138,plain,
% 5.85/5.79 (pred(NSY2!28) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12137, 20])).
% 5.85/5.79 tff(12139,plain,
% 5.85/5.79 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n8, n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12138, 12114])).
% 5.85/5.79 tff(12140,plain,
% 5.85/5.79 (sum(pred(NSY2!28), succ(NPY2!30)) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12139, 27])).
% 5.85/5.79 tff(12141,plain,
% 5.85/5.79 (sum(pred(Y1!58), succ(X1!59)) = sum(n4, n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[11984, 12066])).
% 5.85/5.79 tff(12142,plain,
% 5.85/5.79 (sum(pred(Y1!58), succ(X1!59)) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12141, 12])).
% 5.85/5.79 tff(12143,plain,
% 5.85/5.79 (sum(pred(X1!59), succ(Y1!58)) = sum(n4, n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12040, 12008])).
% 5.85/5.79 tff(12144,plain,
% 5.85/5.79 (sum(pred(X1!59), succ(Y1!58)) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12143, 12])).
% 5.85/5.79 tff(12145,plain,
% 5.85/5.79 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n10, n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12144, 12142])).
% 5.85/5.79 tff(12146,plain,
% 5.85/5.79 (X2!57 = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[209, 12145, 29])).
% 5.85/5.79 tff(12147,plain,
% 5.85/5.79 (pred(X2!57) = pred(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12146])).
% 5.85/5.79 tff(12148,plain,
% 5.85/5.79 (pred(X2!57) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12147, 20])).
% 5.85/5.79 tff(12149,plain,
% 5.85/5.79 (pred(pred(X2!57)) = pred(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12148])).
% 5.85/5.79 tff(12150,plain,
% 5.85/5.79 (pred(pred(X2!57)) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12149, 19])).
% 5.85/5.79 tff(12151,plain,
% 5.85/5.79 (pred(pred(pred(X2!57))) = pred(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12150])).
% 5.85/5.79 tff(12152,plain,
% 5.85/5.79 (pred(pred(pred(X2!57))) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12151, 18])).
% 5.85/5.79 tff(12153,plain,
% 5.85/5.79 (pred(pred(pred(pred(X2!57)))) = pred(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12152])).
% 5.85/5.79 tff(12154,plain,
% 5.85/5.79 (pred(pred(pred(pred(X2!57)))) = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[12153, 17])).
% 5.85/5.79 tff(12155,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(X2!57))))) = pred(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12154])).
% 5.85/5.79 tff(12156,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(X2!57))))) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12155, 16])).
% 5.85/5.79 tff(12157,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12156])).
% 5.85/5.79 tff(12158,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[12157, 15])).
% 5.85/5.79 tff(12159,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12158])).
% 5.85/5.79 tff(12160,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12159, 25])).
% 5.85/5.79 tff(12161,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12160])).
% 5.85/5.79 tff(12162,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12161, 24])).
% 5.85/5.79 tff(12163,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12162])).
% 5.85/5.79 tff(12164,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12163, 23])).
% 5.85/5.79 tff(12165,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12164])).
% 5.85/5.79 tff(12166,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12165, 22])).
% 5.85/5.79 tff(12167,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12166])).
% 5.85/5.79 tff(12168,plain,
% 5.85/5.79 (NPX2!31 = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[395, 12167, 21])).
% 5.85/5.79 tff(12169,plain,
% 5.85/5.79 (succ(NPX2!31) = succ(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12168])).
% 5.85/5.79 tff(12170,plain,
% 5.85/5.79 (succ(NPX2!31) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12169, 28])).
% 5.85/5.79 tff(12171,plain,
% 5.85/5.79 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n10, n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12170, 12140])).
% 5.85/5.79 tff(12172,plain,
% 5.85/5.79 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12171, 69])).
% 5.85/5.79 tff(12173,plain,
% 5.85/5.79 (succ(X2!57) = succ(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12146])).
% 5.85/5.79 tff(12174,plain,
% 5.85/5.79 (succ(X2!57) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12173, 28])).
% 5.85/5.79 tff(12175,plain,
% 5.85/5.79 (succ(succ(X2!57)) = succ(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12174])).
% 5.85/5.79 tff(12176,plain,
% 5.85/5.79 (succ(succ(X2!57)) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12175, 42])).
% 5.85/5.79 tff(12177,plain,
% 5.85/5.79 (succ(succ(succ(X2!57))) = succ(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12176])).
% 5.85/5.79 tff(12178,plain,
% 5.85/5.79 (succ(succ(succ(X2!57))) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12177, 58])).
% 5.85/5.79 tff(12179,plain,
% 5.85/5.79 (succ(succ(succ(succ(X2!57)))) = succ(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12178])).
% 5.85/5.79 tff(12180,plain,
% 5.85/5.79 (succ(succ(succ(succ(X2!57)))) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12179, 36])).
% 5.85/5.79 tff(12181,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(X2!57))))) = succ(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12180])).
% 5.85/5.79 tff(12182,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(X2!57))))) = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[12181, 48])).
% 5.85/5.79 tff(12183,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12182])).
% 5.85/5.79 tff(12184,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n4),
% 5.85/5.79 inference(transitivity,[status(thm)],[12183, 14])).
% 5.85/5.79 tff(12185,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n4)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12184])).
% 5.85/5.79 tff(12186,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n5),
% 5.85/5.79 inference(transitivity,[status(thm)],[12185, 33])).
% 5.85/5.79 tff(12187,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n5)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12186])).
% 5.85/5.79 tff(12188,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n6),
% 5.85/5.79 inference(transitivity,[status(thm)],[12187, 30])).
% 5.85/5.79 tff(12189,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12188])).
% 5.85/5.79 tff(12190,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n7),
% 5.85/5.79 inference(transitivity,[status(thm)],[12189, 39])).
% 5.85/5.79 tff(12191,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n7)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12190])).
% 5.85/5.79 tff(12192,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12191, 53])).
% 5.85/5.79 tff(12193,plain,
% 5.85/5.79 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12192])).
% 5.85/5.79 tff(12194,plain,
% 5.85/5.79 (NSX2!29 = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[420, 12193, 45])).
% 5.85/5.79 tff(12195,plain,
% 5.85/5.79 (pred(NSX2!29) = pred(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12194])).
% 5.85/5.79 tff(12196,plain,
% 5.85/5.79 (pred(NSX2!29) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12195, 20])).
% 5.85/5.79 tff(12197,plain,
% 5.85/5.79 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n8, n6)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12196, 12172])).
% 5.85/5.79 tff(12198,plain,
% 5.85/5.79 (Y3!54 = n3),
% 5.85/5.79 inference(transitivity,[status(thm)],[425, 12197, 98])).
% 5.85/5.79 tff(12199,plain,
% 5.85/5.79 (pred(Y3!54) = pred(n3)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12198])).
% 5.85/5.79 tff(12200,plain,
% 5.85/5.79 (pred(Y3!54) = n2),
% 5.85/5.79 inference(transitivity,[status(thm)],[12199, 25])).
% 5.85/5.79 tff(12201,plain,
% 5.85/5.79 (pred(pred(Y3!54)) = pred(n2)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12200])).
% 5.85/5.79 tff(12202,plain,
% 5.85/5.79 (pred(pred(Y3!54)) = n1),
% 5.85/5.79 inference(transitivity,[status(thm)],[12201, 24])).
% 5.85/5.79 tff(12203,plain,
% 5.85/5.79 (pred(pred(pred(Y3!54))) = pred(n1)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12202])).
% 5.85/5.79 tff(12204,plain,
% 5.85/5.79 (pred(pred(pred(Y3!54))) = n0),
% 5.85/5.79 inference(transitivity,[status(thm)],[12203, 23])).
% 5.85/5.79 tff(12205,plain,
% 5.85/5.79 (pred(pred(pred(pred(Y3!54)))) = pred(n0)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12204])).
% 5.85/5.79 tff(12206,plain,
% 5.85/5.79 (pred(pred(pred(pred(Y3!54)))) = n10),
% 5.85/5.79 inference(transitivity,[status(thm)],[12205, 22])).
% 5.85/5.79 tff(12207,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n10)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12206])).
% 5.85/5.79 tff(12208,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(Y3!54))))) = n9),
% 5.85/5.79 inference(transitivity,[status(thm)],[12207, 21])).
% 5.85/5.79 tff(12209,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n9)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12208])).
% 5.85/5.79 tff(12210,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n8),
% 5.85/5.79 inference(transitivity,[status(thm)],[12209, 20])).
% 5.85/5.79 tff(12211,plain,
% 5.85/5.79 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n8)),
% 5.85/5.79 inference(monotonicity,[status(thm)],[12210])).
% 5.85/5.79 tff(12212,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12211, 19])).
% 5.85/5.80 tff(12213,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12212])).
% 5.85/5.80 tff(12214,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12213, 18])).
% 5.85/5.80 tff(12215,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12214])).
% 5.85/5.80 tff(12216,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12215, 17])).
% 5.85/5.80 tff(12217,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12216])).
% 5.85/5.80 tff(12218,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12217, 16])).
% 5.85/5.80 tff(12219,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12218])).
% 5.85/5.80 tff(12220,plain,
% 5.85/5.80 (NPY3!26 = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[462, 12219, 15])).
% 5.85/5.80 tff(12221,plain,
% 5.85/5.80 (succ(NPY3!26) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12220])).
% 5.85/5.80 tff(12222,plain,
% 5.85/5.80 (succ(NPY3!26) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12221, 14])).
% 5.85/5.80 tff(12223,plain,
% 5.85/5.80 (succ(Y3!54) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12198])).
% 5.85/5.80 tff(12224,plain,
% 5.85/5.80 (succ(Y3!54) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12223, 14])).
% 5.85/5.80 tff(12225,plain,
% 5.85/5.80 (succ(succ(Y3!54)) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12224])).
% 5.85/5.80 tff(12226,plain,
% 5.85/5.80 (succ(succ(Y3!54)) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12225, 33])).
% 5.85/5.80 tff(12227,plain,
% 5.85/5.80 (succ(succ(succ(Y3!54))) = succ(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12226])).
% 5.85/5.80 tff(12228,plain,
% 5.85/5.80 (succ(succ(succ(Y3!54))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12227, 30])).
% 5.85/5.80 tff(12229,plain,
% 5.85/5.80 (succ(succ(succ(succ(Y3!54)))) = succ(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12228])).
% 5.85/5.80 tff(12230,plain,
% 5.85/5.80 (succ(succ(succ(succ(Y3!54)))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12229, 39])).
% 5.85/5.80 tff(12231,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12230])).
% 5.85/5.80 tff(12232,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(Y3!54))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12231, 53])).
% 5.85/5.80 tff(12233,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12232])).
% 5.85/5.80 tff(12234,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12233, 45])).
% 5.85/5.80 tff(12235,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12234])).
% 5.85/5.80 tff(12236,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12235, 28])).
% 5.85/5.80 tff(12237,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12236])).
% 5.85/5.80 tff(12238,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12237, 42])).
% 5.85/5.80 tff(12239,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12238])).
% 5.85/5.80 tff(12240,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12239, 58])).
% 5.85/5.80 tff(12241,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12240])).
% 5.85/5.80 tff(12242,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12241, 36])).
% 5.85/5.80 tff(12243,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12242])).
% 5.85/5.80 tff(12244,plain,
% 5.85/5.80 (NSY3!24 = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[485, 12243, 48])).
% 5.85/5.80 tff(12245,plain,
% 5.85/5.80 (pred(NSY3!24) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12244])).
% 5.85/5.80 tff(12246,plain,
% 5.85/5.80 (pred(NSY3!24) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12245, 25])).
% 5.85/5.80 tff(12247,plain,
% 5.85/5.80 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n2, n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12246, 12222])).
% 5.85/5.80 tff(12248,plain,
% 5.85/5.80 (sum(pred(NSY3!24), succ(NPY3!26)) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12247, 13])).
% 5.85/5.80 tff(12249,plain,
% 5.85/5.80 (sum(pred(Y2!56), succ(X2!57)) = sum(n8, n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12092, 12174])).
% 5.85/5.80 tff(12250,plain,
% 5.85/5.80 (sum(pred(Y2!56), succ(X2!57)) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12249, 27])).
% 5.85/5.80 tff(12251,plain,
% 5.85/5.80 (sum(pred(X2!57), succ(Y2!56)) = sum(n8, n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12148, 12116])).
% 5.85/5.80 tff(12252,plain,
% 5.85/5.80 (sum(pred(X2!57), succ(Y2!56)) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12251, 27])).
% 5.85/5.80 tff(12253,plain,
% 5.85/5.80 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n7, n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12252, 12250])).
% 5.85/5.80 tff(12254,plain,
% 5.85/5.80 (X3!55 = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[323, 12253, 26])).
% 5.85/5.80 tff(12255,plain,
% 5.85/5.80 (pred(X3!55) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12254])).
% 5.85/5.80 tff(12256,plain,
% 5.85/5.80 (pred(X3!55) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12255, 25])).
% 5.85/5.80 tff(12257,plain,
% 5.85/5.80 (pred(pred(X3!55)) = pred(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12256])).
% 5.85/5.80 tff(12258,plain,
% 5.85/5.80 (pred(pred(X3!55)) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12257, 24])).
% 5.85/5.80 tff(12259,plain,
% 5.85/5.80 (pred(pred(pred(X3!55))) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12258])).
% 5.85/5.80 tff(12260,plain,
% 5.85/5.80 (pred(pred(pred(X3!55))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12259, 23])).
% 5.85/5.80 tff(12261,plain,
% 5.85/5.80 (pred(pred(pred(pred(X3!55)))) = pred(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12260])).
% 5.85/5.80 tff(12262,plain,
% 5.85/5.80 (pred(pred(pred(pred(X3!55)))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12261, 22])).
% 5.85/5.80 tff(12263,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(X3!55))))) = pred(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12262])).
% 5.85/5.80 tff(12264,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(X3!55))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12263, 21])).
% 5.85/5.80 tff(12265,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12264])).
% 5.85/5.80 tff(12266,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12265, 20])).
% 5.85/5.80 tff(12267,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12266])).
% 5.85/5.80 tff(12268,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12267, 19])).
% 5.85/5.80 tff(12269,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12268])).
% 5.85/5.80 tff(12270,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12269, 18])).
% 5.85/5.80 tff(12271,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12270])).
% 5.85/5.80 tff(12272,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12271, 17])).
% 5.85/5.80 tff(12273,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12272])).
% 5.85/5.80 tff(12274,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12273, 16])).
% 5.85/5.80 tff(12275,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12274])).
% 5.85/5.80 tff(12276,plain,
% 5.85/5.80 (NPX3!27 = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[510, 12275, 15])).
% 5.85/5.80 tff(12277,plain,
% 5.85/5.80 (succ(NPX3!27) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12276])).
% 5.85/5.80 tff(12278,plain,
% 5.85/5.80 (succ(NPX3!27) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12277, 14])).
% 5.85/5.80 tff(12279,plain,
% 5.85/5.80 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n4, n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12278, 12248])).
% 5.85/5.80 tff(12280,plain,
% 5.85/5.80 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12279, 12])).
% 5.85/5.80 tff(12281,plain,
% 5.85/5.80 (succ(X3!55) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12254])).
% 5.85/5.80 tff(12282,plain,
% 5.85/5.80 (succ(X3!55) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12281, 14])).
% 5.85/5.80 tff(12283,plain,
% 5.85/5.80 (succ(succ(X3!55)) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12282])).
% 5.85/5.80 tff(12284,plain,
% 5.85/5.80 (succ(succ(X3!55)) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12283, 33])).
% 5.85/5.80 tff(12285,plain,
% 5.85/5.80 (succ(succ(succ(X3!55))) = succ(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12284])).
% 5.85/5.80 tff(12286,plain,
% 5.85/5.80 (succ(succ(succ(X3!55))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12285, 30])).
% 5.85/5.80 tff(12287,plain,
% 5.85/5.80 (succ(succ(succ(succ(X3!55)))) = succ(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12286])).
% 5.85/5.80 tff(12288,plain,
% 5.85/5.80 (succ(succ(succ(succ(X3!55)))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12287, 39])).
% 5.85/5.80 tff(12289,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(X3!55))))) = succ(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12288])).
% 5.85/5.80 tff(12290,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(X3!55))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12289, 53])).
% 5.85/5.80 tff(12291,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12290])).
% 5.85/5.80 tff(12292,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12291, 45])).
% 5.85/5.80 tff(12293,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12292])).
% 5.85/5.80 tff(12294,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12293, 28])).
% 5.85/5.80 tff(12295,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12294])).
% 5.85/5.80 tff(12296,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12295, 42])).
% 5.85/5.80 tff(12297,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12296])).
% 5.85/5.80 tff(12298,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12297, 58])).
% 5.85/5.80 tff(12299,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12298])).
% 5.85/5.80 tff(12300,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12299, 36])).
% 5.85/5.80 tff(12301,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12300])).
% 5.85/5.80 tff(12302,plain,
% 5.85/5.80 (NSX3!25 = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[535, 12301, 48])).
% 5.85/5.80 tff(12303,plain,
% 5.85/5.80 (pred(NSX3!25) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12302])).
% 5.85/5.80 tff(12304,plain,
% 5.85/5.80 (pred(NSX3!25) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12303, 25])).
% 5.85/5.80 tff(12305,plain,
% 5.85/5.80 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n2, n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12304, 12280])).
% 5.85/5.80 tff(12306,plain,
% 5.85/5.80 (Y4!52 = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[540, 12305, 327])).
% 5.85/5.80 tff(12307,plain,
% 5.85/5.80 (pred(Y4!52) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12306])).
% 5.85/5.80 tff(12308,plain,
% 5.85/5.80 (pred(Y4!52) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12307, 23])).
% 5.85/5.80 tff(12309,plain,
% 5.85/5.80 (pred(pred(Y4!52)) = pred(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12308])).
% 5.85/5.80 tff(12310,plain,
% 5.85/5.80 (pred(pred(Y4!52)) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12309, 22])).
% 5.85/5.80 tff(12311,plain,
% 5.85/5.80 (pred(pred(pred(Y4!52))) = pred(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12310])).
% 5.85/5.80 tff(12312,plain,
% 5.85/5.80 (pred(pred(pred(Y4!52))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12311, 21])).
% 5.85/5.80 tff(12313,plain,
% 5.85/5.80 (pred(pred(pred(pred(Y4!52)))) = pred(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12312])).
% 5.85/5.80 tff(12314,plain,
% 5.85/5.80 (pred(pred(pred(pred(Y4!52)))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12313, 20])).
% 5.85/5.80 tff(12315,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12314])).
% 5.85/5.80 tff(12316,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(Y4!52))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12315, 19])).
% 5.85/5.80 tff(12317,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12316])).
% 5.85/5.80 tff(12318,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12317, 18])).
% 5.85/5.80 tff(12319,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12318])).
% 5.85/5.80 tff(12320,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12319, 17])).
% 5.85/5.80 tff(12321,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12320])).
% 5.85/5.80 tff(12322,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12321, 16])).
% 5.85/5.80 tff(12323,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12322])).
% 5.85/5.80 tff(12324,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12323, 15])).
% 5.85/5.80 tff(12325,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12324])).
% 5.85/5.80 tff(12326,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12325, 25])).
% 5.85/5.80 tff(12327,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12326])).
% 5.85/5.80 tff(12328,plain,
% 5.85/5.80 (NPY4!22 = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[578, 12327, 24])).
% 5.85/5.80 tff(12329,plain,
% 5.85/5.80 (succ(NPY4!22) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12328])).
% 5.85/5.80 tff(12330,plain,
% 5.85/5.80 (succ(NPY4!22) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12329, 36])).
% 5.85/5.80 tff(12331,plain,
% 5.85/5.80 (succ(Y4!52) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12306])).
% 5.85/5.80 tff(12332,plain,
% 5.85/5.80 (succ(Y4!52) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12331, 36])).
% 5.85/5.80 tff(12333,plain,
% 5.85/5.80 (succ(succ(Y4!52)) = succ(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12332])).
% 5.85/5.80 tff(12334,plain,
% 5.85/5.80 (succ(succ(Y4!52)) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12333, 48])).
% 5.85/5.80 tff(12335,plain,
% 5.85/5.80 (succ(succ(succ(Y4!52))) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12334])).
% 5.85/5.80 tff(12336,plain,
% 5.85/5.80 (succ(succ(succ(Y4!52))) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12335, 14])).
% 5.85/5.80 tff(12337,plain,
% 5.85/5.80 (succ(succ(succ(succ(Y4!52)))) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12336])).
% 5.85/5.80 tff(12338,plain,
% 5.85/5.80 (succ(succ(succ(succ(Y4!52)))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12337, 33])).
% 5.85/5.80 tff(12339,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12338])).
% 5.85/5.80 tff(12340,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(Y4!52))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12339, 30])).
% 5.85/5.80 tff(12341,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12340])).
% 5.85/5.80 tff(12342,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12341, 39])).
% 5.85/5.80 tff(12343,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12342])).
% 5.85/5.80 tff(12344,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12343, 53])).
% 5.85/5.80 tff(12345,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12344])).
% 5.85/5.80 tff(12346,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12345, 45])).
% 5.85/5.80 tff(12347,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12346])).
% 5.85/5.80 tff(12348,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12347, 28])).
% 5.85/5.80 tff(12349,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12348])).
% 5.85/5.80 tff(12350,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12349, 42])).
% 5.85/5.80 tff(12351,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12350])).
% 5.85/5.80 tff(12352,plain,
% 5.85/5.80 (NSY4!20 = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[601, 12351, 58])).
% 5.85/5.80 tff(12353,plain,
% 5.85/5.80 (pred(NSY4!20) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12352])).
% 5.85/5.80 tff(12354,plain,
% 5.85/5.80 (pred(NSY4!20) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12353, 23])).
% 5.85/5.80 tff(12355,plain,
% 5.85/5.80 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n0, n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12354, 12330])).
% 5.85/5.80 tff(12356,plain,
% 5.85/5.80 (sum(pred(NSY4!20), succ(NPY4!22)) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12355, 35])).
% 5.85/5.80 tff(12357,plain,
% 5.85/5.80 (sum(pred(Y3!54), succ(X3!55)) = sum(n2, n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12200, 12282])).
% 5.85/5.80 tff(12358,plain,
% 5.85/5.80 (sum(pred(Y3!54), succ(X3!55)) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12357, 13])).
% 5.85/5.80 tff(12359,plain,
% 5.85/5.80 (sum(pred(X3!55), succ(Y3!54)) = sum(n2, n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12256, 12224])).
% 5.85/5.80 tff(12360,plain,
% 5.85/5.80 (sum(pred(X3!55), succ(Y3!54)) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12359, 13])).
% 5.85/5.80 tff(12361,plain,
% 5.85/5.80 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n6, n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12360, 12358])).
% 5.85/5.80 tff(12362,plain,
% 5.85/5.80 (X4!53 = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[438, 12361, 37])).
% 5.85/5.80 tff(12363,plain,
% 5.85/5.80 (pred(X4!53) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12362])).
% 5.85/5.80 tff(12364,plain,
% 5.85/5.80 (pred(X4!53) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12363, 23])).
% 5.85/5.80 tff(12365,plain,
% 5.85/5.80 (pred(pred(X4!53)) = pred(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12364])).
% 5.85/5.80 tff(12366,plain,
% 5.85/5.80 (pred(pred(X4!53)) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12365, 22])).
% 5.85/5.80 tff(12367,plain,
% 5.85/5.80 (pred(pred(pred(X4!53))) = pred(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12366])).
% 5.85/5.80 tff(12368,plain,
% 5.85/5.80 (pred(pred(pred(X4!53))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12367, 21])).
% 5.85/5.80 tff(12369,plain,
% 5.85/5.80 (pred(pred(pred(pred(X4!53)))) = pred(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12368])).
% 5.85/5.80 tff(12370,plain,
% 5.85/5.80 (pred(pred(pred(pred(X4!53)))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12369, 20])).
% 5.85/5.80 tff(12371,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(X4!53))))) = pred(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12370])).
% 5.85/5.80 tff(12372,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(X4!53))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12371, 19])).
% 5.85/5.80 tff(12373,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12372])).
% 5.85/5.80 tff(12374,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12373, 18])).
% 5.85/5.80 tff(12375,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12374])).
% 5.85/5.80 tff(12376,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12375, 17])).
% 5.85/5.80 tff(12377,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12376])).
% 5.85/5.80 tff(12378,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12377, 16])).
% 5.85/5.80 tff(12379,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12378])).
% 5.85/5.80 tff(12380,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12379, 15])).
% 5.85/5.80 tff(12381,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12380])).
% 5.85/5.80 tff(12382,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12381, 25])).
% 5.85/5.80 tff(12383,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12382])).
% 5.85/5.80 tff(12384,plain,
% 5.85/5.80 (NPX4!23 = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[626, 12383, 24])).
% 5.85/5.80 tff(12385,plain,
% 5.85/5.80 (succ(NPX4!23) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12384])).
% 5.85/5.80 tff(12386,plain,
% 5.85/5.80 (succ(NPX4!23) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12385, 36])).
% 5.85/5.80 tff(12387,plain,
% 5.85/5.80 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n2, n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12386, 12356])).
% 5.85/5.80 tff(12388,plain,
% 5.85/5.80 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12387, 34])).
% 5.85/5.80 tff(12389,plain,
% 5.85/5.80 (succ(X4!53) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12362])).
% 5.85/5.80 tff(12390,plain,
% 5.85/5.80 (succ(X4!53) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12389, 36])).
% 5.85/5.80 tff(12391,plain,
% 5.85/5.80 (succ(succ(X4!53)) = succ(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12390])).
% 5.85/5.80 tff(12392,plain,
% 5.85/5.80 (succ(succ(X4!53)) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12391, 48])).
% 5.85/5.80 tff(12393,plain,
% 5.85/5.80 (succ(succ(succ(X4!53))) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12392])).
% 5.85/5.80 tff(12394,plain,
% 5.85/5.80 (succ(succ(succ(X4!53))) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12393, 14])).
% 5.85/5.80 tff(12395,plain,
% 5.85/5.80 (succ(succ(succ(succ(X4!53)))) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12394])).
% 5.85/5.80 tff(12396,plain,
% 5.85/5.80 (succ(succ(succ(succ(X4!53)))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12395, 33])).
% 5.85/5.80 tff(12397,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(X4!53))))) = succ(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12396])).
% 5.85/5.80 tff(12398,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(X4!53))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12397, 30])).
% 5.85/5.80 tff(12399,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12398])).
% 5.85/5.80 tff(12400,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12399, 39])).
% 5.85/5.80 tff(12401,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12400])).
% 5.85/5.80 tff(12402,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12401, 53])).
% 5.85/5.80 tff(12403,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12402])).
% 5.85/5.80 tff(12404,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12403, 45])).
% 5.85/5.80 tff(12405,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12404])).
% 5.85/5.80 tff(12406,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12405, 28])).
% 5.85/5.80 tff(12407,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12406])).
% 5.85/5.80 tff(12408,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12407, 42])).
% 5.85/5.80 tff(12409,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12408])).
% 5.85/5.80 tff(12410,plain,
% 5.85/5.80 (NSX4!21 = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[651, 12409, 58])).
% 5.85/5.80 tff(12411,plain,
% 5.85/5.80 (pred(NSX4!21) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12410])).
% 5.85/5.80 tff(12412,plain,
% 5.85/5.80 (pred(NSX4!21) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12411, 23])).
% 5.85/5.80 tff(12413,plain,
% 5.85/5.80 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n0, n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12412, 12388])).
% 5.85/5.80 tff(12414,plain,
% 5.85/5.80 (Y5!50 = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[656, 12413, 442])).
% 5.85/5.80 tff(12415,plain,
% 5.85/5.80 (pred(Y5!50) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12414])).
% 5.85/5.80 tff(12416,plain,
% 5.85/5.80 (pred(Y5!50) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12415, 15])).
% 5.85/5.80 tff(12417,plain,
% 5.85/5.80 (pred(pred(Y5!50)) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12416])).
% 5.85/5.80 tff(12418,plain,
% 5.85/5.80 (pred(pred(Y5!50)) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12417, 25])).
% 5.85/5.80 tff(12419,plain,
% 5.85/5.80 (pred(pred(pred(Y5!50))) = pred(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12418])).
% 5.85/5.80 tff(12420,plain,
% 5.85/5.80 (pred(pred(pred(Y5!50))) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12419, 24])).
% 5.85/5.80 tff(12421,plain,
% 5.85/5.80 (pred(pred(pred(pred(Y5!50)))) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12420])).
% 5.85/5.80 tff(12422,plain,
% 5.85/5.80 (pred(pred(pred(pred(Y5!50)))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12421, 23])).
% 5.85/5.80 tff(12423,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12422])).
% 5.85/5.80 tff(12424,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(Y5!50))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12423, 22])).
% 5.85/5.80 tff(12425,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12424])).
% 5.85/5.80 tff(12426,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12425, 21])).
% 5.85/5.80 tff(12427,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12426])).
% 5.85/5.80 tff(12428,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12427, 20])).
% 5.85/5.80 tff(12429,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12428])).
% 5.85/5.80 tff(12430,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12429, 19])).
% 5.85/5.80 tff(12431,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12430])).
% 5.85/5.80 tff(12432,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12431, 18])).
% 5.85/5.80 tff(12433,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12432])).
% 5.85/5.80 tff(12434,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12433, 17])).
% 5.85/5.80 tff(12435,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12434])).
% 5.85/5.80 tff(12436,plain,
% 5.85/5.80 (NPY5!18 = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[694, 12435, 16])).
% 5.85/5.80 tff(12437,plain,
% 5.85/5.80 (succ(NPY5!18) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12436])).
% 5.85/5.80 tff(12438,plain,
% 5.85/5.80 (succ(NPY5!18) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12437, 33])).
% 5.85/5.80 tff(12439,plain,
% 5.85/5.80 (succ(Y5!50) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12414])).
% 5.85/5.80 tff(12440,plain,
% 5.85/5.80 (succ(Y5!50) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12439, 33])).
% 5.85/5.80 tff(12441,plain,
% 5.85/5.80 (succ(succ(Y5!50)) = succ(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12440])).
% 5.85/5.80 tff(12442,plain,
% 5.85/5.80 (succ(succ(Y5!50)) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12441, 30])).
% 5.85/5.80 tff(12443,plain,
% 5.85/5.80 (succ(succ(succ(Y5!50))) = succ(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12442])).
% 5.85/5.80 tff(12444,plain,
% 5.85/5.80 (succ(succ(succ(Y5!50))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12443, 39])).
% 5.85/5.80 tff(12445,plain,
% 5.85/5.80 (succ(succ(succ(succ(Y5!50)))) = succ(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12444])).
% 5.85/5.80 tff(12446,plain,
% 5.85/5.80 (succ(succ(succ(succ(Y5!50)))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12445, 53])).
% 5.85/5.80 tff(12447,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12446])).
% 5.85/5.80 tff(12448,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(Y5!50))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12447, 45])).
% 5.85/5.80 tff(12449,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12448])).
% 5.85/5.80 tff(12450,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12449, 28])).
% 5.85/5.80 tff(12451,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12450])).
% 5.85/5.80 tff(12452,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12451, 42])).
% 5.85/5.80 tff(12453,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12452])).
% 5.85/5.80 tff(12454,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12453, 58])).
% 5.85/5.80 tff(12455,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12454])).
% 5.85/5.80 tff(12456,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12455, 36])).
% 5.85/5.80 tff(12457,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12456])).
% 5.85/5.80 tff(12458,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12457, 48])).
% 5.85/5.80 tff(12459,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12458])).
% 5.85/5.80 tff(12460,plain,
% 5.85/5.80 (NSY5!16 = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[717, 12459, 14])).
% 5.85/5.80 tff(12461,plain,
% 5.85/5.80 (pred(NSY5!16) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12460])).
% 5.85/5.80 tff(12462,plain,
% 5.85/5.80 (pred(NSY5!16) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12461, 15])).
% 5.85/5.80 tff(12463,plain,
% 5.85/5.80 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n3, n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12462, 12438])).
% 5.85/5.80 tff(12464,plain,
% 5.85/5.80 (sum(pred(NSY5!16), succ(NPY5!18)) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12463, 32])).
% 5.85/5.80 tff(12465,plain,
% 5.85/5.80 (sum(pred(Y4!52), succ(X4!53)) = sum(n0, n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12308, 12390])).
% 5.85/5.80 tff(12466,plain,
% 5.85/5.80 (sum(pred(Y4!52), succ(X4!53)) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12465, 35])).
% 5.85/5.80 tff(12467,plain,
% 5.85/5.80 (sum(pred(X4!53), succ(Y4!52)) = sum(n0, n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12364, 12332])).
% 5.85/5.80 tff(12468,plain,
% 5.85/5.80 (sum(pred(X4!53), succ(Y4!52)) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12467, 35])).
% 5.85/5.80 tff(12469,plain,
% 5.85/5.80 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n2, n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12468, 12466])).
% 5.85/5.80 tff(12470,plain,
% 5.85/5.80 (X5!51 = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[553, 12469, 34])).
% 5.85/5.80 tff(12471,plain,
% 5.85/5.80 (pred(X5!51) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12470])).
% 5.85/5.80 tff(12472,plain,
% 5.85/5.80 (pred(X5!51) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12471, 15])).
% 5.85/5.80 tff(12473,plain,
% 5.85/5.80 (pred(pred(X5!51)) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12472])).
% 5.85/5.80 tff(12474,plain,
% 5.85/5.80 (pred(pred(X5!51)) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12473, 25])).
% 5.85/5.80 tff(12475,plain,
% 5.85/5.80 (pred(pred(pred(X5!51))) = pred(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12474])).
% 5.85/5.80 tff(12476,plain,
% 5.85/5.80 (pred(pred(pred(X5!51))) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12475, 24])).
% 5.85/5.80 tff(12477,plain,
% 5.85/5.80 (pred(pred(pred(pred(X5!51)))) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12476])).
% 5.85/5.80 tff(12478,plain,
% 5.85/5.80 (pred(pred(pred(pred(X5!51)))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12477, 23])).
% 5.85/5.80 tff(12479,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(X5!51))))) = pred(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12478])).
% 5.85/5.80 tff(12480,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(X5!51))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12479, 22])).
% 5.85/5.80 tff(12481,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12480])).
% 5.85/5.80 tff(12482,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12481, 21])).
% 5.85/5.80 tff(12483,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12482])).
% 5.85/5.80 tff(12484,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12483, 20])).
% 5.85/5.80 tff(12485,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12484])).
% 5.85/5.80 tff(12486,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12485, 19])).
% 5.85/5.80 tff(12487,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12486])).
% 5.85/5.80 tff(12488,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12487, 18])).
% 5.85/5.80 tff(12489,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12488])).
% 5.85/5.80 tff(12490,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12489, 17])).
% 5.85/5.80 tff(12491,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12490])).
% 5.85/5.80 tff(12492,plain,
% 5.85/5.80 (NPX5!19 = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[742, 12491, 16])).
% 5.85/5.80 tff(12493,plain,
% 5.85/5.80 (succ(NPX5!19) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12492])).
% 5.85/5.80 tff(12494,plain,
% 5.85/5.80 (succ(NPX5!19) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12493, 33])).
% 5.85/5.80 tff(12495,plain,
% 5.85/5.80 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n5, n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12494, 12464])).
% 5.85/5.80 tff(12496,plain,
% 5.85/5.80 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12495, 558])).
% 5.85/5.80 tff(12497,plain,
% 5.85/5.80 (succ(X5!51) = succ(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12470])).
% 5.85/5.80 tff(12498,plain,
% 5.85/5.80 (succ(X5!51) = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[12497, 33])).
% 5.85/5.80 tff(12499,plain,
% 5.85/5.80 (succ(succ(X5!51)) = succ(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12498])).
% 5.85/5.80 tff(12500,plain,
% 5.85/5.80 (succ(succ(X5!51)) = n6),
% 5.85/5.80 inference(transitivity,[status(thm)],[12499, 30])).
% 5.85/5.80 tff(12501,plain,
% 5.85/5.80 (succ(succ(succ(X5!51))) = succ(n6)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12500])).
% 5.85/5.80 tff(12502,plain,
% 5.85/5.80 (succ(succ(succ(X5!51))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12501, 39])).
% 5.85/5.80 tff(12503,plain,
% 5.85/5.80 (succ(succ(succ(succ(X5!51)))) = succ(n7)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12502])).
% 5.85/5.80 tff(12504,plain,
% 5.85/5.80 (succ(succ(succ(succ(X5!51)))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12503, 53])).
% 5.85/5.80 tff(12505,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(X5!51))))) = succ(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12504])).
% 5.85/5.80 tff(12506,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(X5!51))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12505, 45])).
% 5.85/5.80 tff(12507,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12506])).
% 5.85/5.80 tff(12508,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12507, 28])).
% 5.85/5.80 tff(12509,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12508])).
% 5.85/5.80 tff(12510,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12509, 42])).
% 5.85/5.80 tff(12511,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12510])).
% 5.85/5.80 tff(12512,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12511, 58])).
% 5.85/5.80 tff(12513,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12512])).
% 5.85/5.80 tff(12514,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12513, 36])).
% 5.85/5.80 tff(12515,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12514])).
% 5.85/5.80 tff(12516,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12515, 48])).
% 5.85/5.80 tff(12517,plain,
% 5.85/5.80 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12516])).
% 5.85/5.80 tff(12518,plain,
% 5.85/5.80 (NSX5!17 = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[767, 12517, 14])).
% 5.85/5.80 tff(12519,plain,
% 5.85/5.80 (pred(NSX5!17) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12518])).
% 5.85/5.80 tff(12520,plain,
% 5.85/5.80 (pred(NSX5!17) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12519, 15])).
% 5.85/5.80 tff(12521,plain,
% 5.85/5.80 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n3, n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12520, 12496])).
% 5.85/5.80 tff(12522,plain,
% 5.85/5.80 (Y6!48 = n5),
% 5.85/5.80 inference(transitivity,[status(thm)],[772, 12521, 557])).
% 5.85/5.80 tff(12523,plain,
% 5.85/5.80 (pred(Y6!48) = pred(n5)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12522])).
% 5.85/5.80 tff(12524,plain,
% 5.85/5.80 (pred(Y6!48) = n4),
% 5.85/5.80 inference(transitivity,[status(thm)],[12523, 16])).
% 5.85/5.80 tff(12525,plain,
% 5.85/5.80 (pred(pred(Y6!48)) = pred(n4)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12524])).
% 5.85/5.80 tff(12526,plain,
% 5.85/5.80 (pred(pred(Y6!48)) = n3),
% 5.85/5.80 inference(transitivity,[status(thm)],[12525, 15])).
% 5.85/5.80 tff(12527,plain,
% 5.85/5.80 (pred(pred(pred(Y6!48))) = pred(n3)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12526])).
% 5.85/5.80 tff(12528,plain,
% 5.85/5.80 (pred(pred(pred(Y6!48))) = n2),
% 5.85/5.80 inference(transitivity,[status(thm)],[12527, 25])).
% 5.85/5.80 tff(12529,plain,
% 5.85/5.80 (pred(pred(pred(pred(Y6!48)))) = pred(n2)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12528])).
% 5.85/5.80 tff(12530,plain,
% 5.85/5.80 (pred(pred(pred(pred(Y6!48)))) = n1),
% 5.85/5.80 inference(transitivity,[status(thm)],[12529, 24])).
% 5.85/5.80 tff(12531,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n1)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12530])).
% 5.85/5.80 tff(12532,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(Y6!48))))) = n0),
% 5.85/5.80 inference(transitivity,[status(thm)],[12531, 23])).
% 5.85/5.80 tff(12533,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n0)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12532])).
% 5.85/5.80 tff(12534,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n10),
% 5.85/5.80 inference(transitivity,[status(thm)],[12533, 22])).
% 5.85/5.80 tff(12535,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n10)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12534])).
% 5.85/5.80 tff(12536,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n9),
% 5.85/5.80 inference(transitivity,[status(thm)],[12535, 21])).
% 5.85/5.80 tff(12537,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n9)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12536])).
% 5.85/5.80 tff(12538,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n8),
% 5.85/5.80 inference(transitivity,[status(thm)],[12537, 20])).
% 5.85/5.80 tff(12539,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n8)),
% 5.85/5.80 inference(monotonicity,[status(thm)],[12538])).
% 5.85/5.80 tff(12540,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n7),
% 5.85/5.80 inference(transitivity,[status(thm)],[12539, 19])).
% 5.85/5.80 tff(12541,plain,
% 5.85/5.80 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12540])).
% 5.85/5.81 tff(12542,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12541, 18])).
% 5.85/5.81 tff(12543,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12542])).
% 5.85/5.81 tff(12544,plain,
% 5.85/5.81 (NPY6!14 = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[1465, 12543, 17])).
% 5.85/5.81 tff(12545,plain,
% 5.85/5.81 (succ(NPY6!14) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12544])).
% 5.85/5.81 tff(12546,plain,
% 5.85/5.81 (succ(NPY6!14) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12545, 30])).
% 5.85/5.81 tff(12547,plain,
% 5.85/5.81 (succ(Y6!48) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12522])).
% 5.85/5.81 tff(12548,plain,
% 5.85/5.81 (succ(Y6!48) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12547, 30])).
% 5.85/5.81 tff(12549,plain,
% 5.85/5.81 (succ(succ(Y6!48)) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12548])).
% 5.85/5.81 tff(12550,plain,
% 5.85/5.81 (succ(succ(Y6!48)) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12549, 39])).
% 5.85/5.81 tff(12551,plain,
% 5.85/5.81 (succ(succ(succ(Y6!48))) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12550])).
% 5.85/5.81 tff(12552,plain,
% 5.85/5.81 (succ(succ(succ(Y6!48))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12551, 53])).
% 5.85/5.81 tff(12553,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y6!48)))) = succ(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12552])).
% 5.85/5.81 tff(12554,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y6!48)))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12553, 45])).
% 5.85/5.81 tff(12555,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12554])).
% 5.85/5.81 tff(12556,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y6!48))))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12555, 28])).
% 5.85/5.81 tff(12557,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12556])).
% 5.85/5.81 tff(12558,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12557, 42])).
% 5.85/5.81 tff(12559,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12558])).
% 5.85/5.81 tff(12560,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12559, 58])).
% 5.85/5.81 tff(12561,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12560])).
% 5.85/5.81 tff(12562,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12561, 36])).
% 5.85/5.81 tff(12563,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12562])).
% 5.85/5.81 tff(12564,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12563, 48])).
% 5.85/5.81 tff(12565,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12564])).
% 5.85/5.81 tff(12566,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12565, 14])).
% 5.85/5.81 tff(12567,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12566])).
% 5.85/5.81 tff(12568,plain,
% 5.85/5.81 (NSY6!12 = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[1490, 12567, 33])).
% 5.85/5.81 tff(12569,plain,
% 5.85/5.81 (pred(NSY6!12) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12568])).
% 5.85/5.81 tff(12570,plain,
% 5.85/5.81 (pred(NSY6!12) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12569, 16])).
% 5.85/5.81 tff(12571,plain,
% 5.85/5.81 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n4, n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12570, 12546])).
% 5.85/5.81 tff(12572,plain,
% 5.85/5.81 (sum(pred(NSY6!12), succ(NPY6!14)) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12571, 12])).
% 5.85/5.81 tff(12573,plain,
% 5.85/5.81 (sum(pred(Y5!50), succ(X5!51)) = sum(n3, n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12416, 12498])).
% 5.85/5.81 tff(12574,plain,
% 5.85/5.81 (sum(pred(Y5!50), succ(X5!51)) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12573, 32])).
% 5.85/5.81 tff(12575,plain,
% 5.85/5.81 (sum(pred(X5!51), succ(Y5!50)) = sum(n3, n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12472, 12440])).
% 5.85/5.81 tff(12576,plain,
% 5.85/5.81 (sum(pred(X5!51), succ(Y5!50)) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12575, 32])).
% 5.85/5.81 tff(12577,plain,
% 5.85/5.81 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n8, n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12576, 12574])).
% 5.85/5.81 tff(12578,plain,
% 5.85/5.81 (X6!49 = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[669, 12577, 31])).
% 5.85/5.81 tff(12579,plain,
% 5.85/5.81 (pred(X6!49) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12578])).
% 5.85/5.81 tff(12580,plain,
% 5.85/5.81 (pred(X6!49) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12579, 16])).
% 5.85/5.81 tff(12581,plain,
% 5.85/5.81 (pred(pred(X6!49)) = pred(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12580])).
% 5.85/5.81 tff(12582,plain,
% 5.85/5.81 (pred(pred(X6!49)) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12581, 15])).
% 5.85/5.81 tff(12583,plain,
% 5.85/5.81 (pred(pred(pred(X6!49))) = pred(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12582])).
% 5.85/5.81 tff(12584,plain,
% 5.85/5.81 (pred(pred(pred(X6!49))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12583, 25])).
% 5.85/5.81 tff(12585,plain,
% 5.85/5.81 (pred(pred(pred(pred(X6!49)))) = pred(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12584])).
% 5.85/5.81 tff(12586,plain,
% 5.85/5.81 (pred(pred(pred(pred(X6!49)))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12585, 24])).
% 5.85/5.81 tff(12587,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(X6!49))))) = pred(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12586])).
% 5.85/5.81 tff(12588,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(X6!49))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12587, 23])).
% 5.85/5.81 tff(12589,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12588])).
% 5.85/5.81 tff(12590,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12589, 22])).
% 5.85/5.81 tff(12591,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12590])).
% 5.85/5.81 tff(12592,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12591, 21])).
% 5.85/5.81 tff(12593,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12592])).
% 5.85/5.81 tff(12594,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12593, 20])).
% 5.85/5.81 tff(12595,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12594])).
% 5.85/5.81 tff(12596,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12595, 19])).
% 5.85/5.81 tff(12597,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12596])).
% 5.85/5.81 tff(12598,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12597, 18])).
% 5.85/5.81 tff(12599,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12598])).
% 5.85/5.81 tff(12600,plain,
% 5.85/5.81 (NPX6!15 = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[1523, 12599, 17])).
% 5.85/5.81 tff(12601,plain,
% 5.85/5.81 (succ(NPX6!15) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12600])).
% 5.85/5.81 tff(12602,plain,
% 5.85/5.81 (succ(NPX6!15) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12601, 30])).
% 5.85/5.81 tff(12603,plain,
% 5.85/5.81 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n6, n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12602, 12572])).
% 5.85/5.81 tff(12604,plain,
% 5.85/5.81 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12603, 674])).
% 5.85/5.81 tff(12605,plain,
% 5.85/5.81 (succ(X6!49) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12578])).
% 5.85/5.81 tff(12606,plain,
% 5.85/5.81 (succ(X6!49) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12605, 30])).
% 5.85/5.81 tff(12607,plain,
% 5.85/5.81 (succ(succ(X6!49)) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12606])).
% 5.85/5.81 tff(12608,plain,
% 5.85/5.81 (succ(succ(X6!49)) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12607, 39])).
% 5.85/5.81 tff(12609,plain,
% 5.85/5.81 (succ(succ(succ(X6!49))) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12608])).
% 5.85/5.81 tff(12610,plain,
% 5.85/5.81 (succ(succ(succ(X6!49))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12609, 53])).
% 5.85/5.81 tff(12611,plain,
% 5.85/5.81 (succ(succ(succ(succ(X6!49)))) = succ(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12610])).
% 5.85/5.81 tff(12612,plain,
% 5.85/5.81 (succ(succ(succ(succ(X6!49)))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12611, 45])).
% 5.85/5.81 tff(12613,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(X6!49))))) = succ(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12612])).
% 5.85/5.81 tff(12614,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(X6!49))))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12613, 28])).
% 5.85/5.81 tff(12615,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12614])).
% 5.85/5.81 tff(12616,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12615, 42])).
% 5.85/5.81 tff(12617,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12616])).
% 5.85/5.81 tff(12618,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12617, 58])).
% 5.85/5.81 tff(12619,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12618])).
% 5.85/5.81 tff(12620,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12619, 36])).
% 5.85/5.81 tff(12621,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12620])).
% 5.85/5.81 tff(12622,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12621, 48])).
% 5.85/5.81 tff(12623,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12622])).
% 5.85/5.81 tff(12624,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12623, 14])).
% 5.85/5.81 tff(12625,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12624])).
% 5.85/5.81 tff(12626,plain,
% 5.85/5.81 (NSX6!13 = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[1550, 12625, 33])).
% 5.85/5.81 tff(12627,plain,
% 5.85/5.81 (pred(NSX6!13) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12626])).
% 5.85/5.81 tff(12628,plain,
% 5.85/5.81 (pred(NSX6!13) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12627, 16])).
% 5.85/5.81 tff(12629,plain,
% 5.85/5.81 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n4, n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12628, 12604])).
% 5.85/5.81 tff(12630,plain,
% 5.85/5.81 (sum(n4, n5) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.85/5.81 inference(symmetry,[status(thm)],[12629])).
% 5.85/5.81 tff(12631,plain,
% 5.85/5.81 (sum(pred(Y6!48), succ(X6!49)) = sum(n4, n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12524, 12606])).
% 5.85/5.81 tff(12632,plain,
% 5.85/5.81 (sum(pred(Y6!48), succ(X6!49)) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12631, 12])).
% 5.85/5.81 tff(12633,plain,
% 5.85/5.81 (sum(pred(X6!49), succ(Y6!48)) = sum(n4, n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12580, 12548])).
% 5.85/5.81 tff(12634,plain,
% 5.85/5.81 (sum(pred(X6!49), succ(Y6!48)) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12633, 12])).
% 5.85/5.81 tff(12635,plain,
% 5.85/5.81 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n10, n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12634, 12632])).
% 5.85/5.81 tff(12636,plain,
% 5.85/5.81 (X7!47 = Y7!46),
% 5.85/5.81 inference(transitivity,[status(thm)],[785, 12635, 29, 10596, 12630, 794])).
% 5.85/5.81 tff(12637,plain,
% 5.85/5.81 ($false),
% 5.85/5.81 inference(unit_resolution,[status(thm)],[792, 12636])).
% 5.85/5.81 tff(12638,plain,((~(Y0!60 = n4)) | (X7!47 = Y7!46) | (~(X0!61 = n4))), inference(lemma,lemma(discharge,[]))).
% 5.85/5.81 tff(12639,plain,
% 5.85/5.81 (~(Y0!60 = n4)),
% 5.85/5.81 inference(unit_resolution,[status(thm)],[12638, 11930, 792])).
% 5.85/5.81 tff(12640,plain,
% 5.85/5.81 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n5, n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[11954, 3768])).
% 5.85/5.81 tff(12641,plain,
% 5.85/5.81 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12640, 3051])).
% 5.85/5.81 tff(12642,plain,
% 5.85/5.81 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n3, n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[11980, 12641])).
% 5.85/5.81 tff(12643,plain,
% 5.85/5.81 (Y1!58 = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[196, 12642, 786])).
% 5.85/5.81 tff(12644,plain,
% 5.85/5.81 (pred(Y1!58) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12643])).
% 5.85/5.81 tff(12645,plain,
% 5.85/5.81 (pred(Y1!58) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12644, 18])).
% 5.85/5.81 tff(12646,plain,
% 5.85/5.81 (pred(pred(Y1!58)) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12645])).
% 5.85/5.81 tff(12647,plain,
% 5.85/5.81 (pred(pred(Y1!58)) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12646, 17])).
% 5.85/5.81 tff(12648,plain,
% 5.85/5.81 (pred(pred(pred(Y1!58))) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12647])).
% 5.85/5.81 tff(12649,plain,
% 5.85/5.81 (pred(pred(pred(Y1!58))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12648, 16])).
% 5.85/5.81 tff(12650,plain,
% 5.85/5.81 (pred(pred(pred(pred(Y1!58)))) = pred(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12649])).
% 5.85/5.81 tff(12651,plain,
% 5.85/5.81 (pred(pred(pred(pred(Y1!58)))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12650, 15])).
% 5.85/5.81 tff(12652,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12651])).
% 5.85/5.81 tff(12653,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(Y1!58))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12652, 25])).
% 5.85/5.81 tff(12654,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12653])).
% 5.85/5.81 tff(12655,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12654, 24])).
% 5.85/5.81 tff(12656,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12655])).
% 5.85/5.81 tff(12657,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12656, 23])).
% 5.85/5.81 tff(12658,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12657])).
% 5.85/5.81 tff(12659,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12658, 22])).
% 5.85/5.81 tff(12660,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12659])).
% 5.85/5.81 tff(12661,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12660, 21])).
% 5.85/5.81 tff(12662,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12661])).
% 5.85/5.81 tff(12663,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12662, 20])).
% 5.85/5.81 tff(12664,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12663])).
% 5.85/5.81 tff(12665,plain,
% 5.85/5.81 (NPY1!34 = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[232, 12664, 19])).
% 5.85/5.81 tff(12666,plain,
% 5.85/5.81 (succ(NPY1!34) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12665])).
% 5.85/5.81 tff(12667,plain,
% 5.85/5.81 (succ(NPY1!34) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12666, 53])).
% 5.85/5.81 tff(12668,plain,
% 5.85/5.81 (succ(Y1!58) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12643])).
% 5.85/5.81 tff(12669,plain,
% 5.85/5.81 (succ(Y1!58) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12668, 53])).
% 5.85/5.81 tff(12670,plain,
% 5.85/5.81 (succ(succ(Y1!58)) = succ(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12669])).
% 5.85/5.81 tff(12671,plain,
% 5.85/5.81 (succ(succ(Y1!58)) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12670, 45])).
% 5.85/5.81 tff(12672,plain,
% 5.85/5.81 (succ(succ(succ(Y1!58))) = succ(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12671])).
% 5.85/5.81 tff(12673,plain,
% 5.85/5.81 (succ(succ(succ(Y1!58))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12672, 28])).
% 5.85/5.81 tff(12674,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y1!58)))) = succ(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12673])).
% 5.85/5.81 tff(12675,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y1!58)))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12674, 42])).
% 5.85/5.81 tff(12676,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12675])).
% 5.85/5.81 tff(12677,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y1!58))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12676, 58])).
% 5.85/5.81 tff(12678,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12677])).
% 5.85/5.81 tff(12679,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12678, 36])).
% 5.85/5.81 tff(12680,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12679])).
% 5.85/5.81 tff(12681,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12680, 48])).
% 5.85/5.81 tff(12682,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12681])).
% 5.85/5.81 tff(12683,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12682, 14])).
% 5.85/5.81 tff(12684,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12683])).
% 5.85/5.81 tff(12685,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12684, 33])).
% 5.85/5.81 tff(12686,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12685])).
% 5.85/5.81 tff(12687,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12686, 30])).
% 5.85/5.81 tff(12688,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12687])).
% 5.85/5.81 tff(12689,plain,
% 5.85/5.81 (NSY1!32 = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[255, 12688, 39])).
% 5.85/5.81 tff(12690,plain,
% 5.85/5.81 (pred(NSY1!32) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12689])).
% 5.85/5.81 tff(12691,plain,
% 5.85/5.81 (pred(NSY1!32) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12690, 18])).
% 5.85/5.81 tff(12692,plain,
% 5.85/5.81 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n6, n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12691, 12667])).
% 5.85/5.81 tff(12693,plain,
% 5.85/5.81 (sum(pred(NSY1!32), succ(NPY1!34)) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12692, 52])).
% 5.85/5.81 tff(12694,plain,
% 5.85/5.81 (sum(pred(Y0!60), succ(X0!61)) = sum(n4, n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[3720, 11958])).
% 5.85/5.81 tff(12695,plain,
% 5.85/5.81 (sum(pred(Y0!60), succ(X0!61)) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12694, 673])).
% 5.85/5.81 tff(12696,plain,
% 5.85/5.81 (sum(n3, n6) = n9),
% 5.85/5.81 inference(and_elim,[status(thm)],[9])).
% 5.85/5.81 tff(12697,plain,
% 5.85/5.81 (sum(pred(X0!61), succ(Y0!60)) = sum(n3, n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[11932, 3744])).
% 5.85/5.81 tff(12698,plain,
% 5.85/5.81 (sum(pred(X0!61), succ(Y0!60)) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12697, 12696])).
% 5.85/5.81 tff(12699,plain,
% 5.85/5.81 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n9, n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12698, 12695])).
% 5.85/5.81 tff(12700,plain,
% 5.85/5.81 (X1!59 = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[93, 12699, 54])).
% 5.85/5.81 tff(12701,plain,
% 5.85/5.81 (pred(X1!59) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12700])).
% 5.85/5.81 tff(12702,plain,
% 5.85/5.81 (pred(X1!59) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12701, 18])).
% 5.85/5.81 tff(12703,plain,
% 5.85/5.81 (pred(pred(X1!59)) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12702])).
% 5.85/5.81 tff(12704,plain,
% 5.85/5.81 (pred(pred(X1!59)) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12703, 17])).
% 5.85/5.81 tff(12705,plain,
% 5.85/5.81 (pred(pred(pred(X1!59))) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12704])).
% 5.85/5.81 tff(12706,plain,
% 5.85/5.81 (pred(pred(pred(X1!59))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12705, 16])).
% 5.85/5.81 tff(12707,plain,
% 5.85/5.81 (pred(pred(pred(pred(X1!59)))) = pred(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12706])).
% 5.85/5.81 tff(12708,plain,
% 5.85/5.81 (pred(pred(pred(pred(X1!59)))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12707, 15])).
% 5.85/5.81 tff(12709,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(X1!59))))) = pred(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12708])).
% 5.85/5.81 tff(12710,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(X1!59))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12709, 25])).
% 5.85/5.81 tff(12711,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12710])).
% 5.85/5.81 tff(12712,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12711, 24])).
% 5.85/5.81 tff(12713,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12712])).
% 5.85/5.81 tff(12714,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12713, 23])).
% 5.85/5.81 tff(12715,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12714])).
% 5.85/5.81 tff(12716,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12715, 22])).
% 5.85/5.81 tff(12717,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12716])).
% 5.85/5.81 tff(12718,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12717, 21])).
% 5.85/5.81 tff(12719,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12718])).
% 5.85/5.81 tff(12720,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12719, 20])).
% 5.85/5.81 tff(12721,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12720])).
% 5.85/5.81 tff(12722,plain,
% 5.85/5.81 (NPX1!35 = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[280, 12721, 19])).
% 5.85/5.81 tff(12723,plain,
% 5.85/5.81 (succ(NPX1!35) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12722])).
% 5.85/5.81 tff(12724,plain,
% 5.85/5.81 (succ(NPX1!35) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12723, 53])).
% 5.85/5.81 tff(12725,plain,
% 5.85/5.81 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n8, n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12724, 12693])).
% 5.85/5.81 tff(12726,plain,
% 5.85/5.81 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12725, 64])).
% 5.85/5.81 tff(12727,plain,
% 5.85/5.81 (succ(X1!59) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12700])).
% 5.85/5.81 tff(12728,plain,
% 5.85/5.81 (succ(X1!59) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12727, 53])).
% 5.85/5.81 tff(12729,plain,
% 5.85/5.81 (succ(succ(X1!59)) = succ(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12728])).
% 5.85/5.81 tff(12730,plain,
% 5.85/5.81 (succ(succ(X1!59)) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12729, 45])).
% 5.85/5.81 tff(12731,plain,
% 5.85/5.81 (succ(succ(succ(X1!59))) = succ(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12730])).
% 5.85/5.81 tff(12732,plain,
% 5.85/5.81 (succ(succ(succ(X1!59))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12731, 28])).
% 5.85/5.81 tff(12733,plain,
% 5.85/5.81 (succ(succ(succ(succ(X1!59)))) = succ(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12732])).
% 5.85/5.81 tff(12734,plain,
% 5.85/5.81 (succ(succ(succ(succ(X1!59)))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12733, 42])).
% 5.85/5.81 tff(12735,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(X1!59))))) = succ(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12734])).
% 5.85/5.81 tff(12736,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(X1!59))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12735, 58])).
% 5.85/5.81 tff(12737,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12736])).
% 5.85/5.81 tff(12738,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12737, 36])).
% 5.85/5.81 tff(12739,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12738])).
% 5.85/5.81 tff(12740,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12739, 48])).
% 5.85/5.81 tff(12741,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12740])).
% 5.85/5.81 tff(12742,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12741, 14])).
% 5.85/5.81 tff(12743,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12742])).
% 5.85/5.81 tff(12744,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12743, 33])).
% 5.85/5.81 tff(12745,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12744])).
% 5.85/5.81 tff(12746,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12745, 30])).
% 5.85/5.81 tff(12747,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12746])).
% 5.85/5.81 tff(12748,plain,
% 5.85/5.81 (NSX1!33 = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[305, 12747, 39])).
% 5.85/5.81 tff(12749,plain,
% 5.85/5.81 (pred(NSX1!33) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12748])).
% 5.85/5.81 tff(12750,plain,
% 5.85/5.81 (pred(NSX1!33) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12749, 18])).
% 5.85/5.81 tff(12751,plain,
% 5.85/5.81 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n6, n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12750, 12726])).
% 5.85/5.81 tff(12752,plain,
% 5.85/5.81 (Y2!56 = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[310, 12751, 788])).
% 5.85/5.81 tff(12753,plain,
% 5.85/5.81 (pred(Y2!56) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12752])).
% 5.85/5.81 tff(12754,plain,
% 5.85/5.81 (pred(Y2!56) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12753, 17])).
% 5.85/5.81 tff(12755,plain,
% 5.85/5.81 (pred(pred(Y2!56)) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12754])).
% 5.85/5.81 tff(12756,plain,
% 5.85/5.81 (pred(pred(Y2!56)) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12755, 16])).
% 5.85/5.81 tff(12757,plain,
% 5.85/5.81 (pred(pred(pred(Y2!56))) = pred(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12756])).
% 5.85/5.81 tff(12758,plain,
% 5.85/5.81 (pred(pred(pred(Y2!56))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12757, 15])).
% 5.85/5.81 tff(12759,plain,
% 5.85/5.81 (pred(pred(pred(pred(Y2!56)))) = pred(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12758])).
% 5.85/5.81 tff(12760,plain,
% 5.85/5.81 (pred(pred(pred(pred(Y2!56)))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12759, 25])).
% 5.85/5.81 tff(12761,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12760])).
% 5.85/5.81 tff(12762,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(Y2!56))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12761, 24])).
% 5.85/5.81 tff(12763,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12762])).
% 5.85/5.81 tff(12764,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12763, 23])).
% 5.85/5.81 tff(12765,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12764])).
% 5.85/5.81 tff(12766,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12765, 22])).
% 5.85/5.81 tff(12767,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12766])).
% 5.85/5.81 tff(12768,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12767, 21])).
% 5.85/5.81 tff(12769,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12768])).
% 5.85/5.81 tff(12770,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12769, 20])).
% 5.85/5.81 tff(12771,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12770])).
% 5.85/5.81 tff(12772,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12771, 19])).
% 5.85/5.81 tff(12773,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12772])).
% 5.85/5.81 tff(12774,plain,
% 5.85/5.81 (NPY2!30 = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[347, 12773, 18])).
% 5.85/5.81 tff(12775,plain,
% 5.85/5.81 (succ(NPY2!30) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12774])).
% 5.85/5.81 tff(12776,plain,
% 5.85/5.81 (succ(NPY2!30) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12775, 39])).
% 5.85/5.81 tff(12777,plain,
% 5.85/5.81 (succ(Y2!56) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12752])).
% 5.85/5.81 tff(12778,plain,
% 5.85/5.81 (succ(Y2!56) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12777, 39])).
% 5.85/5.81 tff(12779,plain,
% 5.85/5.81 (succ(succ(Y2!56)) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12778])).
% 5.85/5.81 tff(12780,plain,
% 5.85/5.81 (succ(succ(Y2!56)) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12779, 53])).
% 5.85/5.81 tff(12781,plain,
% 5.85/5.81 (succ(succ(succ(Y2!56))) = succ(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12780])).
% 5.85/5.81 tff(12782,plain,
% 5.85/5.81 (succ(succ(succ(Y2!56))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12781, 45])).
% 5.85/5.81 tff(12783,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y2!56)))) = succ(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12782])).
% 5.85/5.81 tff(12784,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y2!56)))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12783, 28])).
% 5.85/5.81 tff(12785,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12784])).
% 5.85/5.81 tff(12786,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y2!56))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12785, 42])).
% 5.85/5.81 tff(12787,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12786])).
% 5.85/5.81 tff(12788,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12787, 58])).
% 5.85/5.81 tff(12789,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12788])).
% 5.85/5.81 tff(12790,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12789, 36])).
% 5.85/5.81 tff(12791,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12790])).
% 5.85/5.81 tff(12792,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12791, 48])).
% 5.85/5.81 tff(12793,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12792])).
% 5.85/5.81 tff(12794,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12793, 14])).
% 5.85/5.81 tff(12795,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12794])).
% 5.85/5.81 tff(12796,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12795, 33])).
% 5.85/5.81 tff(12797,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12796])).
% 5.85/5.81 tff(12798,plain,
% 5.85/5.81 (NSY2!28 = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[370, 12797, 30])).
% 5.85/5.81 tff(12799,plain,
% 5.85/5.81 (pred(NSY2!28) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12798])).
% 5.85/5.81 tff(12800,plain,
% 5.85/5.81 (pred(NSY2!28) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12799, 17])).
% 5.85/5.81 tff(12801,plain,
% 5.85/5.81 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n5, n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12800, 12776])).
% 5.85/5.81 tff(12802,plain,
% 5.85/5.81 (sum(pred(NSY2!28), succ(NPY2!30)) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12801, 50])).
% 5.85/5.81 tff(12803,plain,
% 5.85/5.81 (sum(pred(Y1!58), succ(X1!59)) = sum(n6, n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12645, 12728])).
% 5.85/5.81 tff(12804,plain,
% 5.85/5.81 (sum(pred(Y1!58), succ(X1!59)) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12803, 52])).
% 5.85/5.81 tff(12805,plain,
% 5.85/5.81 (sum(pred(X1!59), succ(Y1!58)) = sum(n6, n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12702, 12669])).
% 5.85/5.81 tff(12806,plain,
% 5.85/5.81 (sum(pred(X1!59), succ(Y1!58)) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12805, 52])).
% 5.85/5.81 tff(12807,plain,
% 5.85/5.81 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n3, n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12806, 12804])).
% 5.85/5.81 tff(12808,plain,
% 5.85/5.81 (X2!57 = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[209, 12807, 51])).
% 5.85/5.81 tff(12809,plain,
% 5.85/5.81 (pred(X2!57) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12808])).
% 5.85/5.81 tff(12810,plain,
% 5.85/5.81 (pred(X2!57) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12809, 17])).
% 5.85/5.81 tff(12811,plain,
% 5.85/5.81 (pred(pred(X2!57)) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12810])).
% 5.85/5.81 tff(12812,plain,
% 5.85/5.81 (pred(pred(X2!57)) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12811, 16])).
% 5.85/5.81 tff(12813,plain,
% 5.85/5.81 (pred(pred(pred(X2!57))) = pred(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12812])).
% 5.85/5.81 tff(12814,plain,
% 5.85/5.81 (pred(pred(pred(X2!57))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12813, 15])).
% 5.85/5.81 tff(12815,plain,
% 5.85/5.81 (pred(pred(pred(pred(X2!57)))) = pred(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12814])).
% 5.85/5.81 tff(12816,plain,
% 5.85/5.81 (pred(pred(pred(pred(X2!57)))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12815, 25])).
% 5.85/5.81 tff(12817,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(X2!57))))) = pred(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12816])).
% 5.85/5.81 tff(12818,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(X2!57))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12817, 24])).
% 5.85/5.81 tff(12819,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12818])).
% 5.85/5.81 tff(12820,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12819, 23])).
% 5.85/5.81 tff(12821,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12820])).
% 5.85/5.81 tff(12822,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12821, 22])).
% 5.85/5.81 tff(12823,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12822])).
% 5.85/5.81 tff(12824,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12823, 21])).
% 5.85/5.81 tff(12825,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12824])).
% 5.85/5.81 tff(12826,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12825, 20])).
% 5.85/5.81 tff(12827,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12826])).
% 5.85/5.81 tff(12828,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12827, 19])).
% 5.85/5.81 tff(12829,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12828])).
% 5.85/5.81 tff(12830,plain,
% 5.85/5.81 (NPX2!31 = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[395, 12829, 18])).
% 5.85/5.81 tff(12831,plain,
% 5.85/5.81 (succ(NPX2!31) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12830])).
% 5.85/5.81 tff(12832,plain,
% 5.85/5.81 (succ(NPX2!31) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12831, 39])).
% 5.85/5.81 tff(12833,plain,
% 5.85/5.81 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n7, n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12832, 12802])).
% 5.85/5.81 tff(12834,plain,
% 5.85/5.81 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12833, 787])).
% 5.85/5.81 tff(12835,plain,
% 5.85/5.81 (succ(X2!57) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12808])).
% 5.85/5.81 tff(12836,plain,
% 5.85/5.81 (succ(X2!57) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12835, 39])).
% 5.85/5.81 tff(12837,plain,
% 5.85/5.81 (succ(succ(X2!57)) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12836])).
% 5.85/5.81 tff(12838,plain,
% 5.85/5.81 (succ(succ(X2!57)) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12837, 53])).
% 5.85/5.81 tff(12839,plain,
% 5.85/5.81 (succ(succ(succ(X2!57))) = succ(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12838])).
% 5.85/5.81 tff(12840,plain,
% 5.85/5.81 (succ(succ(succ(X2!57))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12839, 45])).
% 5.85/5.81 tff(12841,plain,
% 5.85/5.81 (succ(succ(succ(succ(X2!57)))) = succ(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12840])).
% 5.85/5.81 tff(12842,plain,
% 5.85/5.81 (succ(succ(succ(succ(X2!57)))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12841, 28])).
% 5.85/5.81 tff(12843,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(X2!57))))) = succ(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12842])).
% 5.85/5.81 tff(12844,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(X2!57))))) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12843, 42])).
% 5.85/5.81 tff(12845,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12844])).
% 5.85/5.81 tff(12846,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12845, 58])).
% 5.85/5.81 tff(12847,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12846])).
% 5.85/5.81 tff(12848,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[12847, 36])).
% 5.85/5.81 tff(12849,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12848])).
% 5.85/5.81 tff(12850,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12849, 48])).
% 5.85/5.81 tff(12851,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12850])).
% 5.85/5.81 tff(12852,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12851, 14])).
% 5.85/5.81 tff(12853,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12852])).
% 5.85/5.81 tff(12854,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12853, 33])).
% 5.85/5.81 tff(12855,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12854])).
% 5.85/5.81 tff(12856,plain,
% 5.85/5.81 (NSX2!29 = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[420, 12855, 30])).
% 5.85/5.81 tff(12857,plain,
% 5.85/5.81 (pred(NSX2!29) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12856])).
% 5.85/5.81 tff(12858,plain,
% 5.85/5.81 (pred(NSX2!29) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12857, 17])).
% 5.85/5.81 tff(12859,plain,
% 5.85/5.81 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n5, n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12858, 12834])).
% 5.85/5.81 tff(12860,plain,
% 5.85/5.81 (Y3!54 = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[425, 12859, 558])).
% 5.85/5.81 tff(12861,plain,
% 5.85/5.81 (pred(Y3!54) = pred(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12860])).
% 5.85/5.81 tff(12862,plain,
% 5.85/5.81 (pred(Y3!54) = n1),
% 5.85/5.81 inference(transitivity,[status(thm)],[12861, 24])).
% 5.85/5.81 tff(12863,plain,
% 5.85/5.81 (pred(pred(Y3!54)) = pred(n1)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12862])).
% 5.85/5.81 tff(12864,plain,
% 5.85/5.81 (pred(pred(Y3!54)) = n0),
% 5.85/5.81 inference(transitivity,[status(thm)],[12863, 23])).
% 5.85/5.81 tff(12865,plain,
% 5.85/5.81 (pred(pred(pred(Y3!54))) = pred(n0)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12864])).
% 5.85/5.81 tff(12866,plain,
% 5.85/5.81 (pred(pred(pred(Y3!54))) = n10),
% 5.85/5.81 inference(transitivity,[status(thm)],[12865, 22])).
% 5.85/5.81 tff(12867,plain,
% 5.85/5.81 (pred(pred(pred(pred(Y3!54)))) = pred(n10)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12866])).
% 5.85/5.81 tff(12868,plain,
% 5.85/5.81 (pred(pred(pred(pred(Y3!54)))) = n9),
% 5.85/5.81 inference(transitivity,[status(thm)],[12867, 21])).
% 5.85/5.81 tff(12869,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n9)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12868])).
% 5.85/5.81 tff(12870,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(Y3!54))))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12869, 20])).
% 5.85/5.81 tff(12871,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n8)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12870])).
% 5.85/5.81 tff(12872,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12871, 19])).
% 5.85/5.81 tff(12873,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12872])).
% 5.85/5.81 tff(12874,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12873, 18])).
% 5.85/5.81 tff(12875,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12874])).
% 5.85/5.81 tff(12876,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12875, 17])).
% 5.85/5.81 tff(12877,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12876])).
% 5.85/5.81 tff(12878,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12877, 16])).
% 5.85/5.81 tff(12879,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12878])).
% 5.85/5.81 tff(12880,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12879, 15])).
% 5.85/5.81 tff(12881,plain,
% 5.85/5.81 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12880])).
% 5.85/5.81 tff(12882,plain,
% 5.85/5.81 (NPY3!26 = n2),
% 5.85/5.81 inference(transitivity,[status(thm)],[462, 12881, 25])).
% 5.85/5.81 tff(12883,plain,
% 5.85/5.81 (succ(NPY3!26) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12882])).
% 5.85/5.81 tff(12884,plain,
% 5.85/5.81 (succ(NPY3!26) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12883, 48])).
% 5.85/5.81 tff(12885,plain,
% 5.85/5.81 (succ(Y3!54) = succ(n2)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12860])).
% 5.85/5.81 tff(12886,plain,
% 5.85/5.81 (succ(Y3!54) = n3),
% 5.85/5.81 inference(transitivity,[status(thm)],[12885, 48])).
% 5.85/5.81 tff(12887,plain,
% 5.85/5.81 (succ(succ(Y3!54)) = succ(n3)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12886])).
% 5.85/5.81 tff(12888,plain,
% 5.85/5.81 (succ(succ(Y3!54)) = n4),
% 5.85/5.81 inference(transitivity,[status(thm)],[12887, 14])).
% 5.85/5.81 tff(12889,plain,
% 5.85/5.81 (succ(succ(succ(Y3!54))) = succ(n4)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12888])).
% 5.85/5.81 tff(12890,plain,
% 5.85/5.81 (succ(succ(succ(Y3!54))) = n5),
% 5.85/5.81 inference(transitivity,[status(thm)],[12889, 33])).
% 5.85/5.81 tff(12891,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y3!54)))) = succ(n5)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12890])).
% 5.85/5.81 tff(12892,plain,
% 5.85/5.81 (succ(succ(succ(succ(Y3!54)))) = n6),
% 5.85/5.81 inference(transitivity,[status(thm)],[12891, 30])).
% 5.85/5.81 tff(12893,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n6)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12892])).
% 5.85/5.81 tff(12894,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(Y3!54))))) = n7),
% 5.85/5.81 inference(transitivity,[status(thm)],[12893, 39])).
% 5.85/5.81 tff(12895,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n7)),
% 5.85/5.81 inference(monotonicity,[status(thm)],[12894])).
% 5.85/5.81 tff(12896,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n8),
% 5.85/5.81 inference(transitivity,[status(thm)],[12895, 53])).
% 5.85/5.81 tff(12897,plain,
% 5.85/5.81 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12896])).
% 5.85/5.82 tff(12898,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[12897, 45])).
% 5.85/5.82 tff(12899,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12898])).
% 5.85/5.82 tff(12900,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[12899, 28])).
% 5.85/5.82 tff(12901,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12900])).
% 5.85/5.82 tff(12902,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[12901, 42])).
% 5.85/5.82 tff(12903,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12902])).
% 5.85/5.82 tff(12904,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12903, 58])).
% 5.85/5.82 tff(12905,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12904])).
% 5.85/5.82 tff(12906,plain,
% 5.85/5.82 (NSY3!24 = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[485, 12905, 36])).
% 5.85/5.82 tff(12907,plain,
% 5.85/5.82 (pred(NSY3!24) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12906])).
% 5.85/5.82 tff(12908,plain,
% 5.85/5.82 (pred(NSY3!24) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12907, 24])).
% 5.85/5.82 tff(12909,plain,
% 5.85/5.82 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n1, n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12908, 12884])).
% 5.85/5.82 tff(12910,plain,
% 5.85/5.82 (sum(pred(NSY3!24), succ(NPY3!26)) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[12909, 47])).
% 5.85/5.82 tff(12911,plain,
% 5.85/5.82 (sum(pred(Y2!56), succ(X2!57)) = sum(n5, n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12754, 12836])).
% 5.85/5.82 tff(12912,plain,
% 5.85/5.82 (sum(pred(Y2!56), succ(X2!57)) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12911, 50])).
% 5.85/5.82 tff(12913,plain,
% 5.85/5.82 (sum(pred(X2!57), succ(Y2!56)) = sum(n5, n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12810, 12778])).
% 5.85/5.82 tff(12914,plain,
% 5.85/5.82 (sum(pred(X2!57), succ(Y2!56)) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12913, 50])).
% 5.85/5.82 tff(12915,plain,
% 5.85/5.82 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n1, n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12914, 12912])).
% 5.85/5.82 tff(12916,plain,
% 5.85/5.82 (X3!55 = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[323, 12915, 49])).
% 5.85/5.82 tff(12917,plain,
% 5.85/5.82 (pred(X3!55) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12916])).
% 5.85/5.82 tff(12918,plain,
% 5.85/5.82 (pred(X3!55) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12917, 24])).
% 5.85/5.82 tff(12919,plain,
% 5.85/5.82 (pred(pred(X3!55)) = pred(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12918])).
% 5.85/5.82 tff(12920,plain,
% 5.85/5.82 (pred(pred(X3!55)) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[12919, 23])).
% 5.85/5.82 tff(12921,plain,
% 5.85/5.82 (pred(pred(pred(X3!55))) = pred(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12920])).
% 5.85/5.82 tff(12922,plain,
% 5.85/5.82 (pred(pred(pred(X3!55))) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[12921, 22])).
% 5.85/5.82 tff(12923,plain,
% 5.85/5.82 (pred(pred(pred(pred(X3!55)))) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12922])).
% 5.85/5.82 tff(12924,plain,
% 5.85/5.82 (pred(pred(pred(pred(X3!55)))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[12923, 21])).
% 5.85/5.82 tff(12925,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(X3!55))))) = pred(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12924])).
% 5.85/5.82 tff(12926,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(X3!55))))) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[12925, 20])).
% 5.85/5.82 tff(12927,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12926])).
% 5.85/5.82 tff(12928,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[12927, 19])).
% 5.85/5.82 tff(12929,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12928])).
% 5.85/5.82 tff(12930,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[12929, 18])).
% 5.85/5.82 tff(12931,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12930])).
% 5.85/5.82 tff(12932,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[12931, 17])).
% 5.85/5.82 tff(12933,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12932])).
% 5.85/5.82 tff(12934,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[12933, 16])).
% 5.85/5.82 tff(12935,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12934])).
% 5.85/5.82 tff(12936,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[12935, 15])).
% 5.85/5.82 tff(12937,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12936])).
% 5.85/5.82 tff(12938,plain,
% 5.85/5.82 (NPX3!27 = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[510, 12937, 25])).
% 5.85/5.82 tff(12939,plain,
% 5.85/5.82 (succ(NPX3!27) = succ(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12938])).
% 5.85/5.82 tff(12940,plain,
% 5.85/5.82 (succ(NPX3!27) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[12939, 48])).
% 5.85/5.82 tff(12941,plain,
% 5.85/5.82 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n3, n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12940, 12910])).
% 5.85/5.82 tff(12942,plain,
% 5.85/5.82 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[12941, 786])).
% 5.85/5.82 tff(12943,plain,
% 5.85/5.82 (succ(X3!55) = succ(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12916])).
% 5.85/5.82 tff(12944,plain,
% 5.85/5.82 (succ(X3!55) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[12943, 48])).
% 5.85/5.82 tff(12945,plain,
% 5.85/5.82 (succ(succ(X3!55)) = succ(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12944])).
% 5.85/5.82 tff(12946,plain,
% 5.85/5.82 (succ(succ(X3!55)) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[12945, 14])).
% 5.85/5.82 tff(12947,plain,
% 5.85/5.82 (succ(succ(succ(X3!55))) = succ(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12946])).
% 5.85/5.82 tff(12948,plain,
% 5.85/5.82 (succ(succ(succ(X3!55))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[12947, 33])).
% 5.85/5.82 tff(12949,plain,
% 5.85/5.82 (succ(succ(succ(succ(X3!55)))) = succ(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12948])).
% 5.85/5.82 tff(12950,plain,
% 5.85/5.82 (succ(succ(succ(succ(X3!55)))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[12949, 30])).
% 5.85/5.82 tff(12951,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(X3!55))))) = succ(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12950])).
% 5.85/5.82 tff(12952,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(X3!55))))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[12951, 39])).
% 5.85/5.82 tff(12953,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12952])).
% 5.85/5.82 tff(12954,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[12953, 53])).
% 5.85/5.82 tff(12955,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12954])).
% 5.85/5.82 tff(12956,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[12955, 45])).
% 5.85/5.82 tff(12957,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12956])).
% 5.85/5.82 tff(12958,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[12957, 28])).
% 5.85/5.82 tff(12959,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12958])).
% 5.85/5.82 tff(12960,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[12959, 42])).
% 5.85/5.82 tff(12961,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12960])).
% 5.85/5.82 tff(12962,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12961, 58])).
% 5.85/5.82 tff(12963,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12962])).
% 5.85/5.82 tff(12964,plain,
% 5.85/5.82 (NSX3!25 = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[535, 12963, 36])).
% 5.85/5.82 tff(12965,plain,
% 5.85/5.82 (pred(NSX3!25) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12964])).
% 5.85/5.82 tff(12966,plain,
% 5.85/5.82 (pred(NSX3!25) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12965, 24])).
% 5.85/5.82 tff(12967,plain,
% 5.85/5.82 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n1, n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12966, 12942])).
% 5.85/5.82 tff(12968,plain,
% 5.85/5.82 (Y4!52 = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[540, 12967, 791])).
% 5.85/5.82 tff(12969,plain,
% 5.85/5.82 (pred(Y4!52) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12968])).
% 5.85/5.82 tff(12970,plain,
% 5.85/5.82 (pred(Y4!52) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[12969, 19])).
% 5.85/5.82 tff(12971,plain,
% 5.85/5.82 (pred(pred(Y4!52)) = pred(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12970])).
% 5.85/5.82 tff(12972,plain,
% 5.85/5.82 (pred(pred(Y4!52)) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[12971, 18])).
% 5.85/5.82 tff(12973,plain,
% 5.85/5.82 (pred(pred(pred(Y4!52))) = pred(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12972])).
% 5.85/5.82 tff(12974,plain,
% 5.85/5.82 (pred(pred(pred(Y4!52))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[12973, 17])).
% 5.85/5.82 tff(12975,plain,
% 5.85/5.82 (pred(pred(pred(pred(Y4!52)))) = pred(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12974])).
% 5.85/5.82 tff(12976,plain,
% 5.85/5.82 (pred(pred(pred(pred(Y4!52)))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[12975, 16])).
% 5.85/5.82 tff(12977,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12976])).
% 5.85/5.82 tff(12978,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(Y4!52))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[12977, 15])).
% 5.85/5.82 tff(12979,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12978])).
% 5.85/5.82 tff(12980,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[12979, 25])).
% 5.85/5.82 tff(12981,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12980])).
% 5.85/5.82 tff(12982,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12981, 24])).
% 5.85/5.82 tff(12983,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12982])).
% 5.85/5.82 tff(12984,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[12983, 23])).
% 5.85/5.82 tff(12985,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12984])).
% 5.85/5.82 tff(12986,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[12985, 22])).
% 5.85/5.82 tff(12987,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12986])).
% 5.85/5.82 tff(12988,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[12987, 21])).
% 5.85/5.82 tff(12989,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12988])).
% 5.85/5.82 tff(12990,plain,
% 5.85/5.82 (NPY4!22 = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[578, 12989, 20])).
% 5.85/5.82 tff(12991,plain,
% 5.85/5.82 (succ(NPY4!22) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12990])).
% 5.85/5.82 tff(12992,plain,
% 5.85/5.82 (succ(NPY4!22) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[12991, 45])).
% 5.85/5.82 tff(12993,plain,
% 5.85/5.82 (succ(Y4!52) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12968])).
% 5.85/5.82 tff(12994,plain,
% 5.85/5.82 (succ(Y4!52) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[12993, 45])).
% 5.85/5.82 tff(12995,plain,
% 5.85/5.82 (succ(succ(Y4!52)) = succ(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12994])).
% 5.85/5.82 tff(12996,plain,
% 5.85/5.82 (succ(succ(Y4!52)) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[12995, 28])).
% 5.85/5.82 tff(12997,plain,
% 5.85/5.82 (succ(succ(succ(Y4!52))) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12996])).
% 5.85/5.82 tff(12998,plain,
% 5.85/5.82 (succ(succ(succ(Y4!52))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[12997, 42])).
% 5.85/5.82 tff(12999,plain,
% 5.85/5.82 (succ(succ(succ(succ(Y4!52)))) = succ(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12998])).
% 5.85/5.82 tff(13000,plain,
% 5.85/5.82 (succ(succ(succ(succ(Y4!52)))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[12999, 58])).
% 5.85/5.82 tff(13001,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13000])).
% 5.85/5.82 tff(13002,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(Y4!52))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13001, 36])).
% 5.85/5.82 tff(13003,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13002])).
% 5.85/5.82 tff(13004,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13003, 48])).
% 5.85/5.82 tff(13005,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13004])).
% 5.85/5.82 tff(13006,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13005, 14])).
% 5.85/5.82 tff(13007,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13006])).
% 5.85/5.82 tff(13008,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13007, 33])).
% 5.85/5.82 tff(13009,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13008])).
% 5.85/5.82 tff(13010,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13009, 30])).
% 5.85/5.82 tff(13011,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13010])).
% 5.85/5.82 tff(13012,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13011, 39])).
% 5.85/5.82 tff(13013,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13012])).
% 5.85/5.82 tff(13014,plain,
% 5.85/5.82 (NSY4!20 = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[601, 13013, 53])).
% 5.85/5.82 tff(13015,plain,
% 5.85/5.82 (pred(NSY4!20) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13014])).
% 5.85/5.82 tff(13016,plain,
% 5.85/5.82 (pred(NSY4!20) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13015, 19])).
% 5.85/5.82 tff(13017,plain,
% 5.85/5.82 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n7, n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13016, 12992])).
% 5.85/5.82 tff(13018,plain,
% 5.85/5.82 (sum(pred(NSY4!20), succ(NPY4!22)) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13017, 44])).
% 5.85/5.82 tff(13019,plain,
% 5.85/5.82 (sum(pred(Y3!54), succ(X3!55)) = sum(n1, n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12862, 12944])).
% 5.85/5.82 tff(13020,plain,
% 5.85/5.82 (sum(pred(Y3!54), succ(X3!55)) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13019, 47])).
% 5.85/5.82 tff(13021,plain,
% 5.85/5.82 (sum(pred(X3!55), succ(Y3!54)) = sum(n1, n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12918, 12886])).
% 5.85/5.82 tff(13022,plain,
% 5.85/5.82 (sum(pred(X3!55), succ(Y3!54)) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13021, 47])).
% 5.85/5.82 tff(13023,plain,
% 5.85/5.82 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n4, n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13022, 13020])).
% 5.85/5.82 tff(13024,plain,
% 5.85/5.82 (X4!53 = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[438, 13023, 46])).
% 5.85/5.82 tff(13025,plain,
% 5.85/5.82 (pred(X4!53) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13024])).
% 5.85/5.82 tff(13026,plain,
% 5.85/5.82 (pred(X4!53) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13025, 19])).
% 5.85/5.82 tff(13027,plain,
% 5.85/5.82 (pred(pred(X4!53)) = pred(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13026])).
% 5.85/5.82 tff(13028,plain,
% 5.85/5.82 (pred(pred(X4!53)) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13027, 18])).
% 5.85/5.82 tff(13029,plain,
% 5.85/5.82 (pred(pred(pred(X4!53))) = pred(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13028])).
% 5.85/5.82 tff(13030,plain,
% 5.85/5.82 (pred(pred(pred(X4!53))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13029, 17])).
% 5.85/5.82 tff(13031,plain,
% 5.85/5.82 (pred(pred(pred(pred(X4!53)))) = pred(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13030])).
% 5.85/5.82 tff(13032,plain,
% 5.85/5.82 (pred(pred(pred(pred(X4!53)))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13031, 16])).
% 5.85/5.82 tff(13033,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(X4!53))))) = pred(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13032])).
% 5.85/5.82 tff(13034,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(X4!53))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13033, 15])).
% 5.85/5.82 tff(13035,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13034])).
% 5.85/5.82 tff(13036,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13035, 25])).
% 5.85/5.82 tff(13037,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13036])).
% 5.85/5.82 tff(13038,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13037, 24])).
% 5.85/5.82 tff(13039,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13038])).
% 5.85/5.82 tff(13040,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13039, 23])).
% 5.85/5.82 tff(13041,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13040])).
% 5.85/5.82 tff(13042,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[13041, 22])).
% 5.85/5.82 tff(13043,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13042])).
% 5.85/5.82 tff(13044,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13043, 21])).
% 5.85/5.82 tff(13045,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13044])).
% 5.85/5.82 tff(13046,plain,
% 5.85/5.82 (NPX4!23 = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[626, 13045, 20])).
% 5.85/5.82 tff(13047,plain,
% 5.85/5.82 (succ(NPX4!23) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13046])).
% 5.85/5.82 tff(13048,plain,
% 5.85/5.82 (succ(NPX4!23) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13047, 45])).
% 5.85/5.82 tff(13049,plain,
% 5.85/5.82 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n9, n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13048, 13018])).
% 5.85/5.82 tff(13050,plain,
% 5.85/5.82 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13049, 790])).
% 5.85/5.82 tff(13051,plain,
% 5.85/5.82 (succ(X4!53) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13024])).
% 5.85/5.82 tff(13052,plain,
% 5.85/5.82 (succ(X4!53) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13051, 45])).
% 5.85/5.82 tff(13053,plain,
% 5.85/5.82 (succ(succ(X4!53)) = succ(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13052])).
% 5.85/5.82 tff(13054,plain,
% 5.85/5.82 (succ(succ(X4!53)) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[13053, 28])).
% 5.85/5.82 tff(13055,plain,
% 5.85/5.82 (succ(succ(succ(X4!53))) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13054])).
% 5.85/5.82 tff(13056,plain,
% 5.85/5.82 (succ(succ(succ(X4!53))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13055, 42])).
% 5.85/5.82 tff(13057,plain,
% 5.85/5.82 (succ(succ(succ(succ(X4!53)))) = succ(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13056])).
% 5.85/5.82 tff(13058,plain,
% 5.85/5.82 (succ(succ(succ(succ(X4!53)))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13057, 58])).
% 5.85/5.82 tff(13059,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(X4!53))))) = succ(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13058])).
% 5.85/5.82 tff(13060,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(X4!53))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13059, 36])).
% 5.85/5.82 tff(13061,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13060])).
% 5.85/5.82 tff(13062,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13061, 48])).
% 5.85/5.82 tff(13063,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13062])).
% 5.85/5.82 tff(13064,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13063, 14])).
% 5.85/5.82 tff(13065,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13064])).
% 5.85/5.82 tff(13066,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13065, 33])).
% 5.85/5.82 tff(13067,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13066])).
% 5.85/5.82 tff(13068,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13067, 30])).
% 5.85/5.82 tff(13069,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13068])).
% 5.85/5.82 tff(13070,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13069, 39])).
% 5.85/5.82 tff(13071,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13070])).
% 5.85/5.82 tff(13072,plain,
% 5.85/5.82 (NSX4!21 = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[651, 13071, 53])).
% 5.85/5.82 tff(13073,plain,
% 5.85/5.82 (pred(NSX4!21) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13072])).
% 5.85/5.82 tff(13074,plain,
% 5.85/5.82 (pred(NSX4!21) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13073, 19])).
% 5.85/5.82 tff(13075,plain,
% 5.85/5.82 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n7, n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13074, 13050])).
% 5.85/5.82 tff(13076,plain,
% 5.85/5.82 (Y5!50 = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[656, 13075, 789])).
% 5.85/5.82 tff(13077,plain,
% 5.85/5.82 (pred(Y5!50) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13076])).
% 5.85/5.82 tff(13078,plain,
% 5.85/5.82 (pred(Y5!50) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13077, 21])).
% 5.85/5.82 tff(13079,plain,
% 5.85/5.82 (pred(pred(Y5!50)) = pred(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13078])).
% 5.85/5.82 tff(13080,plain,
% 5.85/5.82 (pred(pred(Y5!50)) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[13079, 20])).
% 5.85/5.82 tff(13081,plain,
% 5.85/5.82 (pred(pred(pred(Y5!50))) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13080])).
% 5.85/5.82 tff(13082,plain,
% 5.85/5.82 (pred(pred(pred(Y5!50))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13081, 19])).
% 5.85/5.82 tff(13083,plain,
% 5.85/5.82 (pred(pred(pred(pred(Y5!50)))) = pred(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13082])).
% 5.85/5.82 tff(13084,plain,
% 5.85/5.82 (pred(pred(pred(pred(Y5!50)))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13083, 18])).
% 5.85/5.82 tff(13085,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13084])).
% 5.85/5.82 tff(13086,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(Y5!50))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13085, 17])).
% 5.85/5.82 tff(13087,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13086])).
% 5.85/5.82 tff(13088,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13087, 16])).
% 5.85/5.82 tff(13089,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13088])).
% 5.85/5.82 tff(13090,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13089, 15])).
% 5.85/5.82 tff(13091,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13090])).
% 5.85/5.82 tff(13092,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13091, 25])).
% 5.85/5.82 tff(13093,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13092])).
% 5.85/5.82 tff(13094,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13093, 24])).
% 5.85/5.82 tff(13095,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13094])).
% 5.85/5.82 tff(13096,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13095, 23])).
% 5.85/5.82 tff(13097,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13096])).
% 5.85/5.82 tff(13098,plain,
% 5.85/5.82 (NPY5!18 = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[694, 13097, 22])).
% 5.85/5.82 tff(13099,plain,
% 5.85/5.82 (succ(NPY5!18) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13098])).
% 5.85/5.82 tff(13100,plain,
% 5.85/5.82 (succ(NPY5!18) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13099, 42])).
% 5.85/5.82 tff(13101,plain,
% 5.85/5.82 (succ(Y5!50) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13076])).
% 5.85/5.82 tff(13102,plain,
% 5.85/5.82 (succ(Y5!50) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13101, 42])).
% 5.85/5.82 tff(13103,plain,
% 5.85/5.82 (succ(succ(Y5!50)) = succ(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13102])).
% 5.85/5.82 tff(13104,plain,
% 5.85/5.82 (succ(succ(Y5!50)) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13103, 58])).
% 5.85/5.82 tff(13105,plain,
% 5.85/5.82 (succ(succ(succ(Y5!50))) = succ(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13104])).
% 5.85/5.82 tff(13106,plain,
% 5.85/5.82 (succ(succ(succ(Y5!50))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13105, 36])).
% 5.85/5.82 tff(13107,plain,
% 5.85/5.82 (succ(succ(succ(succ(Y5!50)))) = succ(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13106])).
% 5.85/5.82 tff(13108,plain,
% 5.85/5.82 (succ(succ(succ(succ(Y5!50)))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13107, 48])).
% 5.85/5.82 tff(13109,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13108])).
% 5.85/5.82 tff(13110,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(Y5!50))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13109, 14])).
% 5.85/5.82 tff(13111,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13110])).
% 5.85/5.82 tff(13112,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13111, 33])).
% 5.85/5.82 tff(13113,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13112])).
% 5.85/5.82 tff(13114,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13113, 30])).
% 5.85/5.82 tff(13115,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13114])).
% 5.85/5.82 tff(13116,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13115, 39])).
% 5.85/5.82 tff(13117,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13116])).
% 5.85/5.82 tff(13118,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[13117, 53])).
% 5.85/5.82 tff(13119,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13118])).
% 5.85/5.82 tff(13120,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13119, 45])).
% 5.85/5.82 tff(13121,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13120])).
% 5.85/5.82 tff(13122,plain,
% 5.85/5.82 (NSY5!16 = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[717, 13121, 28])).
% 5.85/5.82 tff(13123,plain,
% 5.85/5.82 (pred(NSY5!16) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13122])).
% 5.85/5.82 tff(13124,plain,
% 5.85/5.82 (pred(NSY5!16) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13123, 21])).
% 5.85/5.82 tff(13125,plain,
% 5.85/5.82 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n9, n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13124, 13100])).
% 5.85/5.82 tff(13126,plain,
% 5.85/5.82 (sum(pred(NSY5!16), succ(NPY5!18)) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13125, 41])).
% 5.85/5.82 tff(13127,plain,
% 5.85/5.82 (sum(pred(Y4!52), succ(X4!53)) = sum(n7, n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[12970, 13052])).
% 5.85/5.82 tff(13128,plain,
% 5.85/5.82 (sum(pred(Y4!52), succ(X4!53)) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13127, 44])).
% 5.85/5.82 tff(13129,plain,
% 5.85/5.82 (sum(pred(X4!53), succ(Y4!52)) = sum(n7, n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13026, 12994])).
% 5.85/5.82 tff(13130,plain,
% 5.85/5.82 (sum(pred(X4!53), succ(Y4!52)) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13129, 44])).
% 5.85/5.82 tff(13131,plain,
% 5.85/5.82 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n5, n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13130, 13128])).
% 5.85/5.82 tff(13132,plain,
% 5.85/5.82 (X5!51 = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[553, 13131, 43])).
% 5.85/5.82 tff(13133,plain,
% 5.85/5.82 (pred(X5!51) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13132])).
% 5.85/5.82 tff(13134,plain,
% 5.85/5.82 (pred(X5!51) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13133, 21])).
% 5.85/5.82 tff(13135,plain,
% 5.85/5.82 (pred(pred(X5!51)) = pred(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13134])).
% 5.85/5.82 tff(13136,plain,
% 5.85/5.82 (pred(pred(X5!51)) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[13135, 20])).
% 5.85/5.82 tff(13137,plain,
% 5.85/5.82 (pred(pred(pred(X5!51))) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13136])).
% 5.85/5.82 tff(13138,plain,
% 5.85/5.82 (pred(pred(pred(X5!51))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13137, 19])).
% 5.85/5.82 tff(13139,plain,
% 5.85/5.82 (pred(pred(pred(pred(X5!51)))) = pred(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13138])).
% 5.85/5.82 tff(13140,plain,
% 5.85/5.82 (pred(pred(pred(pred(X5!51)))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13139, 18])).
% 5.85/5.82 tff(13141,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(X5!51))))) = pred(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13140])).
% 5.85/5.82 tff(13142,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(X5!51))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13141, 17])).
% 5.85/5.82 tff(13143,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13142])).
% 5.85/5.82 tff(13144,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13143, 16])).
% 5.85/5.82 tff(13145,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13144])).
% 5.85/5.82 tff(13146,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13145, 15])).
% 5.85/5.82 tff(13147,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13146])).
% 5.85/5.82 tff(13148,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13147, 25])).
% 5.85/5.82 tff(13149,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13148])).
% 5.85/5.82 tff(13150,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13149, 24])).
% 5.85/5.82 tff(13151,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13150])).
% 5.85/5.82 tff(13152,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13151, 23])).
% 5.85/5.82 tff(13153,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13152])).
% 5.85/5.82 tff(13154,plain,
% 5.85/5.82 (NPX5!19 = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[742, 13153, 22])).
% 5.85/5.82 tff(13155,plain,
% 5.85/5.82 (succ(NPX5!19) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13154])).
% 5.85/5.82 tff(13156,plain,
% 5.85/5.82 (succ(NPX5!19) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13155, 42])).
% 5.85/5.82 tff(13157,plain,
% 5.85/5.82 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n0, n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13156, 13126])).
% 5.85/5.82 tff(13158,plain,
% 5.85/5.82 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13157, 40])).
% 5.85/5.82 tff(13159,plain,
% 5.85/5.82 (succ(X5!51) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13132])).
% 5.85/5.82 tff(13160,plain,
% 5.85/5.82 (succ(X5!51) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13159, 42])).
% 5.85/5.82 tff(13161,plain,
% 5.85/5.82 (succ(succ(X5!51)) = succ(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13160])).
% 5.85/5.82 tff(13162,plain,
% 5.85/5.82 (succ(succ(X5!51)) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13161, 58])).
% 5.85/5.82 tff(13163,plain,
% 5.85/5.82 (succ(succ(succ(X5!51))) = succ(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13162])).
% 5.85/5.82 tff(13164,plain,
% 5.85/5.82 (succ(succ(succ(X5!51))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13163, 36])).
% 5.85/5.82 tff(13165,plain,
% 5.85/5.82 (succ(succ(succ(succ(X5!51)))) = succ(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13164])).
% 5.85/5.82 tff(13166,plain,
% 5.85/5.82 (succ(succ(succ(succ(X5!51)))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13165, 48])).
% 5.85/5.82 tff(13167,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(X5!51))))) = succ(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13166])).
% 5.85/5.82 tff(13168,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(X5!51))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13167, 14])).
% 5.85/5.82 tff(13169,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13168])).
% 5.85/5.82 tff(13170,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13169, 33])).
% 5.85/5.82 tff(13171,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13170])).
% 5.85/5.82 tff(13172,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13171, 30])).
% 5.85/5.82 tff(13173,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13172])).
% 5.85/5.82 tff(13174,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[13173, 39])).
% 5.85/5.82 tff(13175,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13174])).
% 5.85/5.82 tff(13176,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[13175, 53])).
% 5.85/5.82 tff(13177,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13176])).
% 5.85/5.82 tff(13178,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13177, 45])).
% 5.85/5.82 tff(13179,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13178])).
% 5.85/5.82 tff(13180,plain,
% 5.85/5.82 (NSX5!17 = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[767, 13179, 28])).
% 5.85/5.82 tff(13181,plain,
% 5.85/5.82 (pred(NSX5!17) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13180])).
% 5.85/5.82 tff(13182,plain,
% 5.85/5.82 (pred(NSX5!17) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13181, 21])).
% 5.85/5.82 tff(13183,plain,
% 5.85/5.82 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n9, n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13182, 13158])).
% 5.85/5.82 tff(13184,plain,
% 5.85/5.82 (Y6!48 = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[772, 13183, 54])).
% 5.85/5.82 tff(13185,plain,
% 5.85/5.82 (pred(Y6!48) = pred(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13184])).
% 5.85/5.82 tff(13186,plain,
% 5.85/5.82 (pred(Y6!48) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13185, 18])).
% 5.85/5.82 tff(13187,plain,
% 5.85/5.82 (pred(pred(Y6!48)) = pred(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13186])).
% 5.85/5.82 tff(13188,plain,
% 5.85/5.82 (pred(pred(Y6!48)) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13187, 17])).
% 5.85/5.82 tff(13189,plain,
% 5.85/5.82 (pred(pred(pred(Y6!48))) = pred(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13188])).
% 5.85/5.82 tff(13190,plain,
% 5.85/5.82 (pred(pred(pred(Y6!48))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13189, 16])).
% 5.85/5.82 tff(13191,plain,
% 5.85/5.82 (pred(pred(pred(pred(Y6!48)))) = pred(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13190])).
% 5.85/5.82 tff(13192,plain,
% 5.85/5.82 (pred(pred(pred(pred(Y6!48)))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13191, 15])).
% 5.85/5.82 tff(13193,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13192])).
% 5.85/5.82 tff(13194,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(Y6!48))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13193, 25])).
% 5.85/5.82 tff(13195,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13194])).
% 5.85/5.82 tff(13196,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13195, 24])).
% 5.85/5.82 tff(13197,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13196])).
% 5.85/5.82 tff(13198,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13197, 23])).
% 5.85/5.82 tff(13199,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13198])).
% 5.85/5.82 tff(13200,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[13199, 22])).
% 5.85/5.82 tff(13201,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13200])).
% 5.85/5.82 tff(13202,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13201, 21])).
% 5.85/5.82 tff(13203,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13202])).
% 5.85/5.82 tff(13204,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[13203, 20])).
% 5.85/5.82 tff(13205,plain,
% 5.85/5.82 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13204])).
% 5.85/5.82 tff(13206,plain,
% 5.85/5.82 (NPY6!14 = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[1465, 13205, 19])).
% 5.85/5.82 tff(13207,plain,
% 5.85/5.82 (succ(NPY6!14) = succ(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13206])).
% 5.85/5.82 tff(13208,plain,
% 5.85/5.82 (succ(NPY6!14) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[13207, 53])).
% 5.85/5.82 tff(13209,plain,
% 5.85/5.82 (succ(Y6!48) = succ(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13184])).
% 5.85/5.82 tff(13210,plain,
% 5.85/5.82 (succ(Y6!48) = n8),
% 5.85/5.82 inference(transitivity,[status(thm)],[13209, 53])).
% 5.85/5.82 tff(13211,plain,
% 5.85/5.82 (succ(succ(Y6!48)) = succ(n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13210])).
% 5.85/5.82 tff(13212,plain,
% 5.85/5.82 (succ(succ(Y6!48)) = n9),
% 5.85/5.82 inference(transitivity,[status(thm)],[13211, 45])).
% 5.85/5.82 tff(13213,plain,
% 5.85/5.82 (succ(succ(succ(Y6!48))) = succ(n9)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13212])).
% 5.85/5.82 tff(13214,plain,
% 5.85/5.82 (succ(succ(succ(Y6!48))) = n10),
% 5.85/5.82 inference(transitivity,[status(thm)],[13213, 28])).
% 5.85/5.82 tff(13215,plain,
% 5.85/5.82 (succ(succ(succ(succ(Y6!48)))) = succ(n10)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13214])).
% 5.85/5.82 tff(13216,plain,
% 5.85/5.82 (succ(succ(succ(succ(Y6!48)))) = n0),
% 5.85/5.82 inference(transitivity,[status(thm)],[13215, 42])).
% 5.85/5.82 tff(13217,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n0)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13216])).
% 5.85/5.82 tff(13218,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(Y6!48))))) = n1),
% 5.85/5.82 inference(transitivity,[status(thm)],[13217, 58])).
% 5.85/5.82 tff(13219,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n1)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13218])).
% 5.85/5.82 tff(13220,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n2),
% 5.85/5.82 inference(transitivity,[status(thm)],[13219, 36])).
% 5.85/5.82 tff(13221,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n2)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13220])).
% 5.85/5.82 tff(13222,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13221, 48])).
% 5.85/5.82 tff(13223,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n3)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13222])).
% 5.85/5.82 tff(13224,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n4),
% 5.85/5.82 inference(transitivity,[status(thm)],[13223, 14])).
% 5.85/5.82 tff(13225,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n4)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13224])).
% 5.85/5.82 tff(13226,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n5),
% 5.85/5.82 inference(transitivity,[status(thm)],[13225, 33])).
% 5.85/5.82 tff(13227,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n5)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13226])).
% 5.85/5.82 tff(13228,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13227, 30])).
% 5.85/5.82 tff(13229,plain,
% 5.85/5.82 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n6)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13228])).
% 5.85/5.82 tff(13230,plain,
% 5.85/5.82 (NSY6!12 = n7),
% 5.85/5.82 inference(transitivity,[status(thm)],[1490, 13229, 39])).
% 5.85/5.82 tff(13231,plain,
% 5.85/5.82 (pred(NSY6!12) = pred(n7)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13230])).
% 5.85/5.82 tff(13232,plain,
% 5.85/5.82 (pred(NSY6!12) = n6),
% 5.85/5.82 inference(transitivity,[status(thm)],[13231, 18])).
% 5.85/5.82 tff(13233,plain,
% 5.85/5.82 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n6, n8)),
% 5.85/5.82 inference(monotonicity,[status(thm)],[13232, 13208])).
% 5.85/5.82 tff(13234,plain,
% 5.85/5.82 (sum(pred(NSY6!12), succ(NPY6!14)) = n3),
% 5.85/5.82 inference(transitivity,[status(thm)],[13233, 52])).
% 5.85/5.82 tff(13235,plain,
% 5.85/5.82 (sum(pred(Y5!50), succ(X5!51)) = sum(n9, n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13078, 13160])).
% 5.85/5.83 tff(13236,plain,
% 5.85/5.83 (sum(pred(Y5!50), succ(X5!51)) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13235, 41])).
% 5.85/5.83 tff(13237,plain,
% 5.85/5.83 (sum(pred(X5!51), succ(Y5!50)) = sum(n9, n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13134, 13102])).
% 5.85/5.83 tff(13238,plain,
% 5.85/5.83 (sum(pred(X5!51), succ(Y5!50)) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13237, 41])).
% 5.85/5.83 tff(13239,plain,
% 5.85/5.83 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n9, n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13238, 13236])).
% 5.85/5.83 tff(13240,plain,
% 5.85/5.83 (X6!49 = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[669, 13239, 54])).
% 5.85/5.83 tff(13241,plain,
% 5.85/5.83 (pred(X6!49) = pred(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13240])).
% 5.85/5.83 tff(13242,plain,
% 5.85/5.83 (pred(X6!49) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13241, 18])).
% 5.85/5.83 tff(13243,plain,
% 5.85/5.83 (pred(pred(X6!49)) = pred(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13242])).
% 5.85/5.83 tff(13244,plain,
% 5.85/5.83 (pred(pred(X6!49)) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13243, 17])).
% 5.85/5.83 tff(13245,plain,
% 5.85/5.83 (pred(pred(pred(X6!49))) = pred(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13244])).
% 5.85/5.83 tff(13246,plain,
% 5.85/5.83 (pred(pred(pred(X6!49))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13245, 16])).
% 5.85/5.83 tff(13247,plain,
% 5.85/5.83 (pred(pred(pred(pred(X6!49)))) = pred(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13246])).
% 5.85/5.83 tff(13248,plain,
% 5.85/5.83 (pred(pred(pred(pred(X6!49)))) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13247, 15])).
% 5.85/5.83 tff(13249,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(X6!49))))) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13248])).
% 5.85/5.83 tff(13250,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(X6!49))))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13249, 25])).
% 5.85/5.83 tff(13251,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13250])).
% 5.85/5.83 tff(13252,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13251, 24])).
% 5.85/5.83 tff(13253,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13252])).
% 5.85/5.83 tff(13254,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13253, 23])).
% 5.85/5.83 tff(13255,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13254])).
% 5.85/5.83 tff(13256,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13255, 22])).
% 5.85/5.83 tff(13257,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13256])).
% 5.85/5.83 tff(13258,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13257, 21])).
% 5.85/5.83 tff(13259,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13258])).
% 5.85/5.83 tff(13260,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13259, 20])).
% 5.85/5.83 tff(13261,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13260])).
% 5.85/5.83 tff(13262,plain,
% 5.85/5.83 (NPX6!15 = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[1523, 13261, 19])).
% 5.85/5.83 tff(13263,plain,
% 5.85/5.83 (succ(NPX6!15) = succ(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13262])).
% 5.85/5.83 tff(13264,plain,
% 5.85/5.83 (succ(NPX6!15) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13263, 53])).
% 5.85/5.83 tff(13265,plain,
% 5.85/5.83 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n8, n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13264, 13234])).
% 5.85/5.83 tff(13266,plain,
% 5.85/5.83 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13265, 64])).
% 5.85/5.83 tff(13267,plain,
% 5.85/5.83 (succ(X6!49) = succ(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13240])).
% 5.85/5.83 tff(13268,plain,
% 5.85/5.83 (succ(X6!49) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13267, 53])).
% 5.85/5.83 tff(13269,plain,
% 5.85/5.83 (succ(succ(X6!49)) = succ(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13268])).
% 5.85/5.83 tff(13270,plain,
% 5.85/5.83 (succ(succ(X6!49)) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13269, 45])).
% 5.85/5.83 tff(13271,plain,
% 5.85/5.83 (succ(succ(succ(X6!49))) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13270])).
% 5.85/5.83 tff(13272,plain,
% 5.85/5.83 (succ(succ(succ(X6!49))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13271, 28])).
% 5.85/5.83 tff(13273,plain,
% 5.85/5.83 (succ(succ(succ(succ(X6!49)))) = succ(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13272])).
% 5.85/5.83 tff(13274,plain,
% 5.85/5.83 (succ(succ(succ(succ(X6!49)))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13273, 42])).
% 5.85/5.83 tff(13275,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(X6!49))))) = succ(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13274])).
% 5.85/5.83 tff(13276,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(X6!49))))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13275, 58])).
% 5.85/5.83 tff(13277,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13276])).
% 5.85/5.83 tff(13278,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13277, 36])).
% 5.85/5.83 tff(13279,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13278])).
% 5.85/5.83 tff(13280,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13279, 48])).
% 5.85/5.83 tff(13281,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13280])).
% 5.85/5.83 tff(13282,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13281, 14])).
% 5.85/5.83 tff(13283,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13282])).
% 5.85/5.83 tff(13284,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13283, 33])).
% 5.85/5.83 tff(13285,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13284])).
% 5.85/5.83 tff(13286,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13285, 30])).
% 5.85/5.83 tff(13287,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13286])).
% 5.85/5.83 tff(13288,plain,
% 5.85/5.83 (NSX6!13 = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[1550, 13287, 39])).
% 5.85/5.83 tff(13289,plain,
% 5.85/5.83 (pred(NSX6!13) = pred(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13288])).
% 5.85/5.83 tff(13290,plain,
% 5.85/5.83 (pred(NSX6!13) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13289, 18])).
% 5.85/5.83 tff(13291,plain,
% 5.85/5.83 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n6, n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13290, 13266])).
% 5.85/5.83 tff(13292,plain,
% 5.85/5.83 (sum(n6, n0) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.85/5.83 inference(symmetry,[status(thm)],[13291])).
% 5.85/5.83 tff(13293,plain,
% 5.85/5.83 (sum(pred(Y6!48), succ(X6!49)) = sum(n6, n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13186, 13268])).
% 5.85/5.83 tff(13294,plain,
% 5.85/5.83 (sum(pred(Y6!48), succ(X6!49)) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13293, 52])).
% 5.85/5.83 tff(13295,plain,
% 5.85/5.83 (sum(pred(X6!49), succ(Y6!48)) = sum(n6, n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13242, 13210])).
% 5.85/5.83 tff(13296,plain,
% 5.85/5.83 (sum(pred(X6!49), succ(Y6!48)) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13295, 52])).
% 5.85/5.83 tff(13297,plain,
% 5.85/5.83 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n3, n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13296, 13294])).
% 5.85/5.83 tff(13298,plain,
% 5.85/5.83 (X7!47 = Y7!46),
% 5.85/5.83 inference(transitivity,[status(thm)],[785, 13297, 51, 11259, 13292, 794])).
% 5.85/5.83 tff(13299,plain,
% 5.85/5.83 ($false),
% 5.85/5.83 inference(unit_resolution,[status(thm)],[792, 13298])).
% 5.85/5.83 tff(13300,plain,((~(Y0!60 = n5)) | (X7!47 = Y7!46) | (~(X0!61 = n4))), inference(lemma,lemma(discharge,[]))).
% 5.85/5.83 tff(13301,plain,
% 5.85/5.83 (~(Y0!60 = n5)),
% 5.85/5.83 inference(unit_resolution,[status(thm)],[13300, 11930, 792])).
% 5.85/5.83 tff(13302,plain,
% 5.85/5.83 (sum(n5, n1) = n6),
% 5.85/5.83 inference(and_elim,[status(thm)],[9])).
% 5.85/5.83 tff(13303,plain,
% 5.85/5.83 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n5, n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[11954, 1622])).
% 5.85/5.83 tff(13304,plain,
% 5.85/5.83 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13303, 13302])).
% 5.85/5.83 tff(13305,plain,
% 5.85/5.83 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n3, n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[11980, 13304])).
% 5.85/5.83 tff(13306,plain,
% 5.85/5.83 (Y1!58 = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[196, 13305, 12696])).
% 5.85/5.83 tff(13307,plain,
% 5.85/5.83 (pred(Y1!58) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13306])).
% 5.85/5.83 tff(13308,plain,
% 5.85/5.83 (pred(Y1!58) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13307, 20])).
% 5.85/5.83 tff(13309,plain,
% 5.85/5.83 (pred(pred(Y1!58)) = pred(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13308])).
% 5.85/5.83 tff(13310,plain,
% 5.85/5.83 (pred(pred(Y1!58)) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13309, 19])).
% 5.85/5.83 tff(13311,plain,
% 5.85/5.83 (pred(pred(pred(Y1!58))) = pred(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13310])).
% 5.85/5.83 tff(13312,plain,
% 5.85/5.83 (pred(pred(pred(Y1!58))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13311, 18])).
% 5.85/5.83 tff(13313,plain,
% 5.85/5.83 (pred(pred(pred(pred(Y1!58)))) = pred(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13312])).
% 5.85/5.83 tff(13314,plain,
% 5.85/5.83 (pred(pred(pred(pred(Y1!58)))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13313, 17])).
% 5.85/5.83 tff(13315,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13314])).
% 5.85/5.83 tff(13316,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(Y1!58))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13315, 16])).
% 5.85/5.83 tff(13317,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13316])).
% 5.85/5.83 tff(13318,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13317, 15])).
% 5.85/5.83 tff(13319,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13318])).
% 5.85/5.83 tff(13320,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13319, 25])).
% 5.85/5.83 tff(13321,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13320])).
% 5.85/5.83 tff(13322,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13321, 24])).
% 5.85/5.83 tff(13323,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13322])).
% 5.85/5.83 tff(13324,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13323, 23])).
% 5.85/5.83 tff(13325,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13324])).
% 5.85/5.83 tff(13326,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13325, 22])).
% 5.85/5.83 tff(13327,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13326])).
% 5.85/5.83 tff(13328,plain,
% 5.85/5.83 (NPY1!34 = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[232, 13327, 21])).
% 5.85/5.83 tff(13329,plain,
% 5.85/5.83 (succ(NPY1!34) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13328])).
% 5.85/5.83 tff(13330,plain,
% 5.85/5.83 (succ(NPY1!34) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13329, 28])).
% 5.85/5.83 tff(13331,plain,
% 5.85/5.83 (succ(Y1!58) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13306])).
% 5.85/5.83 tff(13332,plain,
% 5.85/5.83 (succ(Y1!58) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13331, 28])).
% 5.85/5.83 tff(13333,plain,
% 5.85/5.83 (succ(succ(Y1!58)) = succ(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13332])).
% 5.85/5.83 tff(13334,plain,
% 5.85/5.83 (succ(succ(Y1!58)) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13333, 42])).
% 5.85/5.83 tff(13335,plain,
% 5.85/5.83 (succ(succ(succ(Y1!58))) = succ(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13334])).
% 5.85/5.83 tff(13336,plain,
% 5.85/5.83 (succ(succ(succ(Y1!58))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13335, 58])).
% 5.85/5.83 tff(13337,plain,
% 5.85/5.83 (succ(succ(succ(succ(Y1!58)))) = succ(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13336])).
% 5.85/5.83 tff(13338,plain,
% 5.85/5.83 (succ(succ(succ(succ(Y1!58)))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13337, 36])).
% 5.85/5.83 tff(13339,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13338])).
% 5.85/5.83 tff(13340,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(Y1!58))))) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13339, 48])).
% 5.85/5.83 tff(13341,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13340])).
% 5.85/5.83 tff(13342,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13341, 14])).
% 5.85/5.83 tff(13343,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13342])).
% 5.85/5.83 tff(13344,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13343, 33])).
% 5.85/5.83 tff(13345,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13344])).
% 5.85/5.83 tff(13346,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13345, 30])).
% 5.85/5.83 tff(13347,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13346])).
% 5.85/5.83 tff(13348,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13347, 39])).
% 5.85/5.83 tff(13349,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13348])).
% 5.85/5.83 tff(13350,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13349, 53])).
% 5.85/5.83 tff(13351,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13350])).
% 5.85/5.83 tff(13352,plain,
% 5.85/5.83 (NSY1!32 = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[255, 13351, 45])).
% 5.85/5.83 tff(13353,plain,
% 5.85/5.83 (pred(NSY1!32) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13352])).
% 5.85/5.83 tff(13354,plain,
% 5.85/5.83 (pred(NSY1!32) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13353, 20])).
% 5.85/5.83 tff(13355,plain,
% 5.85/5.83 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n8, n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13354, 13330])).
% 5.85/5.83 tff(13356,plain,
% 5.85/5.83 (sum(pred(NSY1!32), succ(NPY1!34)) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13355, 27])).
% 5.85/5.83 tff(13357,plain,
% 5.85/5.83 (sum(pred(Y0!60), succ(X0!61)) = sum(n5, n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[1574, 11958])).
% 5.85/5.83 tff(13358,plain,
% 5.85/5.83 (sum(pred(Y0!60), succ(X0!61)) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13357, 43])).
% 5.85/5.83 tff(13359,plain,
% 5.85/5.83 (sum(pred(X0!61), succ(Y0!60)) = sum(n3, n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[11932, 1598])).
% 5.85/5.83 tff(13360,plain,
% 5.85/5.83 (sum(pred(X0!61), succ(Y0!60)) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13359, 953])).
% 5.85/5.83 tff(13361,plain,
% 5.85/5.83 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n10, n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13360, 13358])).
% 5.85/5.83 tff(13362,plain,
% 5.85/5.83 (X1!59 = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[93, 13361, 29])).
% 5.85/5.83 tff(13363,plain,
% 5.85/5.83 (pred(X1!59) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13362])).
% 5.85/5.83 tff(13364,plain,
% 5.85/5.83 (pred(X1!59) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13363, 20])).
% 5.85/5.83 tff(13365,plain,
% 5.85/5.83 (pred(pred(X1!59)) = pred(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13364])).
% 5.85/5.83 tff(13366,plain,
% 5.85/5.83 (pred(pred(X1!59)) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13365, 19])).
% 5.85/5.83 tff(13367,plain,
% 5.85/5.83 (pred(pred(pred(X1!59))) = pred(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13366])).
% 5.85/5.83 tff(13368,plain,
% 5.85/5.83 (pred(pred(pred(X1!59))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13367, 18])).
% 5.85/5.83 tff(13369,plain,
% 5.85/5.83 (pred(pred(pred(pred(X1!59)))) = pred(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13368])).
% 5.85/5.83 tff(13370,plain,
% 5.85/5.83 (pred(pred(pred(pred(X1!59)))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13369, 17])).
% 5.85/5.83 tff(13371,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(X1!59))))) = pred(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13370])).
% 5.85/5.83 tff(13372,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(X1!59))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13371, 16])).
% 5.85/5.83 tff(13373,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13372])).
% 5.85/5.83 tff(13374,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13373, 15])).
% 5.85/5.83 tff(13375,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13374])).
% 5.85/5.83 tff(13376,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13375, 25])).
% 5.85/5.83 tff(13377,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13376])).
% 5.85/5.83 tff(13378,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13377, 24])).
% 5.85/5.83 tff(13379,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13378])).
% 5.85/5.83 tff(13380,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13379, 23])).
% 5.85/5.83 tff(13381,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13380])).
% 5.85/5.83 tff(13382,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13381, 22])).
% 5.85/5.83 tff(13383,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13382])).
% 5.85/5.83 tff(13384,plain,
% 5.85/5.83 (NPX1!35 = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[280, 13383, 21])).
% 5.85/5.83 tff(13385,plain,
% 5.85/5.83 (succ(NPX1!35) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13384])).
% 5.85/5.83 tff(13386,plain,
% 5.85/5.83 (succ(NPX1!35) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13385, 28])).
% 5.85/5.83 tff(13387,plain,
% 5.85/5.83 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n10, n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13386, 13356])).
% 5.85/5.83 tff(13388,plain,
% 5.85/5.83 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13387, 69])).
% 5.85/5.83 tff(13389,plain,
% 5.85/5.83 (succ(X1!59) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13362])).
% 5.85/5.83 tff(13390,plain,
% 5.85/5.83 (succ(X1!59) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13389, 28])).
% 5.85/5.83 tff(13391,plain,
% 5.85/5.83 (succ(succ(X1!59)) = succ(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13390])).
% 5.85/5.83 tff(13392,plain,
% 5.85/5.83 (succ(succ(X1!59)) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13391, 42])).
% 5.85/5.83 tff(13393,plain,
% 5.85/5.83 (succ(succ(succ(X1!59))) = succ(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13392])).
% 5.85/5.83 tff(13394,plain,
% 5.85/5.83 (succ(succ(succ(X1!59))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13393, 58])).
% 5.85/5.83 tff(13395,plain,
% 5.85/5.83 (succ(succ(succ(succ(X1!59)))) = succ(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13394])).
% 5.85/5.83 tff(13396,plain,
% 5.85/5.83 (succ(succ(succ(succ(X1!59)))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13395, 36])).
% 5.85/5.83 tff(13397,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(X1!59))))) = succ(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13396])).
% 5.85/5.83 tff(13398,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(X1!59))))) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13397, 48])).
% 5.85/5.83 tff(13399,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13398])).
% 5.85/5.83 tff(13400,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13399, 14])).
% 5.85/5.83 tff(13401,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13400])).
% 5.85/5.83 tff(13402,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13401, 33])).
% 5.85/5.83 tff(13403,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13402])).
% 5.85/5.83 tff(13404,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13403, 30])).
% 5.85/5.83 tff(13405,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13404])).
% 5.85/5.83 tff(13406,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13405, 39])).
% 5.85/5.83 tff(13407,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13406])).
% 5.85/5.83 tff(13408,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13407, 53])).
% 5.85/5.83 tff(13409,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13408])).
% 5.85/5.83 tff(13410,plain,
% 5.85/5.83 (NSX1!33 = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[305, 13409, 45])).
% 5.85/5.83 tff(13411,plain,
% 5.85/5.83 (pred(NSX1!33) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13410])).
% 5.85/5.83 tff(13412,plain,
% 5.85/5.83 (pred(NSX1!33) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13411, 20])).
% 5.85/5.83 tff(13413,plain,
% 5.85/5.83 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n8, n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13412, 13388])).
% 5.85/5.83 tff(13414,plain,
% 5.85/5.83 (Y2!56 = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[310, 13413, 98])).
% 5.85/5.83 tff(13415,plain,
% 5.85/5.83 (pred(Y2!56) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13414])).
% 5.85/5.83 tff(13416,plain,
% 5.85/5.83 (pred(Y2!56) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13415, 25])).
% 5.85/5.83 tff(13417,plain,
% 5.85/5.83 (pred(pred(Y2!56)) = pred(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13416])).
% 5.85/5.83 tff(13418,plain,
% 5.85/5.83 (pred(pred(Y2!56)) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13417, 24])).
% 5.85/5.83 tff(13419,plain,
% 5.85/5.83 (pred(pred(pred(Y2!56))) = pred(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13418])).
% 5.85/5.83 tff(13420,plain,
% 5.85/5.83 (pred(pred(pred(Y2!56))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13419, 23])).
% 5.85/5.83 tff(13421,plain,
% 5.85/5.83 (pred(pred(pred(pred(Y2!56)))) = pred(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13420])).
% 5.85/5.83 tff(13422,plain,
% 5.85/5.83 (pred(pred(pred(pred(Y2!56)))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13421, 22])).
% 5.85/5.83 tff(13423,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13422])).
% 5.85/5.83 tff(13424,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(Y2!56))))) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13423, 21])).
% 5.85/5.83 tff(13425,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13424])).
% 5.85/5.83 tff(13426,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13425, 20])).
% 5.85/5.83 tff(13427,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13426])).
% 5.85/5.83 tff(13428,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13427, 19])).
% 5.85/5.83 tff(13429,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13428])).
% 5.85/5.83 tff(13430,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13429, 18])).
% 5.85/5.83 tff(13431,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13430])).
% 5.85/5.83 tff(13432,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13431, 17])).
% 5.85/5.83 tff(13433,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13432])).
% 5.85/5.83 tff(13434,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13433, 16])).
% 5.85/5.83 tff(13435,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13434])).
% 5.85/5.83 tff(13436,plain,
% 5.85/5.83 (NPY2!30 = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[347, 13435, 15])).
% 5.85/5.83 tff(13437,plain,
% 5.85/5.83 (succ(NPY2!30) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13436])).
% 5.85/5.83 tff(13438,plain,
% 5.85/5.83 (succ(NPY2!30) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13437, 14])).
% 5.85/5.83 tff(13439,plain,
% 5.85/5.83 (succ(Y2!56) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13414])).
% 5.85/5.83 tff(13440,plain,
% 5.85/5.83 (succ(Y2!56) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13439, 14])).
% 5.85/5.83 tff(13441,plain,
% 5.85/5.83 (succ(succ(Y2!56)) = succ(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13440])).
% 5.85/5.83 tff(13442,plain,
% 5.85/5.83 (succ(succ(Y2!56)) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13441, 33])).
% 5.85/5.83 tff(13443,plain,
% 5.85/5.83 (succ(succ(succ(Y2!56))) = succ(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13442])).
% 5.85/5.83 tff(13444,plain,
% 5.85/5.83 (succ(succ(succ(Y2!56))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13443, 30])).
% 5.85/5.83 tff(13445,plain,
% 5.85/5.83 (succ(succ(succ(succ(Y2!56)))) = succ(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13444])).
% 5.85/5.83 tff(13446,plain,
% 5.85/5.83 (succ(succ(succ(succ(Y2!56)))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13445, 39])).
% 5.85/5.83 tff(13447,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13446])).
% 5.85/5.83 tff(13448,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(Y2!56))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13447, 53])).
% 5.85/5.83 tff(13449,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13448])).
% 5.85/5.83 tff(13450,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13449, 45])).
% 5.85/5.83 tff(13451,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13450])).
% 5.85/5.83 tff(13452,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13451, 28])).
% 5.85/5.83 tff(13453,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13452])).
% 5.85/5.83 tff(13454,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13453, 42])).
% 5.85/5.83 tff(13455,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13454])).
% 5.85/5.83 tff(13456,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13455, 58])).
% 5.85/5.83 tff(13457,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13456])).
% 5.85/5.83 tff(13458,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13457, 36])).
% 5.85/5.83 tff(13459,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13458])).
% 5.85/5.83 tff(13460,plain,
% 5.85/5.83 (NSY2!28 = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[370, 13459, 48])).
% 5.85/5.83 tff(13461,plain,
% 5.85/5.83 (pred(NSY2!28) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13460])).
% 5.85/5.83 tff(13462,plain,
% 5.85/5.83 (pred(NSY2!28) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13461, 25])).
% 5.85/5.83 tff(13463,plain,
% 5.85/5.83 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n2, n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13462, 13438])).
% 5.85/5.83 tff(13464,plain,
% 5.85/5.83 (sum(pred(NSY2!28), succ(NPY2!30)) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13463, 13])).
% 5.85/5.83 tff(13465,plain,
% 5.85/5.83 (sum(pred(Y1!58), succ(X1!59)) = sum(n8, n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13308, 13390])).
% 5.85/5.83 tff(13466,plain,
% 5.85/5.83 (sum(pred(Y1!58), succ(X1!59)) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13465, 27])).
% 5.85/5.83 tff(13467,plain,
% 5.85/5.83 (sum(pred(X1!59), succ(Y1!58)) = sum(n8, n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13364, 13332])).
% 5.85/5.83 tff(13468,plain,
% 5.85/5.83 (sum(pred(X1!59), succ(Y1!58)) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13467, 27])).
% 5.85/5.83 tff(13469,plain,
% 5.85/5.83 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n7, n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13468, 13466])).
% 5.85/5.83 tff(13470,plain,
% 5.85/5.83 (X2!57 = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[209, 13469, 26])).
% 5.85/5.83 tff(13471,plain,
% 5.85/5.83 (pred(X2!57) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13470])).
% 5.85/5.83 tff(13472,plain,
% 5.85/5.83 (pred(X2!57) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13471, 25])).
% 5.85/5.83 tff(13473,plain,
% 5.85/5.83 (pred(pred(X2!57)) = pred(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13472])).
% 5.85/5.83 tff(13474,plain,
% 5.85/5.83 (pred(pred(X2!57)) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13473, 24])).
% 5.85/5.83 tff(13475,plain,
% 5.85/5.83 (pred(pred(pred(X2!57))) = pred(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13474])).
% 5.85/5.83 tff(13476,plain,
% 5.85/5.83 (pred(pred(pred(X2!57))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13475, 23])).
% 5.85/5.83 tff(13477,plain,
% 5.85/5.83 (pred(pred(pred(pred(X2!57)))) = pred(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13476])).
% 5.85/5.83 tff(13478,plain,
% 5.85/5.83 (pred(pred(pred(pred(X2!57)))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13477, 22])).
% 5.85/5.83 tff(13479,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(X2!57))))) = pred(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13478])).
% 5.85/5.83 tff(13480,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(X2!57))))) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13479, 21])).
% 5.85/5.83 tff(13481,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13480])).
% 5.85/5.83 tff(13482,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13481, 20])).
% 5.85/5.83 tff(13483,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13482])).
% 5.85/5.83 tff(13484,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13483, 19])).
% 5.85/5.83 tff(13485,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13484])).
% 5.85/5.83 tff(13486,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13485, 18])).
% 5.85/5.83 tff(13487,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13486])).
% 5.85/5.83 tff(13488,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13487, 17])).
% 5.85/5.83 tff(13489,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13488])).
% 5.85/5.83 tff(13490,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13489, 16])).
% 5.85/5.83 tff(13491,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13490])).
% 5.85/5.83 tff(13492,plain,
% 5.85/5.83 (NPX2!31 = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[395, 13491, 15])).
% 5.85/5.83 tff(13493,plain,
% 5.85/5.83 (succ(NPX2!31) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13492])).
% 5.85/5.83 tff(13494,plain,
% 5.85/5.83 (succ(NPX2!31) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13493, 14])).
% 5.85/5.83 tff(13495,plain,
% 5.85/5.83 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n4, n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13494, 13464])).
% 5.85/5.83 tff(13496,plain,
% 5.85/5.83 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13495, 12])).
% 5.85/5.83 tff(13497,plain,
% 5.85/5.83 (succ(X2!57) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13470])).
% 5.85/5.83 tff(13498,plain,
% 5.85/5.83 (succ(X2!57) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13497, 14])).
% 5.85/5.83 tff(13499,plain,
% 5.85/5.83 (succ(succ(X2!57)) = succ(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13498])).
% 5.85/5.83 tff(13500,plain,
% 5.85/5.83 (succ(succ(X2!57)) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13499, 33])).
% 5.85/5.83 tff(13501,plain,
% 5.85/5.83 (succ(succ(succ(X2!57))) = succ(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13500])).
% 5.85/5.83 tff(13502,plain,
% 5.85/5.83 (succ(succ(succ(X2!57))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13501, 30])).
% 5.85/5.83 tff(13503,plain,
% 5.85/5.83 (succ(succ(succ(succ(X2!57)))) = succ(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13502])).
% 5.85/5.83 tff(13504,plain,
% 5.85/5.83 (succ(succ(succ(succ(X2!57)))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13503, 39])).
% 5.85/5.83 tff(13505,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(X2!57))))) = succ(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13504])).
% 5.85/5.83 tff(13506,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(X2!57))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13505, 53])).
% 5.85/5.83 tff(13507,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13506])).
% 5.85/5.83 tff(13508,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13507, 45])).
% 5.85/5.83 tff(13509,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13508])).
% 5.85/5.83 tff(13510,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13509, 28])).
% 5.85/5.83 tff(13511,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13510])).
% 5.85/5.83 tff(13512,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13511, 42])).
% 5.85/5.83 tff(13513,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13512])).
% 5.85/5.83 tff(13514,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[13513, 58])).
% 5.85/5.83 tff(13515,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13514])).
% 5.85/5.83 tff(13516,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13515, 36])).
% 5.85/5.83 tff(13517,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13516])).
% 5.85/5.83 tff(13518,plain,
% 5.85/5.83 (NSX2!29 = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[420, 13517, 48])).
% 5.85/5.83 tff(13519,plain,
% 5.85/5.83 (pred(NSX2!29) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13518])).
% 5.85/5.83 tff(13520,plain,
% 5.85/5.83 (pred(NSX2!29) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13519, 25])).
% 5.85/5.83 tff(13521,plain,
% 5.85/5.83 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n2, n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13520, 13496])).
% 5.85/5.83 tff(13522,plain,
% 5.85/5.83 (Y3!54 = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[425, 13521, 327])).
% 5.85/5.83 tff(13523,plain,
% 5.85/5.83 (pred(Y3!54) = pred(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13522])).
% 5.85/5.83 tff(13524,plain,
% 5.85/5.83 (pred(Y3!54) = n0),
% 5.85/5.83 inference(transitivity,[status(thm)],[13523, 23])).
% 5.85/5.83 tff(13525,plain,
% 5.85/5.83 (pred(pred(Y3!54)) = pred(n0)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13524])).
% 5.85/5.83 tff(13526,plain,
% 5.85/5.83 (pred(pred(Y3!54)) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13525, 22])).
% 5.85/5.83 tff(13527,plain,
% 5.85/5.83 (pred(pred(pred(Y3!54))) = pred(n10)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13526])).
% 5.85/5.83 tff(13528,plain,
% 5.85/5.83 (pred(pred(pred(Y3!54))) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13527, 21])).
% 5.85/5.83 tff(13529,plain,
% 5.85/5.83 (pred(pred(pred(pred(Y3!54)))) = pred(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13528])).
% 5.85/5.83 tff(13530,plain,
% 5.85/5.83 (pred(pred(pred(pred(Y3!54)))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13529, 20])).
% 5.85/5.83 tff(13531,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13530])).
% 5.85/5.83 tff(13532,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(Y3!54))))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13531, 19])).
% 5.85/5.83 tff(13533,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13532])).
% 5.85/5.83 tff(13534,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13533, 18])).
% 5.85/5.83 tff(13535,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13534])).
% 5.85/5.83 tff(13536,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13535, 17])).
% 5.85/5.83 tff(13537,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13536])).
% 5.85/5.83 tff(13538,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13537, 16])).
% 5.85/5.83 tff(13539,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13538])).
% 5.85/5.83 tff(13540,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13539, 15])).
% 5.85/5.83 tff(13541,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13540])).
% 5.85/5.83 tff(13542,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13541, 25])).
% 5.85/5.83 tff(13543,plain,
% 5.85/5.83 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13542])).
% 5.85/5.83 tff(13544,plain,
% 5.85/5.83 (NPY3!26 = n1),
% 5.85/5.83 inference(transitivity,[status(thm)],[462, 13543, 24])).
% 5.85/5.83 tff(13545,plain,
% 5.85/5.83 (succ(NPY3!26) = succ(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13544])).
% 5.85/5.83 tff(13546,plain,
% 5.85/5.83 (succ(NPY3!26) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13545, 36])).
% 5.85/5.83 tff(13547,plain,
% 5.85/5.83 (succ(Y3!54) = succ(n1)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13522])).
% 5.85/5.83 tff(13548,plain,
% 5.85/5.83 (succ(Y3!54) = n2),
% 5.85/5.83 inference(transitivity,[status(thm)],[13547, 36])).
% 5.85/5.83 tff(13549,plain,
% 5.85/5.83 (succ(succ(Y3!54)) = succ(n2)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13548])).
% 5.85/5.83 tff(13550,plain,
% 5.85/5.83 (succ(succ(Y3!54)) = n3),
% 5.85/5.83 inference(transitivity,[status(thm)],[13549, 48])).
% 5.85/5.83 tff(13551,plain,
% 5.85/5.83 (succ(succ(succ(Y3!54))) = succ(n3)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13550])).
% 5.85/5.83 tff(13552,plain,
% 5.85/5.83 (succ(succ(succ(Y3!54))) = n4),
% 5.85/5.83 inference(transitivity,[status(thm)],[13551, 14])).
% 5.85/5.83 tff(13553,plain,
% 5.85/5.83 (succ(succ(succ(succ(Y3!54)))) = succ(n4)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13552])).
% 5.85/5.83 tff(13554,plain,
% 5.85/5.83 (succ(succ(succ(succ(Y3!54)))) = n5),
% 5.85/5.83 inference(transitivity,[status(thm)],[13553, 33])).
% 5.85/5.83 tff(13555,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n5)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13554])).
% 5.85/5.83 tff(13556,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(Y3!54))))) = n6),
% 5.85/5.83 inference(transitivity,[status(thm)],[13555, 30])).
% 5.85/5.83 tff(13557,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n6)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13556])).
% 5.85/5.83 tff(13558,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n7),
% 5.85/5.83 inference(transitivity,[status(thm)],[13557, 39])).
% 5.85/5.83 tff(13559,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n7)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13558])).
% 5.85/5.83 tff(13560,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n8),
% 5.85/5.83 inference(transitivity,[status(thm)],[13559, 53])).
% 5.85/5.83 tff(13561,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n8)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13560])).
% 5.85/5.83 tff(13562,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n9),
% 5.85/5.83 inference(transitivity,[status(thm)],[13561, 45])).
% 5.85/5.83 tff(13563,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n9)),
% 5.85/5.83 inference(monotonicity,[status(thm)],[13562])).
% 5.85/5.83 tff(13564,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n10),
% 5.85/5.83 inference(transitivity,[status(thm)],[13563, 28])).
% 5.85/5.83 tff(13565,plain,
% 5.85/5.83 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13564])).
% 5.85/5.84 tff(13566,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13565, 42])).
% 5.85/5.84 tff(13567,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13566])).
% 5.85/5.84 tff(13568,plain,
% 5.85/5.84 (NSY3!24 = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[485, 13567, 58])).
% 5.85/5.84 tff(13569,plain,
% 5.85/5.84 (pred(NSY3!24) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13568])).
% 5.85/5.84 tff(13570,plain,
% 5.85/5.84 (pred(NSY3!24) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13569, 23])).
% 5.85/5.84 tff(13571,plain,
% 5.85/5.84 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n0, n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13570, 13546])).
% 5.85/5.84 tff(13572,plain,
% 5.85/5.84 (sum(pred(NSY3!24), succ(NPY3!26)) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13571, 35])).
% 5.85/5.84 tff(13573,plain,
% 5.85/5.84 (sum(pred(Y2!56), succ(X2!57)) = sum(n2, n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13416, 13498])).
% 5.85/5.84 tff(13574,plain,
% 5.85/5.84 (sum(pred(Y2!56), succ(X2!57)) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13573, 13])).
% 5.85/5.84 tff(13575,plain,
% 5.85/5.84 (sum(pred(X2!57), succ(Y2!56)) = sum(n2, n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13472, 13440])).
% 5.85/5.84 tff(13576,plain,
% 5.85/5.84 (sum(pred(X2!57), succ(Y2!56)) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13575, 13])).
% 5.85/5.84 tff(13577,plain,
% 5.85/5.84 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n6, n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13576, 13574])).
% 5.85/5.84 tff(13578,plain,
% 5.85/5.84 (X3!55 = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[323, 13577, 37])).
% 5.85/5.84 tff(13579,plain,
% 5.85/5.84 (pred(X3!55) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13578])).
% 5.85/5.84 tff(13580,plain,
% 5.85/5.84 (pred(X3!55) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13579, 23])).
% 5.85/5.84 tff(13581,plain,
% 5.85/5.84 (pred(pred(X3!55)) = pred(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13580])).
% 5.85/5.84 tff(13582,plain,
% 5.85/5.84 (pred(pred(X3!55)) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13581, 22])).
% 5.85/5.84 tff(13583,plain,
% 5.85/5.84 (pred(pred(pred(X3!55))) = pred(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13582])).
% 5.85/5.84 tff(13584,plain,
% 5.85/5.84 (pred(pred(pred(X3!55))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13583, 21])).
% 5.85/5.84 tff(13585,plain,
% 5.85/5.84 (pred(pred(pred(pred(X3!55)))) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13584])).
% 5.85/5.84 tff(13586,plain,
% 5.85/5.84 (pred(pred(pred(pred(X3!55)))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13585, 20])).
% 5.85/5.84 tff(13587,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X3!55))))) = pred(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13586])).
% 5.85/5.84 tff(13588,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X3!55))))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13587, 19])).
% 5.85/5.84 tff(13589,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13588])).
% 5.85/5.84 tff(13590,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13589, 18])).
% 5.85/5.84 tff(13591,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13590])).
% 5.85/5.84 tff(13592,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13591, 17])).
% 5.85/5.84 tff(13593,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13592])).
% 5.85/5.84 tff(13594,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13593, 16])).
% 5.85/5.84 tff(13595,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13594])).
% 5.85/5.84 tff(13596,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13595, 15])).
% 5.85/5.84 tff(13597,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13596])).
% 5.85/5.84 tff(13598,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13597, 25])).
% 5.85/5.84 tff(13599,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13598])).
% 5.85/5.84 tff(13600,plain,
% 5.85/5.84 (NPX3!27 = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[510, 13599, 24])).
% 5.85/5.84 tff(13601,plain,
% 5.85/5.84 (succ(NPX3!27) = succ(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13600])).
% 5.85/5.84 tff(13602,plain,
% 5.85/5.84 (succ(NPX3!27) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13601, 36])).
% 5.85/5.84 tff(13603,plain,
% 5.85/5.84 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n2, n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13602, 13572])).
% 5.85/5.84 tff(13604,plain,
% 5.85/5.84 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13603, 34])).
% 5.85/5.84 tff(13605,plain,
% 5.85/5.84 (succ(X3!55) = succ(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13578])).
% 5.85/5.84 tff(13606,plain,
% 5.85/5.84 (succ(X3!55) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13605, 36])).
% 5.85/5.84 tff(13607,plain,
% 5.85/5.84 (succ(succ(X3!55)) = succ(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13606])).
% 5.85/5.84 tff(13608,plain,
% 5.85/5.84 (succ(succ(X3!55)) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13607, 48])).
% 5.85/5.84 tff(13609,plain,
% 5.85/5.84 (succ(succ(succ(X3!55))) = succ(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13608])).
% 5.85/5.84 tff(13610,plain,
% 5.85/5.84 (succ(succ(succ(X3!55))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13609, 14])).
% 5.85/5.84 tff(13611,plain,
% 5.85/5.84 (succ(succ(succ(succ(X3!55)))) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13610])).
% 5.85/5.84 tff(13612,plain,
% 5.85/5.84 (succ(succ(succ(succ(X3!55)))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13611, 33])).
% 5.85/5.84 tff(13613,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(X3!55))))) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13612])).
% 5.85/5.84 tff(13614,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(X3!55))))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13613, 30])).
% 5.85/5.84 tff(13615,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13614])).
% 5.85/5.84 tff(13616,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13615, 39])).
% 5.85/5.84 tff(13617,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13616])).
% 5.85/5.84 tff(13618,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13617, 53])).
% 5.85/5.84 tff(13619,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13618])).
% 5.85/5.84 tff(13620,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13619, 45])).
% 5.85/5.84 tff(13621,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13620])).
% 5.85/5.84 tff(13622,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13621, 28])).
% 5.85/5.84 tff(13623,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13622])).
% 5.85/5.84 tff(13624,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13623, 42])).
% 5.85/5.84 tff(13625,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13624])).
% 5.85/5.84 tff(13626,plain,
% 5.85/5.84 (NSX3!25 = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[535, 13625, 58])).
% 5.85/5.84 tff(13627,plain,
% 5.85/5.84 (pred(NSX3!25) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13626])).
% 5.85/5.84 tff(13628,plain,
% 5.85/5.84 (pred(NSX3!25) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13627, 23])).
% 5.85/5.84 tff(13629,plain,
% 5.85/5.84 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n0, n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13628, 13604])).
% 5.85/5.84 tff(13630,plain,
% 5.85/5.84 (Y4!52 = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[540, 13629, 442])).
% 5.85/5.84 tff(13631,plain,
% 5.85/5.84 (pred(Y4!52) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13630])).
% 5.85/5.84 tff(13632,plain,
% 5.85/5.84 (pred(Y4!52) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13631, 15])).
% 5.85/5.84 tff(13633,plain,
% 5.85/5.84 (pred(pred(Y4!52)) = pred(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13632])).
% 5.85/5.84 tff(13634,plain,
% 5.85/5.84 (pred(pred(Y4!52)) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13633, 25])).
% 5.85/5.84 tff(13635,plain,
% 5.85/5.84 (pred(pred(pred(Y4!52))) = pred(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13634])).
% 5.85/5.84 tff(13636,plain,
% 5.85/5.84 (pred(pred(pred(Y4!52))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13635, 24])).
% 5.85/5.84 tff(13637,plain,
% 5.85/5.84 (pred(pred(pred(pred(Y4!52)))) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13636])).
% 5.85/5.84 tff(13638,plain,
% 5.85/5.84 (pred(pred(pred(pred(Y4!52)))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13637, 23])).
% 5.85/5.84 tff(13639,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13638])).
% 5.85/5.84 tff(13640,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(Y4!52))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13639, 22])).
% 5.85/5.84 tff(13641,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13640])).
% 5.85/5.84 tff(13642,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13641, 21])).
% 5.85/5.84 tff(13643,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13642])).
% 5.85/5.84 tff(13644,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13643, 20])).
% 5.85/5.84 tff(13645,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13644])).
% 5.85/5.84 tff(13646,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13645, 19])).
% 5.85/5.84 tff(13647,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13646])).
% 5.85/5.84 tff(13648,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13647, 18])).
% 5.85/5.84 tff(13649,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13648])).
% 5.85/5.84 tff(13650,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13649, 17])).
% 5.85/5.84 tff(13651,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13650])).
% 5.85/5.84 tff(13652,plain,
% 5.85/5.84 (NPY4!22 = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[578, 13651, 16])).
% 5.85/5.84 tff(13653,plain,
% 5.85/5.84 (succ(NPY4!22) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13652])).
% 5.85/5.84 tff(13654,plain,
% 5.85/5.84 (succ(NPY4!22) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13653, 33])).
% 5.85/5.84 tff(13655,plain,
% 5.85/5.84 (succ(Y4!52) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13630])).
% 5.85/5.84 tff(13656,plain,
% 5.85/5.84 (succ(Y4!52) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13655, 33])).
% 5.85/5.84 tff(13657,plain,
% 5.85/5.84 (succ(succ(Y4!52)) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13656])).
% 5.85/5.84 tff(13658,plain,
% 5.85/5.84 (succ(succ(Y4!52)) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13657, 30])).
% 5.85/5.84 tff(13659,plain,
% 5.85/5.84 (succ(succ(succ(Y4!52))) = succ(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13658])).
% 5.85/5.84 tff(13660,plain,
% 5.85/5.84 (succ(succ(succ(Y4!52))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13659, 39])).
% 5.85/5.84 tff(13661,plain,
% 5.85/5.84 (succ(succ(succ(succ(Y4!52)))) = succ(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13660])).
% 5.85/5.84 tff(13662,plain,
% 5.85/5.84 (succ(succ(succ(succ(Y4!52)))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13661, 53])).
% 5.85/5.84 tff(13663,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13662])).
% 5.85/5.84 tff(13664,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(Y4!52))))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13663, 45])).
% 5.85/5.84 tff(13665,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13664])).
% 5.85/5.84 tff(13666,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13665, 28])).
% 5.85/5.84 tff(13667,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13666])).
% 5.85/5.84 tff(13668,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13667, 42])).
% 5.85/5.84 tff(13669,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13668])).
% 5.85/5.84 tff(13670,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13669, 58])).
% 5.85/5.84 tff(13671,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13670])).
% 5.85/5.84 tff(13672,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13671, 36])).
% 5.85/5.84 tff(13673,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13672])).
% 5.85/5.84 tff(13674,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13673, 48])).
% 5.85/5.84 tff(13675,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13674])).
% 5.85/5.84 tff(13676,plain,
% 5.85/5.84 (NSY4!20 = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[601, 13675, 14])).
% 5.85/5.84 tff(13677,plain,
% 5.85/5.84 (pred(NSY4!20) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13676])).
% 5.85/5.84 tff(13678,plain,
% 5.85/5.84 (pred(NSY4!20) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13677, 15])).
% 5.85/5.84 tff(13679,plain,
% 5.85/5.84 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n3, n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13678, 13654])).
% 5.85/5.84 tff(13680,plain,
% 5.85/5.84 (sum(pred(NSY4!20), succ(NPY4!22)) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13679, 32])).
% 5.85/5.84 tff(13681,plain,
% 5.85/5.84 (sum(pred(Y3!54), succ(X3!55)) = sum(n0, n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13524, 13606])).
% 5.85/5.84 tff(13682,plain,
% 5.85/5.84 (sum(pred(Y3!54), succ(X3!55)) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13681, 35])).
% 5.85/5.84 tff(13683,plain,
% 5.85/5.84 (sum(pred(X3!55), succ(Y3!54)) = sum(n0, n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13580, 13548])).
% 5.85/5.84 tff(13684,plain,
% 5.85/5.84 (sum(pred(X3!55), succ(Y3!54)) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13683, 35])).
% 5.85/5.84 tff(13685,plain,
% 5.85/5.84 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n2, n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13684, 13682])).
% 5.85/5.84 tff(13686,plain,
% 5.85/5.84 (X4!53 = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[438, 13685, 34])).
% 5.85/5.84 tff(13687,plain,
% 5.85/5.84 (pred(X4!53) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13686])).
% 5.85/5.84 tff(13688,plain,
% 5.85/5.84 (pred(X4!53) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13687, 15])).
% 5.85/5.84 tff(13689,plain,
% 5.85/5.84 (pred(pred(X4!53)) = pred(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13688])).
% 5.85/5.84 tff(13690,plain,
% 5.85/5.84 (pred(pred(X4!53)) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13689, 25])).
% 5.85/5.84 tff(13691,plain,
% 5.85/5.84 (pred(pred(pred(X4!53))) = pred(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13690])).
% 5.85/5.84 tff(13692,plain,
% 5.85/5.84 (pred(pred(pred(X4!53))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13691, 24])).
% 5.85/5.84 tff(13693,plain,
% 5.85/5.84 (pred(pred(pred(pred(X4!53)))) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13692])).
% 5.85/5.84 tff(13694,plain,
% 5.85/5.84 (pred(pred(pred(pred(X4!53)))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13693, 23])).
% 5.85/5.84 tff(13695,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X4!53))))) = pred(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13694])).
% 5.85/5.84 tff(13696,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X4!53))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13695, 22])).
% 5.85/5.84 tff(13697,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13696])).
% 5.85/5.84 tff(13698,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13697, 21])).
% 5.85/5.84 tff(13699,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13698])).
% 5.85/5.84 tff(13700,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13699, 20])).
% 5.85/5.84 tff(13701,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13700])).
% 5.85/5.84 tff(13702,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13701, 19])).
% 5.85/5.84 tff(13703,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13702])).
% 5.85/5.84 tff(13704,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13703, 18])).
% 5.85/5.84 tff(13705,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13704])).
% 5.85/5.84 tff(13706,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13705, 17])).
% 5.85/5.84 tff(13707,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13706])).
% 5.85/5.84 tff(13708,plain,
% 5.85/5.84 (NPX4!23 = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[626, 13707, 16])).
% 5.85/5.84 tff(13709,plain,
% 5.85/5.84 (succ(NPX4!23) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13708])).
% 5.85/5.84 tff(13710,plain,
% 5.85/5.84 (succ(NPX4!23) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13709, 33])).
% 5.85/5.84 tff(13711,plain,
% 5.85/5.84 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n5, n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13710, 13680])).
% 5.85/5.84 tff(13712,plain,
% 5.85/5.84 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13711, 558])).
% 5.85/5.84 tff(13713,plain,
% 5.85/5.84 (succ(X4!53) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13686])).
% 5.85/5.84 tff(13714,plain,
% 5.85/5.84 (succ(X4!53) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13713, 33])).
% 5.85/5.84 tff(13715,plain,
% 5.85/5.84 (succ(succ(X4!53)) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13714])).
% 5.85/5.84 tff(13716,plain,
% 5.85/5.84 (succ(succ(X4!53)) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13715, 30])).
% 5.85/5.84 tff(13717,plain,
% 5.85/5.84 (succ(succ(succ(X4!53))) = succ(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13716])).
% 5.85/5.84 tff(13718,plain,
% 5.85/5.84 (succ(succ(succ(X4!53))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13717, 39])).
% 5.85/5.84 tff(13719,plain,
% 5.85/5.84 (succ(succ(succ(succ(X4!53)))) = succ(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13718])).
% 5.85/5.84 tff(13720,plain,
% 5.85/5.84 (succ(succ(succ(succ(X4!53)))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13719, 53])).
% 5.85/5.84 tff(13721,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(X4!53))))) = succ(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13720])).
% 5.85/5.84 tff(13722,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(X4!53))))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13721, 45])).
% 5.85/5.84 tff(13723,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13722])).
% 5.85/5.84 tff(13724,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13723, 28])).
% 5.85/5.84 tff(13725,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13724])).
% 5.85/5.84 tff(13726,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13725, 42])).
% 5.85/5.84 tff(13727,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13726])).
% 5.85/5.84 tff(13728,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13727, 58])).
% 5.85/5.84 tff(13729,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13728])).
% 5.85/5.84 tff(13730,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13729, 36])).
% 5.85/5.84 tff(13731,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13730])).
% 5.85/5.84 tff(13732,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13731, 48])).
% 5.85/5.84 tff(13733,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13732])).
% 5.85/5.84 tff(13734,plain,
% 5.85/5.84 (NSX4!21 = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[651, 13733, 14])).
% 5.85/5.84 tff(13735,plain,
% 5.85/5.84 (pred(NSX4!21) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13734])).
% 5.85/5.84 tff(13736,plain,
% 5.85/5.84 (pred(NSX4!21) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13735, 15])).
% 5.85/5.84 tff(13737,plain,
% 5.85/5.84 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n3, n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13736, 13712])).
% 5.85/5.84 tff(13738,plain,
% 5.85/5.84 (Y5!50 = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[656, 13737, 557])).
% 5.85/5.84 tff(13739,plain,
% 5.85/5.84 (pred(Y5!50) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13738])).
% 5.85/5.84 tff(13740,plain,
% 5.85/5.84 (pred(Y5!50) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13739, 16])).
% 5.85/5.84 tff(13741,plain,
% 5.85/5.84 (pred(pred(Y5!50)) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13740])).
% 5.85/5.84 tff(13742,plain,
% 5.85/5.84 (pred(pred(Y5!50)) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13741, 15])).
% 5.85/5.84 tff(13743,plain,
% 5.85/5.84 (pred(pred(pred(Y5!50))) = pred(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13742])).
% 5.85/5.84 tff(13744,plain,
% 5.85/5.84 (pred(pred(pred(Y5!50))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13743, 25])).
% 5.85/5.84 tff(13745,plain,
% 5.85/5.84 (pred(pred(pred(pred(Y5!50)))) = pred(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13744])).
% 5.85/5.84 tff(13746,plain,
% 5.85/5.84 (pred(pred(pred(pred(Y5!50)))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13745, 24])).
% 5.85/5.84 tff(13747,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13746])).
% 5.85/5.84 tff(13748,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(Y5!50))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13747, 23])).
% 5.85/5.84 tff(13749,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13748])).
% 5.85/5.84 tff(13750,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13749, 22])).
% 5.85/5.84 tff(13751,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13750])).
% 5.85/5.84 tff(13752,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13751, 21])).
% 5.85/5.84 tff(13753,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13752])).
% 5.85/5.84 tff(13754,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13753, 20])).
% 5.85/5.84 tff(13755,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13754])).
% 5.85/5.84 tff(13756,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13755, 19])).
% 5.85/5.84 tff(13757,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13756])).
% 5.85/5.84 tff(13758,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13757, 18])).
% 5.85/5.84 tff(13759,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13758])).
% 5.85/5.84 tff(13760,plain,
% 5.85/5.84 (NPY5!18 = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[694, 13759, 17])).
% 5.85/5.84 tff(13761,plain,
% 5.85/5.84 (succ(NPY5!18) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13760])).
% 5.85/5.84 tff(13762,plain,
% 5.85/5.84 (succ(NPY5!18) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13761, 30])).
% 5.85/5.84 tff(13763,plain,
% 5.85/5.84 (succ(Y5!50) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13738])).
% 5.85/5.84 tff(13764,plain,
% 5.85/5.84 (succ(Y5!50) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13763, 30])).
% 5.85/5.84 tff(13765,plain,
% 5.85/5.84 (succ(succ(Y5!50)) = succ(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13764])).
% 5.85/5.84 tff(13766,plain,
% 5.85/5.84 (succ(succ(Y5!50)) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13765, 39])).
% 5.85/5.84 tff(13767,plain,
% 5.85/5.84 (succ(succ(succ(Y5!50))) = succ(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13766])).
% 5.85/5.84 tff(13768,plain,
% 5.85/5.84 (succ(succ(succ(Y5!50))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13767, 53])).
% 5.85/5.84 tff(13769,plain,
% 5.85/5.84 (succ(succ(succ(succ(Y5!50)))) = succ(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13768])).
% 5.85/5.84 tff(13770,plain,
% 5.85/5.84 (succ(succ(succ(succ(Y5!50)))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13769, 45])).
% 5.85/5.84 tff(13771,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13770])).
% 5.85/5.84 tff(13772,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(Y5!50))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13771, 28])).
% 5.85/5.84 tff(13773,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13772])).
% 5.85/5.84 tff(13774,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13773, 42])).
% 5.85/5.84 tff(13775,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13774])).
% 5.85/5.84 tff(13776,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13775, 58])).
% 5.85/5.84 tff(13777,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13776])).
% 5.85/5.84 tff(13778,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13777, 36])).
% 5.85/5.84 tff(13779,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13778])).
% 5.85/5.84 tff(13780,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13779, 48])).
% 5.85/5.84 tff(13781,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13780])).
% 5.85/5.84 tff(13782,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13781, 14])).
% 5.85/5.84 tff(13783,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13782])).
% 5.85/5.84 tff(13784,plain,
% 5.85/5.84 (NSY5!16 = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[717, 13783, 33])).
% 5.85/5.84 tff(13785,plain,
% 5.85/5.84 (pred(NSY5!16) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13784])).
% 5.85/5.84 tff(13786,plain,
% 5.85/5.84 (pred(NSY5!16) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13785, 16])).
% 5.85/5.84 tff(13787,plain,
% 5.85/5.84 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n4, n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13786, 13762])).
% 5.85/5.84 tff(13788,plain,
% 5.85/5.84 (sum(pred(NSY5!16), succ(NPY5!18)) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13787, 12])).
% 5.85/5.84 tff(13789,plain,
% 5.85/5.84 (sum(pred(Y4!52), succ(X4!53)) = sum(n3, n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13632, 13714])).
% 5.85/5.84 tff(13790,plain,
% 5.85/5.84 (sum(pred(Y4!52), succ(X4!53)) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13789, 32])).
% 5.85/5.84 tff(13791,plain,
% 5.85/5.84 (sum(pred(X4!53), succ(Y4!52)) = sum(n3, n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13688, 13656])).
% 5.85/5.84 tff(13792,plain,
% 5.85/5.84 (sum(pred(X4!53), succ(Y4!52)) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13791, 32])).
% 5.85/5.84 tff(13793,plain,
% 5.85/5.84 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n8, n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13792, 13790])).
% 5.85/5.84 tff(13794,plain,
% 5.85/5.84 (X5!51 = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[553, 13793, 31])).
% 5.85/5.84 tff(13795,plain,
% 5.85/5.84 (pred(X5!51) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13794])).
% 5.85/5.84 tff(13796,plain,
% 5.85/5.84 (pred(X5!51) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13795, 16])).
% 5.85/5.84 tff(13797,plain,
% 5.85/5.84 (pred(pred(X5!51)) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13796])).
% 5.85/5.84 tff(13798,plain,
% 5.85/5.84 (pred(pred(X5!51)) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13797, 15])).
% 5.85/5.84 tff(13799,plain,
% 5.85/5.84 (pred(pred(pred(X5!51))) = pred(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13798])).
% 5.85/5.84 tff(13800,plain,
% 5.85/5.84 (pred(pred(pred(X5!51))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13799, 25])).
% 5.85/5.84 tff(13801,plain,
% 5.85/5.84 (pred(pred(pred(pred(X5!51)))) = pred(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13800])).
% 5.85/5.84 tff(13802,plain,
% 5.85/5.84 (pred(pred(pred(pred(X5!51)))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13801, 24])).
% 5.85/5.84 tff(13803,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X5!51))))) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13802])).
% 5.85/5.84 tff(13804,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X5!51))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13803, 23])).
% 5.85/5.84 tff(13805,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13804])).
% 5.85/5.84 tff(13806,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13805, 22])).
% 5.85/5.84 tff(13807,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13806])).
% 5.85/5.84 tff(13808,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13807, 21])).
% 5.85/5.84 tff(13809,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13808])).
% 5.85/5.84 tff(13810,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13809, 20])).
% 5.85/5.84 tff(13811,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13810])).
% 5.85/5.84 tff(13812,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13811, 19])).
% 5.85/5.84 tff(13813,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13812])).
% 5.85/5.84 tff(13814,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13813, 18])).
% 5.85/5.84 tff(13815,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13814])).
% 5.85/5.84 tff(13816,plain,
% 5.85/5.84 (NPX5!19 = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[742, 13815, 17])).
% 5.85/5.84 tff(13817,plain,
% 5.85/5.84 (succ(NPX5!19) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13816])).
% 5.85/5.84 tff(13818,plain,
% 5.85/5.84 (succ(NPX5!19) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13817, 30])).
% 5.85/5.84 tff(13819,plain,
% 5.85/5.84 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n6, n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13818, 13788])).
% 5.85/5.84 tff(13820,plain,
% 5.85/5.84 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13819, 674])).
% 5.85/5.84 tff(13821,plain,
% 5.85/5.84 (succ(X5!51) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13794])).
% 5.85/5.84 tff(13822,plain,
% 5.85/5.84 (succ(X5!51) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13821, 30])).
% 5.85/5.84 tff(13823,plain,
% 5.85/5.84 (succ(succ(X5!51)) = succ(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13822])).
% 5.85/5.84 tff(13824,plain,
% 5.85/5.84 (succ(succ(X5!51)) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13823, 39])).
% 5.85/5.84 tff(13825,plain,
% 5.85/5.84 (succ(succ(succ(X5!51))) = succ(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13824])).
% 5.85/5.84 tff(13826,plain,
% 5.85/5.84 (succ(succ(succ(X5!51))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13825, 53])).
% 5.85/5.84 tff(13827,plain,
% 5.85/5.84 (succ(succ(succ(succ(X5!51)))) = succ(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13826])).
% 5.85/5.84 tff(13828,plain,
% 5.85/5.84 (succ(succ(succ(succ(X5!51)))) = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[13827, 45])).
% 5.85/5.84 tff(13829,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(X5!51))))) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13828])).
% 5.85/5.84 tff(13830,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(X5!51))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13829, 28])).
% 5.85/5.84 tff(13831,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13830])).
% 5.85/5.84 tff(13832,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13831, 42])).
% 5.85/5.84 tff(13833,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13832])).
% 5.85/5.84 tff(13834,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13833, 58])).
% 5.85/5.84 tff(13835,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13834])).
% 5.85/5.84 tff(13836,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13835, 36])).
% 5.85/5.84 tff(13837,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13836])).
% 5.85/5.84 tff(13838,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13837, 48])).
% 5.85/5.84 tff(13839,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13838])).
% 5.85/5.84 tff(13840,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13839, 14])).
% 5.85/5.84 tff(13841,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13840])).
% 5.85/5.84 tff(13842,plain,
% 5.85/5.84 (NSX5!17 = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[767, 13841, 33])).
% 5.85/5.84 tff(13843,plain,
% 5.85/5.84 (pred(NSX5!17) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13842])).
% 5.85/5.84 tff(13844,plain,
% 5.85/5.84 (pred(NSX5!17) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13843, 16])).
% 5.85/5.84 tff(13845,plain,
% 5.85/5.84 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n4, n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13844, 13820])).
% 5.85/5.84 tff(13846,plain,
% 5.85/5.84 (Y6!48 = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[772, 13845, 673])).
% 5.85/5.84 tff(13847,plain,
% 5.85/5.84 (pred(Y6!48) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13846])).
% 5.85/5.84 tff(13848,plain,
% 5.85/5.84 (pred(Y6!48) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13847, 20])).
% 5.85/5.84 tff(13849,plain,
% 5.85/5.84 (pred(pred(Y6!48)) = pred(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13848])).
% 5.85/5.84 tff(13850,plain,
% 5.85/5.84 (pred(pred(Y6!48)) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13849, 19])).
% 5.85/5.84 tff(13851,plain,
% 5.85/5.84 (pred(pred(pred(Y6!48))) = pred(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13850])).
% 5.85/5.84 tff(13852,plain,
% 5.85/5.84 (pred(pred(pred(Y6!48))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13851, 18])).
% 5.85/5.84 tff(13853,plain,
% 5.85/5.84 (pred(pred(pred(pred(Y6!48)))) = pred(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13852])).
% 5.85/5.84 tff(13854,plain,
% 5.85/5.84 (pred(pred(pred(pred(Y6!48)))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13853, 17])).
% 5.85/5.84 tff(13855,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13854])).
% 5.85/5.84 tff(13856,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(Y6!48))))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13855, 16])).
% 5.85/5.84 tff(13857,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13856])).
% 5.85/5.84 tff(13858,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13857, 15])).
% 5.85/5.84 tff(13859,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13858])).
% 5.85/5.84 tff(13860,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13859, 25])).
% 5.85/5.84 tff(13861,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13860])).
% 5.85/5.84 tff(13862,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13861, 24])).
% 5.85/5.84 tff(13863,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13862])).
% 5.85/5.84 tff(13864,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13863, 23])).
% 5.85/5.84 tff(13865,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13864])).
% 5.85/5.84 tff(13866,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13865, 22])).
% 5.85/5.84 tff(13867,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13866])).
% 5.85/5.84 tff(13868,plain,
% 5.85/5.84 (NPY6!14 = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[1465, 13867, 21])).
% 5.85/5.84 tff(13869,plain,
% 5.85/5.84 (succ(NPY6!14) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13868])).
% 5.85/5.84 tff(13870,plain,
% 5.85/5.84 (succ(NPY6!14) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13869, 28])).
% 5.85/5.84 tff(13871,plain,
% 5.85/5.84 (succ(Y6!48) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13846])).
% 5.85/5.84 tff(13872,plain,
% 5.85/5.84 (succ(Y6!48) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13871, 28])).
% 5.85/5.84 tff(13873,plain,
% 5.85/5.84 (succ(succ(Y6!48)) = succ(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13872])).
% 5.85/5.84 tff(13874,plain,
% 5.85/5.84 (succ(succ(Y6!48)) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13873, 42])).
% 5.85/5.84 tff(13875,plain,
% 5.85/5.84 (succ(succ(succ(Y6!48))) = succ(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13874])).
% 5.85/5.84 tff(13876,plain,
% 5.85/5.84 (succ(succ(succ(Y6!48))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13875, 58])).
% 5.85/5.84 tff(13877,plain,
% 5.85/5.84 (succ(succ(succ(succ(Y6!48)))) = succ(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13876])).
% 5.85/5.84 tff(13878,plain,
% 5.85/5.84 (succ(succ(succ(succ(Y6!48)))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13877, 36])).
% 5.85/5.84 tff(13879,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13878])).
% 5.85/5.84 tff(13880,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(Y6!48))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13879, 48])).
% 5.85/5.84 tff(13881,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13880])).
% 5.85/5.84 tff(13882,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13881, 14])).
% 5.85/5.84 tff(13883,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13882])).
% 5.85/5.84 tff(13884,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13883, 33])).
% 5.85/5.84 tff(13885,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13884])).
% 5.85/5.84 tff(13886,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13885, 30])).
% 5.85/5.84 tff(13887,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13886])).
% 5.85/5.84 tff(13888,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13887, 39])).
% 5.85/5.84 tff(13889,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13888])).
% 5.85/5.84 tff(13890,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13889, 53])).
% 5.85/5.84 tff(13891,plain,
% 5.85/5.84 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13890])).
% 5.85/5.84 tff(13892,plain,
% 5.85/5.84 (NSY6!12 = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[1490, 13891, 45])).
% 5.85/5.84 tff(13893,plain,
% 5.85/5.84 (pred(NSY6!12) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13892])).
% 5.85/5.84 tff(13894,plain,
% 5.85/5.84 (pred(NSY6!12) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13893, 20])).
% 5.85/5.84 tff(13895,plain,
% 5.85/5.84 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n8, n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13894, 13870])).
% 5.85/5.84 tff(13896,plain,
% 5.85/5.84 (sum(pred(NSY6!12), succ(NPY6!14)) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13895, 27])).
% 5.85/5.84 tff(13897,plain,
% 5.85/5.84 (sum(pred(Y5!50), succ(X5!51)) = sum(n4, n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13740, 13822])).
% 5.85/5.84 tff(13898,plain,
% 5.85/5.84 (sum(pred(Y5!50), succ(X5!51)) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13897, 12])).
% 5.85/5.84 tff(13899,plain,
% 5.85/5.84 (sum(pred(X5!51), succ(Y5!50)) = sum(n4, n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13796, 13764])).
% 5.85/5.84 tff(13900,plain,
% 5.85/5.84 (sum(pred(X5!51), succ(Y5!50)) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13899, 12])).
% 5.85/5.84 tff(13901,plain,
% 5.85/5.84 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n10, n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13900, 13898])).
% 5.85/5.84 tff(13902,plain,
% 5.85/5.84 (X6!49 = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[669, 13901, 29])).
% 5.85/5.84 tff(13903,plain,
% 5.85/5.84 (pred(X6!49) = pred(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13902])).
% 5.85/5.84 tff(13904,plain,
% 5.85/5.84 (pred(X6!49) = n8),
% 5.85/5.84 inference(transitivity,[status(thm)],[13903, 20])).
% 5.85/5.84 tff(13905,plain,
% 5.85/5.84 (pred(pred(X6!49)) = pred(n8)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13904])).
% 5.85/5.84 tff(13906,plain,
% 5.85/5.84 (pred(pred(X6!49)) = n7),
% 5.85/5.84 inference(transitivity,[status(thm)],[13905, 19])).
% 5.85/5.84 tff(13907,plain,
% 5.85/5.84 (pred(pred(pred(X6!49))) = pred(n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13906])).
% 5.85/5.84 tff(13908,plain,
% 5.85/5.84 (pred(pred(pred(X6!49))) = n6),
% 5.85/5.84 inference(transitivity,[status(thm)],[13907, 18])).
% 5.85/5.84 tff(13909,plain,
% 5.85/5.84 (pred(pred(pred(pred(X6!49)))) = pred(n6)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13908])).
% 5.85/5.84 tff(13910,plain,
% 5.85/5.84 (pred(pred(pred(pred(X6!49)))) = n5),
% 5.85/5.84 inference(transitivity,[status(thm)],[13909, 17])).
% 5.85/5.84 tff(13911,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X6!49))))) = pred(n5)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13910])).
% 5.85/5.84 tff(13912,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(X6!49))))) = n4),
% 5.85/5.84 inference(transitivity,[status(thm)],[13911, 16])).
% 5.85/5.84 tff(13913,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n4)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13912])).
% 5.85/5.84 tff(13914,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n3),
% 5.85/5.84 inference(transitivity,[status(thm)],[13913, 15])).
% 5.85/5.84 tff(13915,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n3)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13914])).
% 5.85/5.84 tff(13916,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n2),
% 5.85/5.84 inference(transitivity,[status(thm)],[13915, 25])).
% 5.85/5.84 tff(13917,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n2)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13916])).
% 5.85/5.84 tff(13918,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n1),
% 5.85/5.84 inference(transitivity,[status(thm)],[13917, 24])).
% 5.85/5.84 tff(13919,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n1)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13918])).
% 5.85/5.84 tff(13920,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n0),
% 5.85/5.84 inference(transitivity,[status(thm)],[13919, 23])).
% 5.85/5.84 tff(13921,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n0)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13920])).
% 5.85/5.84 tff(13922,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13921, 22])).
% 5.85/5.84 tff(13923,plain,
% 5.85/5.84 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n10)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13922])).
% 5.85/5.84 tff(13924,plain,
% 5.85/5.84 (NPX6!15 = n9),
% 5.85/5.84 inference(transitivity,[status(thm)],[1523, 13923, 21])).
% 5.85/5.84 tff(13925,plain,
% 5.85/5.84 (succ(NPX6!15) = succ(n9)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13924])).
% 5.85/5.84 tff(13926,plain,
% 5.85/5.84 (succ(NPX6!15) = n10),
% 5.85/5.84 inference(transitivity,[status(thm)],[13925, 28])).
% 5.85/5.84 tff(13927,plain,
% 5.85/5.84 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n10, n7)),
% 5.85/5.84 inference(monotonicity,[status(thm)],[13926, 13896])).
% 5.85/5.84 tff(13928,plain,
% 5.85/5.84 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[13927, 69])).
% 5.85/5.85 tff(13929,plain,
% 5.85/5.85 (succ(X6!49) = succ(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13902])).
% 5.85/5.85 tff(13930,plain,
% 5.85/5.85 (succ(X6!49) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[13929, 28])).
% 5.85/5.85 tff(13931,plain,
% 5.85/5.85 (succ(succ(X6!49)) = succ(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13930])).
% 5.85/5.85 tff(13932,plain,
% 5.85/5.85 (succ(succ(X6!49)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[13931, 42])).
% 5.85/5.85 tff(13933,plain,
% 5.85/5.85 (succ(succ(succ(X6!49))) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13932])).
% 5.85/5.85 tff(13934,plain,
% 5.85/5.85 (succ(succ(succ(X6!49))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[13933, 58])).
% 5.85/5.85 tff(13935,plain,
% 5.85/5.85 (succ(succ(succ(succ(X6!49)))) = succ(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13934])).
% 5.85/5.85 tff(13936,plain,
% 5.85/5.85 (succ(succ(succ(succ(X6!49)))) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[13935, 36])).
% 5.85/5.85 tff(13937,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(X6!49))))) = succ(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13936])).
% 5.85/5.85 tff(13938,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(X6!49))))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[13937, 48])).
% 5.85/5.85 tff(13939,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13938])).
% 5.85/5.85 tff(13940,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[13939, 14])).
% 5.85/5.85 tff(13941,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13940])).
% 5.85/5.85 tff(13942,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[13941, 33])).
% 5.85/5.85 tff(13943,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13942])).
% 5.85/5.85 tff(13944,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[13943, 30])).
% 5.85/5.85 tff(13945,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13944])).
% 5.85/5.85 tff(13946,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[13945, 39])).
% 5.85/5.85 tff(13947,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13946])).
% 5.85/5.85 tff(13948,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[13947, 53])).
% 5.85/5.85 tff(13949,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13948])).
% 5.85/5.85 tff(13950,plain,
% 5.85/5.85 (NSX6!13 = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[1550, 13949, 45])).
% 5.85/5.85 tff(13951,plain,
% 5.85/5.85 (pred(NSX6!13) = pred(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13950])).
% 5.85/5.85 tff(13952,plain,
% 5.85/5.85 (pred(NSX6!13) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[13951, 20])).
% 5.85/5.85 tff(13953,plain,
% 5.85/5.85 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n8, n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13952, 13928])).
% 5.85/5.85 tff(13954,plain,
% 5.85/5.85 (sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.85/5.85 inference(symmetry,[status(thm)],[13953])).
% 5.85/5.85 tff(13955,plain,
% 5.85/5.85 (sum(pred(Y6!48), succ(X6!49)) = sum(n8, n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13848, 13930])).
% 5.85/5.85 tff(13956,plain,
% 5.85/5.85 (sum(pred(Y6!48), succ(X6!49)) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[13955, 27])).
% 5.85/5.85 tff(13957,plain,
% 5.85/5.85 (sum(pred(X6!49), succ(Y6!48)) = sum(n8, n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13904, 13872])).
% 5.85/5.85 tff(13958,plain,
% 5.85/5.85 (sum(pred(X6!49), succ(Y6!48)) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[13957, 27])).
% 5.85/5.85 tff(13959,plain,
% 5.85/5.85 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n7, n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13958, 13956])).
% 5.85/5.85 tff(13960,plain,
% 5.85/5.85 (X7!47 = Y7!46),
% 5.85/5.85 inference(transitivity,[status(thm)],[785, 13959, 26, 1556, 13954, 794])).
% 5.85/5.85 tff(13961,plain,
% 5.85/5.85 ($false),
% 5.85/5.85 inference(unit_resolution,[status(thm)],[792, 13960])).
% 5.85/5.85 tff(13962,plain,((~(Y0!60 = n6)) | (X7!47 = Y7!46) | (~(X0!61 = n4))), inference(lemma,lemma(discharge,[]))).
% 5.85/5.85 tff(13963,plain,
% 5.85/5.85 (~(Y0!60 = n6)),
% 5.85/5.85 inference(unit_resolution,[status(thm)],[13962, 11930, 792])).
% 5.85/5.85 tff(13964,plain,
% 5.85/5.85 (sum(n5, n3) = n8),
% 5.85/5.85 inference(and_elim,[status(thm)],[9])).
% 5.85/5.85 tff(13965,plain,
% 5.85/5.85 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n5, n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[11954, 2335])).
% 5.85/5.85 tff(13966,plain,
% 5.85/5.85 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[13965, 13964])).
% 5.85/5.85 tff(13967,plain,
% 5.85/5.85 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n3, n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[11980, 13966])).
% 5.85/5.85 tff(13968,plain,
% 5.85/5.85 (Y1!58 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[196, 13967, 72])).
% 5.85/5.85 tff(13969,plain,
% 5.85/5.85 (pred(Y1!58) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13968])).
% 5.85/5.85 tff(13970,plain,
% 5.85/5.85 (pred(Y1!58) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[13969, 22])).
% 5.85/5.85 tff(13971,plain,
% 5.85/5.85 (pred(pred(Y1!58)) = pred(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13970])).
% 5.85/5.85 tff(13972,plain,
% 5.85/5.85 (pred(pred(Y1!58)) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[13971, 21])).
% 5.85/5.85 tff(13973,plain,
% 5.85/5.85 (pred(pred(pred(Y1!58))) = pred(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13972])).
% 5.85/5.85 tff(13974,plain,
% 5.85/5.85 (pred(pred(pred(Y1!58))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[13973, 20])).
% 5.85/5.85 tff(13975,plain,
% 5.85/5.85 (pred(pred(pred(pred(Y1!58)))) = pred(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13974])).
% 5.85/5.85 tff(13976,plain,
% 5.85/5.85 (pred(pred(pred(pred(Y1!58)))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[13975, 19])).
% 5.85/5.85 tff(13977,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13976])).
% 5.85/5.85 tff(13978,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(Y1!58))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[13977, 18])).
% 5.85/5.85 tff(13979,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13978])).
% 5.85/5.85 tff(13980,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[13979, 17])).
% 5.85/5.85 tff(13981,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13980])).
% 5.85/5.85 tff(13982,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[13981, 16])).
% 5.85/5.85 tff(13983,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13982])).
% 5.85/5.85 tff(13984,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[13983, 15])).
% 5.85/5.85 tff(13985,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13984])).
% 5.85/5.85 tff(13986,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[13985, 25])).
% 5.85/5.85 tff(13987,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13986])).
% 5.85/5.85 tff(13988,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[13987, 24])).
% 5.85/5.85 tff(13989,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13988])).
% 5.85/5.85 tff(13990,plain,
% 5.85/5.85 (NPY1!34 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[232, 13989, 23])).
% 5.85/5.85 tff(13991,plain,
% 5.85/5.85 (succ(NPY1!34) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13990])).
% 5.85/5.85 tff(13992,plain,
% 5.85/5.85 (succ(NPY1!34) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[13991, 58])).
% 5.85/5.85 tff(13993,plain,
% 5.85/5.85 (succ(Y1!58) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13968])).
% 5.85/5.85 tff(13994,plain,
% 5.85/5.85 (succ(Y1!58) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[13993, 58])).
% 5.85/5.85 tff(13995,plain,
% 5.85/5.85 (succ(succ(Y1!58)) = succ(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13994])).
% 5.85/5.85 tff(13996,plain,
% 5.85/5.85 (succ(succ(Y1!58)) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[13995, 36])).
% 5.85/5.85 tff(13997,plain,
% 5.85/5.85 (succ(succ(succ(Y1!58))) = succ(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13996])).
% 5.85/5.85 tff(13998,plain,
% 5.85/5.85 (succ(succ(succ(Y1!58))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[13997, 48])).
% 5.85/5.85 tff(13999,plain,
% 5.85/5.85 (succ(succ(succ(succ(Y1!58)))) = succ(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13998])).
% 5.85/5.85 tff(14000,plain,
% 5.85/5.85 (succ(succ(succ(succ(Y1!58)))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[13999, 14])).
% 5.85/5.85 tff(14001,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14000])).
% 5.85/5.85 tff(14002,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(Y1!58))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14001, 33])).
% 5.85/5.85 tff(14003,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14002])).
% 5.85/5.85 tff(14004,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14003, 30])).
% 5.85/5.85 tff(14005,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14004])).
% 5.85/5.85 tff(14006,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14005, 39])).
% 5.85/5.85 tff(14007,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14006])).
% 5.85/5.85 tff(14008,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14007, 53])).
% 5.85/5.85 tff(14009,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14008])).
% 5.85/5.85 tff(14010,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14009, 45])).
% 5.85/5.85 tff(14011,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14010])).
% 5.85/5.85 tff(14012,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14011, 28])).
% 5.85/5.85 tff(14013,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14012])).
% 5.85/5.85 tff(14014,plain,
% 5.85/5.85 (NSY1!32 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[255, 14013, 42])).
% 5.85/5.85 tff(14015,plain,
% 5.85/5.85 (pred(NSY1!32) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14014])).
% 5.85/5.85 tff(14016,plain,
% 5.85/5.85 (pred(NSY1!32) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14015, 22])).
% 5.85/5.85 tff(14017,plain,
% 5.85/5.85 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14016, 13992])).
% 5.85/5.85 tff(14018,plain,
% 5.85/5.85 (sum(pred(NSY1!32), succ(NPY1!34)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14017, 57])).
% 5.85/5.85 tff(14019,plain,
% 5.85/5.85 (sum(pred(Y0!60), succ(X0!61)) = sum(n6, n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[2287, 11958])).
% 5.85/5.85 tff(14020,plain,
% 5.85/5.85 (sum(pred(Y0!60), succ(X0!61)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14019, 1569])).
% 5.85/5.85 tff(14021,plain,
% 5.85/5.85 (sum(pred(X0!61), succ(Y0!60)) = sum(n3, n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[11932, 2311])).
% 5.85/5.85 tff(14022,plain,
% 5.85/5.85 (sum(pred(X0!61), succ(Y0!60)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14021, 72])).
% 5.85/5.85 tff(14023,plain,
% 5.85/5.85 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n0, n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14022, 14020])).
% 5.85/5.85 tff(14024,plain,
% 5.85/5.85 (X1!59 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[93, 14023, 59])).
% 5.85/5.85 tff(14025,plain,
% 5.85/5.85 (pred(X1!59) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14024])).
% 5.85/5.85 tff(14026,plain,
% 5.85/5.85 (pred(X1!59) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14025, 22])).
% 5.85/5.85 tff(14027,plain,
% 5.85/5.85 (pred(pred(X1!59)) = pred(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14026])).
% 5.85/5.85 tff(14028,plain,
% 5.85/5.85 (pred(pred(X1!59)) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14027, 21])).
% 5.85/5.85 tff(14029,plain,
% 5.85/5.85 (pred(pred(pred(X1!59))) = pred(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14028])).
% 5.85/5.85 tff(14030,plain,
% 5.85/5.85 (pred(pred(pred(X1!59))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14029, 20])).
% 5.85/5.85 tff(14031,plain,
% 5.85/5.85 (pred(pred(pred(pred(X1!59)))) = pred(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14030])).
% 5.85/5.85 tff(14032,plain,
% 5.85/5.85 (pred(pred(pred(pred(X1!59)))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14031, 19])).
% 5.85/5.85 tff(14033,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(X1!59))))) = pred(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14032])).
% 5.85/5.85 tff(14034,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(X1!59))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14033, 18])).
% 5.85/5.85 tff(14035,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14034])).
% 5.85/5.85 tff(14036,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14035, 17])).
% 5.85/5.85 tff(14037,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14036])).
% 5.85/5.85 tff(14038,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14037, 16])).
% 5.85/5.85 tff(14039,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14038])).
% 5.85/5.85 tff(14040,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14039, 15])).
% 5.85/5.85 tff(14041,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14040])).
% 5.85/5.85 tff(14042,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14041, 25])).
% 5.85/5.85 tff(14043,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14042])).
% 5.85/5.85 tff(14044,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14043, 24])).
% 5.85/5.85 tff(14045,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14044])).
% 5.85/5.85 tff(14046,plain,
% 5.85/5.85 (NPX1!35 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[280, 14045, 23])).
% 5.85/5.85 tff(14047,plain,
% 5.85/5.85 (succ(NPX1!35) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14046])).
% 5.85/5.85 tff(14048,plain,
% 5.85/5.85 (succ(NPX1!35) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14047, 58])).
% 5.85/5.85 tff(14049,plain,
% 5.85/5.85 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n1, n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14048, 14018])).
% 5.85/5.85 tff(14050,plain,
% 5.85/5.85 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14049, 56])).
% 5.85/5.85 tff(14051,plain,
% 5.85/5.85 (succ(X1!59) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14024])).
% 5.85/5.85 tff(14052,plain,
% 5.85/5.85 (succ(X1!59) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14051, 58])).
% 5.85/5.85 tff(14053,plain,
% 5.85/5.85 (succ(succ(X1!59)) = succ(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14052])).
% 5.85/5.85 tff(14054,plain,
% 5.85/5.85 (succ(succ(X1!59)) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14053, 36])).
% 5.85/5.85 tff(14055,plain,
% 5.85/5.85 (succ(succ(succ(X1!59))) = succ(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14054])).
% 5.85/5.85 tff(14056,plain,
% 5.85/5.85 (succ(succ(succ(X1!59))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14055, 48])).
% 5.85/5.85 tff(14057,plain,
% 5.85/5.85 (succ(succ(succ(succ(X1!59)))) = succ(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14056])).
% 5.85/5.85 tff(14058,plain,
% 5.85/5.85 (succ(succ(succ(succ(X1!59)))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14057, 14])).
% 5.85/5.85 tff(14059,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(X1!59))))) = succ(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14058])).
% 5.85/5.85 tff(14060,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(X1!59))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14059, 33])).
% 5.85/5.85 tff(14061,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14060])).
% 5.85/5.85 tff(14062,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14061, 30])).
% 5.85/5.85 tff(14063,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14062])).
% 5.85/5.85 tff(14064,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14063, 39])).
% 5.85/5.85 tff(14065,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14064])).
% 5.85/5.85 tff(14066,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14065, 53])).
% 5.85/5.85 tff(14067,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14066])).
% 5.85/5.85 tff(14068,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14067, 45])).
% 5.85/5.85 tff(14069,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14068])).
% 5.85/5.85 tff(14070,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14069, 28])).
% 5.85/5.85 tff(14071,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14070])).
% 5.85/5.85 tff(14072,plain,
% 5.85/5.85 (NSX1!33 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[305, 14071, 42])).
% 5.85/5.85 tff(14073,plain,
% 5.85/5.85 (pred(NSX1!33) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14072])).
% 5.85/5.85 tff(14074,plain,
% 5.85/5.85 (pred(NSX1!33) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14073, 22])).
% 5.85/5.85 tff(14075,plain,
% 5.85/5.85 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14074, 14050])).
% 5.85/5.85 tff(14076,plain,
% 5.85/5.85 (Y2!56 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[310, 14075, 57])).
% 5.85/5.85 tff(14077,plain,
% 5.85/5.85 (pred(Y2!56) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14076])).
% 5.85/5.85 tff(14078,plain,
% 5.85/5.85 (pred(Y2!56) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14077, 22])).
% 5.85/5.85 tff(14079,plain,
% 5.85/5.85 (pred(pred(Y2!56)) = pred(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14078])).
% 5.85/5.85 tff(14080,plain,
% 5.85/5.85 (pred(pred(Y2!56)) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14079, 21])).
% 5.85/5.85 tff(14081,plain,
% 5.85/5.85 (pred(pred(pred(Y2!56))) = pred(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14080])).
% 5.85/5.85 tff(14082,plain,
% 5.85/5.85 (pred(pred(pred(Y2!56))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14081, 20])).
% 5.85/5.85 tff(14083,plain,
% 5.85/5.85 (pred(pred(pred(pred(Y2!56)))) = pred(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14082])).
% 5.85/5.85 tff(14084,plain,
% 5.85/5.85 (pred(pred(pred(pred(Y2!56)))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14083, 19])).
% 5.85/5.85 tff(14085,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14084])).
% 5.85/5.85 tff(14086,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(Y2!56))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14085, 18])).
% 5.85/5.85 tff(14087,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14086])).
% 5.85/5.85 tff(14088,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14087, 17])).
% 5.85/5.85 tff(14089,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14088])).
% 5.85/5.85 tff(14090,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14089, 16])).
% 5.85/5.85 tff(14091,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14090])).
% 5.85/5.85 tff(14092,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14091, 15])).
% 5.85/5.85 tff(14093,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14092])).
% 5.85/5.85 tff(14094,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14093, 25])).
% 5.85/5.85 tff(14095,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14094])).
% 5.85/5.85 tff(14096,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14095, 24])).
% 5.85/5.85 tff(14097,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14096])).
% 5.85/5.85 tff(14098,plain,
% 5.85/5.85 (NPY2!30 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[347, 14097, 23])).
% 5.85/5.85 tff(14099,plain,
% 5.85/5.85 (succ(NPY2!30) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14098])).
% 5.85/5.85 tff(14100,plain,
% 5.85/5.85 (succ(NPY2!30) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14099, 58])).
% 5.85/5.85 tff(14101,plain,
% 5.85/5.85 (succ(Y2!56) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14076])).
% 5.85/5.85 tff(14102,plain,
% 5.85/5.85 (succ(Y2!56) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14101, 58])).
% 5.85/5.85 tff(14103,plain,
% 5.85/5.85 (succ(succ(Y2!56)) = succ(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14102])).
% 5.85/5.85 tff(14104,plain,
% 5.85/5.85 (succ(succ(Y2!56)) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14103, 36])).
% 5.85/5.85 tff(14105,plain,
% 5.85/5.85 (succ(succ(succ(Y2!56))) = succ(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14104])).
% 5.85/5.85 tff(14106,plain,
% 5.85/5.85 (succ(succ(succ(Y2!56))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14105, 48])).
% 5.85/5.85 tff(14107,plain,
% 5.85/5.85 (succ(succ(succ(succ(Y2!56)))) = succ(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14106])).
% 5.85/5.85 tff(14108,plain,
% 5.85/5.85 (succ(succ(succ(succ(Y2!56)))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14107, 14])).
% 5.85/5.85 tff(14109,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14108])).
% 5.85/5.85 tff(14110,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(Y2!56))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14109, 33])).
% 5.85/5.85 tff(14111,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14110])).
% 5.85/5.85 tff(14112,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14111, 30])).
% 5.85/5.85 tff(14113,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14112])).
% 5.85/5.85 tff(14114,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14113, 39])).
% 5.85/5.85 tff(14115,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14114])).
% 5.85/5.85 tff(14116,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14115, 53])).
% 5.85/5.85 tff(14117,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14116])).
% 5.85/5.85 tff(14118,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14117, 45])).
% 5.85/5.85 tff(14119,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14118])).
% 5.85/5.85 tff(14120,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14119, 28])).
% 5.85/5.85 tff(14121,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14120])).
% 5.85/5.85 tff(14122,plain,
% 5.85/5.85 (NSY2!28 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[370, 14121, 42])).
% 5.85/5.85 tff(14123,plain,
% 5.85/5.85 (pred(NSY2!28) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14122])).
% 5.85/5.85 tff(14124,plain,
% 5.85/5.85 (pred(NSY2!28) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14123, 22])).
% 5.85/5.85 tff(14125,plain,
% 5.85/5.85 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14124, 14100])).
% 5.85/5.85 tff(14126,plain,
% 5.85/5.85 (sum(pred(NSY2!28), succ(NPY2!30)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14125, 57])).
% 5.85/5.85 tff(14127,plain,
% 5.85/5.85 (sum(pred(Y1!58), succ(X1!59)) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[13970, 14052])).
% 5.85/5.85 tff(14128,plain,
% 5.85/5.85 (sum(pred(Y1!58), succ(X1!59)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14127, 57])).
% 5.85/5.85 tff(14129,plain,
% 5.85/5.85 (sum(pred(X1!59), succ(Y1!58)) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14026, 13994])).
% 5.85/5.85 tff(14130,plain,
% 5.85/5.85 (sum(pred(X1!59), succ(Y1!58)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14129, 57])).
% 5.85/5.85 tff(14131,plain,
% 5.85/5.85 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n0, n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14130, 14128])).
% 5.85/5.85 tff(14132,plain,
% 5.85/5.85 (X2!57 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[209, 14131, 59])).
% 5.85/5.85 tff(14133,plain,
% 5.85/5.85 (pred(X2!57) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14132])).
% 5.85/5.85 tff(14134,plain,
% 5.85/5.85 (pred(X2!57) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14133, 22])).
% 5.85/5.85 tff(14135,plain,
% 5.85/5.85 (pred(pred(X2!57)) = pred(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14134])).
% 5.85/5.85 tff(14136,plain,
% 5.85/5.85 (pred(pred(X2!57)) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14135, 21])).
% 5.85/5.85 tff(14137,plain,
% 5.85/5.85 (pred(pred(pred(X2!57))) = pred(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14136])).
% 5.85/5.85 tff(14138,plain,
% 5.85/5.85 (pred(pred(pred(X2!57))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14137, 20])).
% 5.85/5.85 tff(14139,plain,
% 5.85/5.85 (pred(pred(pred(pred(X2!57)))) = pred(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14138])).
% 5.85/5.85 tff(14140,plain,
% 5.85/5.85 (pred(pred(pred(pred(X2!57)))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14139, 19])).
% 5.85/5.85 tff(14141,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(X2!57))))) = pred(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14140])).
% 5.85/5.85 tff(14142,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(X2!57))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14141, 18])).
% 5.85/5.85 tff(14143,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14142])).
% 5.85/5.85 tff(14144,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14143, 17])).
% 5.85/5.85 tff(14145,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14144])).
% 5.85/5.85 tff(14146,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14145, 16])).
% 5.85/5.85 tff(14147,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14146])).
% 5.85/5.85 tff(14148,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14147, 15])).
% 5.85/5.85 tff(14149,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14148])).
% 5.85/5.85 tff(14150,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14149, 25])).
% 5.85/5.85 tff(14151,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14150])).
% 5.85/5.85 tff(14152,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14151, 24])).
% 5.85/5.85 tff(14153,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14152])).
% 5.85/5.85 tff(14154,plain,
% 5.85/5.85 (NPX2!31 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[395, 14153, 23])).
% 5.85/5.85 tff(14155,plain,
% 5.85/5.85 (succ(NPX2!31) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14154])).
% 5.85/5.85 tff(14156,plain,
% 5.85/5.85 (succ(NPX2!31) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14155, 58])).
% 5.85/5.85 tff(14157,plain,
% 5.85/5.85 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n1, n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14156, 14126])).
% 5.85/5.85 tff(14158,plain,
% 5.85/5.85 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14157, 56])).
% 5.85/5.85 tff(14159,plain,
% 5.85/5.85 (succ(X2!57) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14132])).
% 5.85/5.85 tff(14160,plain,
% 5.85/5.85 (succ(X2!57) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14159, 58])).
% 5.85/5.85 tff(14161,plain,
% 5.85/5.85 (succ(succ(X2!57)) = succ(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14160])).
% 5.85/5.85 tff(14162,plain,
% 5.85/5.85 (succ(succ(X2!57)) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14161, 36])).
% 5.85/5.85 tff(14163,plain,
% 5.85/5.85 (succ(succ(succ(X2!57))) = succ(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14162])).
% 5.85/5.85 tff(14164,plain,
% 5.85/5.85 (succ(succ(succ(X2!57))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14163, 48])).
% 5.85/5.85 tff(14165,plain,
% 5.85/5.85 (succ(succ(succ(succ(X2!57)))) = succ(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14164])).
% 5.85/5.85 tff(14166,plain,
% 5.85/5.85 (succ(succ(succ(succ(X2!57)))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14165, 14])).
% 5.85/5.85 tff(14167,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(X2!57))))) = succ(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14166])).
% 5.85/5.85 tff(14168,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(X2!57))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14167, 33])).
% 5.85/5.85 tff(14169,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14168])).
% 5.85/5.85 tff(14170,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14169, 30])).
% 5.85/5.85 tff(14171,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14170])).
% 5.85/5.85 tff(14172,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14171, 39])).
% 5.85/5.85 tff(14173,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14172])).
% 5.85/5.85 tff(14174,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14173, 53])).
% 5.85/5.85 tff(14175,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14174])).
% 5.85/5.85 tff(14176,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14175, 45])).
% 5.85/5.85 tff(14177,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14176])).
% 5.85/5.85 tff(14178,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14177, 28])).
% 5.85/5.85 tff(14179,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14178])).
% 5.85/5.85 tff(14180,plain,
% 5.85/5.85 (NSX2!29 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[420, 14179, 42])).
% 5.85/5.85 tff(14181,plain,
% 5.85/5.85 (pred(NSX2!29) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14180])).
% 5.85/5.85 tff(14182,plain,
% 5.85/5.85 (pred(NSX2!29) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14181, 22])).
% 5.85/5.85 tff(14183,plain,
% 5.85/5.85 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14182, 14158])).
% 5.85/5.85 tff(14184,plain,
% 5.85/5.85 (Y3!54 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[425, 14183, 57])).
% 5.85/5.85 tff(14185,plain,
% 5.85/5.85 (pred(Y3!54) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14184])).
% 5.85/5.85 tff(14186,plain,
% 5.85/5.85 (pred(Y3!54) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14185, 22])).
% 5.85/5.85 tff(14187,plain,
% 5.85/5.85 (pred(pred(Y3!54)) = pred(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14186])).
% 5.85/5.85 tff(14188,plain,
% 5.85/5.85 (pred(pred(Y3!54)) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14187, 21])).
% 5.85/5.85 tff(14189,plain,
% 5.85/5.85 (pred(pred(pred(Y3!54))) = pred(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14188])).
% 5.85/5.85 tff(14190,plain,
% 5.85/5.85 (pred(pred(pred(Y3!54))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14189, 20])).
% 5.85/5.85 tff(14191,plain,
% 5.85/5.85 (pred(pred(pred(pred(Y3!54)))) = pred(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14190])).
% 5.85/5.85 tff(14192,plain,
% 5.85/5.85 (pred(pred(pred(pred(Y3!54)))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14191, 19])).
% 5.85/5.85 tff(14193,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14192])).
% 5.85/5.85 tff(14194,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(Y3!54))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14193, 18])).
% 5.85/5.85 tff(14195,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14194])).
% 5.85/5.85 tff(14196,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14195, 17])).
% 5.85/5.85 tff(14197,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14196])).
% 5.85/5.85 tff(14198,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14197, 16])).
% 5.85/5.85 tff(14199,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14198])).
% 5.85/5.85 tff(14200,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14199, 15])).
% 5.85/5.85 tff(14201,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14200])).
% 5.85/5.85 tff(14202,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14201, 25])).
% 5.85/5.85 tff(14203,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14202])).
% 5.85/5.85 tff(14204,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14203, 24])).
% 5.85/5.85 tff(14205,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14204])).
% 5.85/5.85 tff(14206,plain,
% 5.85/5.85 (NPY3!26 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[462, 14205, 23])).
% 5.85/5.85 tff(14207,plain,
% 5.85/5.85 (succ(NPY3!26) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14206])).
% 5.85/5.85 tff(14208,plain,
% 5.85/5.85 (succ(NPY3!26) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14207, 58])).
% 5.85/5.85 tff(14209,plain,
% 5.85/5.85 (succ(Y3!54) = succ(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14184])).
% 5.85/5.85 tff(14210,plain,
% 5.85/5.85 (succ(Y3!54) = n1),
% 5.85/5.85 inference(transitivity,[status(thm)],[14209, 58])).
% 5.85/5.85 tff(14211,plain,
% 5.85/5.85 (succ(succ(Y3!54)) = succ(n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14210])).
% 5.85/5.85 tff(14212,plain,
% 5.85/5.85 (succ(succ(Y3!54)) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14211, 36])).
% 5.85/5.85 tff(14213,plain,
% 5.85/5.85 (succ(succ(succ(Y3!54))) = succ(n2)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14212])).
% 5.85/5.85 tff(14214,plain,
% 5.85/5.85 (succ(succ(succ(Y3!54))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14213, 48])).
% 5.85/5.85 tff(14215,plain,
% 5.85/5.85 (succ(succ(succ(succ(Y3!54)))) = succ(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14214])).
% 5.85/5.85 tff(14216,plain,
% 5.85/5.85 (succ(succ(succ(succ(Y3!54)))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14215, 14])).
% 5.85/5.85 tff(14217,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14216])).
% 5.85/5.85 tff(14218,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(Y3!54))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14217, 33])).
% 5.85/5.85 tff(14219,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14218])).
% 5.85/5.85 tff(14220,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14219, 30])).
% 5.85/5.85 tff(14221,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14220])).
% 5.85/5.85 tff(14222,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14221, 39])).
% 5.85/5.85 tff(14223,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14222])).
% 5.85/5.85 tff(14224,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14223, 53])).
% 5.85/5.85 tff(14225,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14224])).
% 5.85/5.85 tff(14226,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14225, 45])).
% 5.85/5.85 tff(14227,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14226])).
% 5.85/5.85 tff(14228,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14227, 28])).
% 5.85/5.85 tff(14229,plain,
% 5.85/5.85 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14228])).
% 5.85/5.85 tff(14230,plain,
% 5.85/5.85 (NSY3!24 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[485, 14229, 42])).
% 5.85/5.85 tff(14231,plain,
% 5.85/5.85 (pred(NSY3!24) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14230])).
% 5.85/5.85 tff(14232,plain,
% 5.85/5.85 (pred(NSY3!24) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14231, 22])).
% 5.85/5.85 tff(14233,plain,
% 5.85/5.85 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14232, 14208])).
% 5.85/5.85 tff(14234,plain,
% 5.85/5.85 (sum(pred(NSY3!24), succ(NPY3!26)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14233, 57])).
% 5.85/5.85 tff(14235,plain,
% 5.85/5.85 (sum(pred(Y2!56), succ(X2!57)) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14078, 14160])).
% 5.85/5.85 tff(14236,plain,
% 5.85/5.85 (sum(pred(Y2!56), succ(X2!57)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14235, 57])).
% 5.85/5.85 tff(14237,plain,
% 5.85/5.85 (sum(pred(X2!57), succ(Y2!56)) = sum(n10, n1)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14134, 14102])).
% 5.85/5.85 tff(14238,plain,
% 5.85/5.85 (sum(pred(X2!57), succ(Y2!56)) = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[14237, 57])).
% 5.85/5.85 tff(14239,plain,
% 5.85/5.85 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n0, n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14238, 14236])).
% 5.85/5.85 tff(14240,plain,
% 5.85/5.85 (X3!55 = n0),
% 5.85/5.85 inference(transitivity,[status(thm)],[323, 14239, 59])).
% 5.85/5.85 tff(14241,plain,
% 5.85/5.85 (pred(X3!55) = pred(n0)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14240])).
% 5.85/5.85 tff(14242,plain,
% 5.85/5.85 (pred(X3!55) = n10),
% 5.85/5.85 inference(transitivity,[status(thm)],[14241, 22])).
% 5.85/5.85 tff(14243,plain,
% 5.85/5.85 (pred(pred(X3!55)) = pred(n10)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14242])).
% 5.85/5.85 tff(14244,plain,
% 5.85/5.85 (pred(pred(X3!55)) = n9),
% 5.85/5.85 inference(transitivity,[status(thm)],[14243, 21])).
% 5.85/5.85 tff(14245,plain,
% 5.85/5.85 (pred(pred(pred(X3!55))) = pred(n9)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14244])).
% 5.85/5.85 tff(14246,plain,
% 5.85/5.85 (pred(pred(pred(X3!55))) = n8),
% 5.85/5.85 inference(transitivity,[status(thm)],[14245, 20])).
% 5.85/5.85 tff(14247,plain,
% 5.85/5.85 (pred(pred(pred(pred(X3!55)))) = pred(n8)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14246])).
% 5.85/5.85 tff(14248,plain,
% 5.85/5.85 (pred(pred(pred(pred(X3!55)))) = n7),
% 5.85/5.85 inference(transitivity,[status(thm)],[14247, 19])).
% 5.85/5.85 tff(14249,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(X3!55))))) = pred(n7)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14248])).
% 5.85/5.85 tff(14250,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(X3!55))))) = n6),
% 5.85/5.85 inference(transitivity,[status(thm)],[14249, 18])).
% 5.85/5.85 tff(14251,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n6)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14250])).
% 5.85/5.85 tff(14252,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n5),
% 5.85/5.85 inference(transitivity,[status(thm)],[14251, 17])).
% 5.85/5.85 tff(14253,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n5)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14252])).
% 5.85/5.85 tff(14254,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n4),
% 5.85/5.85 inference(transitivity,[status(thm)],[14253, 16])).
% 5.85/5.85 tff(14255,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n4)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14254])).
% 5.85/5.85 tff(14256,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n3),
% 5.85/5.85 inference(transitivity,[status(thm)],[14255, 15])).
% 5.85/5.85 tff(14257,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n3)),
% 5.85/5.85 inference(monotonicity,[status(thm)],[14256])).
% 5.85/5.85 tff(14258,plain,
% 5.85/5.85 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n2),
% 5.85/5.85 inference(transitivity,[status(thm)],[14257, 25])).
% 5.85/5.86 tff(14259,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14258])).
% 5.85/5.86 tff(14260,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14259, 24])).
% 5.85/5.86 tff(14261,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14260])).
% 5.85/5.86 tff(14262,plain,
% 5.85/5.86 (NPX3!27 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[510, 14261, 23])).
% 5.85/5.86 tff(14263,plain,
% 5.85/5.86 (succ(NPX3!27) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14262])).
% 5.85/5.86 tff(14264,plain,
% 5.85/5.86 (succ(NPX3!27) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14263, 58])).
% 5.85/5.86 tff(14265,plain,
% 5.85/5.86 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n1, n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14264, 14234])).
% 5.85/5.86 tff(14266,plain,
% 5.85/5.86 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14265, 56])).
% 5.85/5.86 tff(14267,plain,
% 5.85/5.86 (succ(X3!55) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14240])).
% 5.85/5.86 tff(14268,plain,
% 5.85/5.86 (succ(X3!55) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14267, 58])).
% 5.85/5.86 tff(14269,plain,
% 5.85/5.86 (succ(succ(X3!55)) = succ(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14268])).
% 5.85/5.86 tff(14270,plain,
% 5.85/5.86 (succ(succ(X3!55)) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14269, 36])).
% 5.85/5.86 tff(14271,plain,
% 5.85/5.86 (succ(succ(succ(X3!55))) = succ(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14270])).
% 5.85/5.86 tff(14272,plain,
% 5.85/5.86 (succ(succ(succ(X3!55))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14271, 48])).
% 5.85/5.86 tff(14273,plain,
% 5.85/5.86 (succ(succ(succ(succ(X3!55)))) = succ(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14272])).
% 5.85/5.86 tff(14274,plain,
% 5.85/5.86 (succ(succ(succ(succ(X3!55)))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14273, 14])).
% 5.85/5.86 tff(14275,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(X3!55))))) = succ(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14274])).
% 5.85/5.86 tff(14276,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(X3!55))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14275, 33])).
% 5.85/5.86 tff(14277,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14276])).
% 5.85/5.86 tff(14278,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14277, 30])).
% 5.85/5.86 tff(14279,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14278])).
% 5.85/5.86 tff(14280,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14279, 39])).
% 5.85/5.86 tff(14281,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14280])).
% 5.85/5.86 tff(14282,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14281, 53])).
% 5.85/5.86 tff(14283,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14282])).
% 5.85/5.86 tff(14284,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14283, 45])).
% 5.85/5.86 tff(14285,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14284])).
% 5.85/5.86 tff(14286,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14285, 28])).
% 5.85/5.86 tff(14287,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14286])).
% 5.85/5.86 tff(14288,plain,
% 5.85/5.86 (NSX3!25 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[535, 14287, 42])).
% 5.85/5.86 tff(14289,plain,
% 5.85/5.86 (pred(NSX3!25) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14288])).
% 5.85/5.86 tff(14290,plain,
% 5.85/5.86 (pred(NSX3!25) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14289, 22])).
% 5.85/5.86 tff(14291,plain,
% 5.85/5.86 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14290, 14266])).
% 5.85/5.86 tff(14292,plain,
% 5.85/5.86 (Y4!52 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[540, 14291, 57])).
% 5.85/5.86 tff(14293,plain,
% 5.85/5.86 (pred(Y4!52) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14292])).
% 5.85/5.86 tff(14294,plain,
% 5.85/5.86 (pred(Y4!52) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14293, 22])).
% 5.85/5.86 tff(14295,plain,
% 5.85/5.86 (pred(pred(Y4!52)) = pred(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14294])).
% 5.85/5.86 tff(14296,plain,
% 5.85/5.86 (pred(pred(Y4!52)) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14295, 21])).
% 5.85/5.86 tff(14297,plain,
% 5.85/5.86 (pred(pred(pred(Y4!52))) = pred(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14296])).
% 5.85/5.86 tff(14298,plain,
% 5.85/5.86 (pred(pred(pred(Y4!52))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14297, 20])).
% 5.85/5.86 tff(14299,plain,
% 5.85/5.86 (pred(pred(pred(pred(Y4!52)))) = pred(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14298])).
% 5.85/5.86 tff(14300,plain,
% 5.85/5.86 (pred(pred(pred(pred(Y4!52)))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14299, 19])).
% 5.85/5.86 tff(14301,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14300])).
% 5.85/5.86 tff(14302,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(Y4!52))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14301, 18])).
% 5.85/5.86 tff(14303,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14302])).
% 5.85/5.86 tff(14304,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14303, 17])).
% 5.85/5.86 tff(14305,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14304])).
% 5.85/5.86 tff(14306,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14305, 16])).
% 5.85/5.86 tff(14307,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14306])).
% 5.85/5.86 tff(14308,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14307, 15])).
% 5.85/5.86 tff(14309,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14308])).
% 5.85/5.86 tff(14310,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14309, 25])).
% 5.85/5.86 tff(14311,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14310])).
% 5.85/5.86 tff(14312,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14311, 24])).
% 5.85/5.86 tff(14313,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14312])).
% 5.85/5.86 tff(14314,plain,
% 5.85/5.86 (NPY4!22 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[578, 14313, 23])).
% 5.85/5.86 tff(14315,plain,
% 5.85/5.86 (succ(NPY4!22) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14314])).
% 5.85/5.86 tff(14316,plain,
% 5.85/5.86 (succ(NPY4!22) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14315, 58])).
% 5.85/5.86 tff(14317,plain,
% 5.85/5.86 (succ(Y4!52) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14292])).
% 5.85/5.86 tff(14318,plain,
% 5.85/5.86 (succ(Y4!52) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14317, 58])).
% 5.85/5.86 tff(14319,plain,
% 5.85/5.86 (succ(succ(Y4!52)) = succ(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14318])).
% 5.85/5.86 tff(14320,plain,
% 5.85/5.86 (succ(succ(Y4!52)) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14319, 36])).
% 5.85/5.86 tff(14321,plain,
% 5.85/5.86 (succ(succ(succ(Y4!52))) = succ(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14320])).
% 5.85/5.86 tff(14322,plain,
% 5.85/5.86 (succ(succ(succ(Y4!52))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14321, 48])).
% 5.85/5.86 tff(14323,plain,
% 5.85/5.86 (succ(succ(succ(succ(Y4!52)))) = succ(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14322])).
% 5.85/5.86 tff(14324,plain,
% 5.85/5.86 (succ(succ(succ(succ(Y4!52)))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14323, 14])).
% 5.85/5.86 tff(14325,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14324])).
% 5.85/5.86 tff(14326,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(Y4!52))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14325, 33])).
% 5.85/5.86 tff(14327,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14326])).
% 5.85/5.86 tff(14328,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14327, 30])).
% 5.85/5.86 tff(14329,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14328])).
% 5.85/5.86 tff(14330,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14329, 39])).
% 5.85/5.86 tff(14331,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14330])).
% 5.85/5.86 tff(14332,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14331, 53])).
% 5.85/5.86 tff(14333,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14332])).
% 5.85/5.86 tff(14334,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14333, 45])).
% 5.85/5.86 tff(14335,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14334])).
% 5.85/5.86 tff(14336,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14335, 28])).
% 5.85/5.86 tff(14337,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14336])).
% 5.85/5.86 tff(14338,plain,
% 5.85/5.86 (NSY4!20 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[601, 14337, 42])).
% 5.85/5.86 tff(14339,plain,
% 5.85/5.86 (pred(NSY4!20) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14338])).
% 5.85/5.86 tff(14340,plain,
% 5.85/5.86 (pred(NSY4!20) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14339, 22])).
% 5.85/5.86 tff(14341,plain,
% 5.85/5.86 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14340, 14316])).
% 5.85/5.86 tff(14342,plain,
% 5.85/5.86 (sum(pred(NSY4!20), succ(NPY4!22)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14341, 57])).
% 5.85/5.86 tff(14343,plain,
% 5.85/5.86 (sum(pred(Y3!54), succ(X3!55)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14186, 14268])).
% 5.85/5.86 tff(14344,plain,
% 5.85/5.86 (sum(pred(Y3!54), succ(X3!55)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14343, 57])).
% 5.85/5.86 tff(14345,plain,
% 5.85/5.86 (sum(pred(X3!55), succ(Y3!54)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14242, 14210])).
% 5.85/5.86 tff(14346,plain,
% 5.85/5.86 (sum(pred(X3!55), succ(Y3!54)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14345, 57])).
% 5.85/5.86 tff(14347,plain,
% 5.85/5.86 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n0, n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14346, 14344])).
% 5.85/5.86 tff(14348,plain,
% 5.85/5.86 (X4!53 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[438, 14347, 59])).
% 5.85/5.86 tff(14349,plain,
% 5.85/5.86 (pred(X4!53) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14348])).
% 5.85/5.86 tff(14350,plain,
% 5.85/5.86 (pred(X4!53) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14349, 22])).
% 5.85/5.86 tff(14351,plain,
% 5.85/5.86 (pred(pred(X4!53)) = pred(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14350])).
% 5.85/5.86 tff(14352,plain,
% 5.85/5.86 (pred(pred(X4!53)) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14351, 21])).
% 5.85/5.86 tff(14353,plain,
% 5.85/5.86 (pred(pred(pred(X4!53))) = pred(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14352])).
% 5.85/5.86 tff(14354,plain,
% 5.85/5.86 (pred(pred(pred(X4!53))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14353, 20])).
% 5.85/5.86 tff(14355,plain,
% 5.85/5.86 (pred(pred(pred(pred(X4!53)))) = pred(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14354])).
% 5.85/5.86 tff(14356,plain,
% 5.85/5.86 (pred(pred(pred(pred(X4!53)))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14355, 19])).
% 5.85/5.86 tff(14357,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(X4!53))))) = pred(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14356])).
% 5.85/5.86 tff(14358,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(X4!53))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14357, 18])).
% 5.85/5.86 tff(14359,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14358])).
% 5.85/5.86 tff(14360,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14359, 17])).
% 5.85/5.86 tff(14361,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14360])).
% 5.85/5.86 tff(14362,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14361, 16])).
% 5.85/5.86 tff(14363,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14362])).
% 5.85/5.86 tff(14364,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14363, 15])).
% 5.85/5.86 tff(14365,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14364])).
% 5.85/5.86 tff(14366,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14365, 25])).
% 5.85/5.86 tff(14367,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14366])).
% 5.85/5.86 tff(14368,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14367, 24])).
% 5.85/5.86 tff(14369,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14368])).
% 5.85/5.86 tff(14370,plain,
% 5.85/5.86 (NPX4!23 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[626, 14369, 23])).
% 5.85/5.86 tff(14371,plain,
% 5.85/5.86 (succ(NPX4!23) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14370])).
% 5.85/5.86 tff(14372,plain,
% 5.85/5.86 (succ(NPX4!23) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14371, 58])).
% 5.85/5.86 tff(14373,plain,
% 5.85/5.86 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n1, n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14372, 14342])).
% 5.85/5.86 tff(14374,plain,
% 5.85/5.86 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14373, 56])).
% 5.85/5.86 tff(14375,plain,
% 5.85/5.86 (succ(X4!53) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14348])).
% 5.85/5.86 tff(14376,plain,
% 5.85/5.86 (succ(X4!53) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14375, 58])).
% 5.85/5.86 tff(14377,plain,
% 5.85/5.86 (succ(succ(X4!53)) = succ(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14376])).
% 5.85/5.86 tff(14378,plain,
% 5.85/5.86 (succ(succ(X4!53)) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14377, 36])).
% 5.85/5.86 tff(14379,plain,
% 5.85/5.86 (succ(succ(succ(X4!53))) = succ(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14378])).
% 5.85/5.86 tff(14380,plain,
% 5.85/5.86 (succ(succ(succ(X4!53))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14379, 48])).
% 5.85/5.86 tff(14381,plain,
% 5.85/5.86 (succ(succ(succ(succ(X4!53)))) = succ(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14380])).
% 5.85/5.86 tff(14382,plain,
% 5.85/5.86 (succ(succ(succ(succ(X4!53)))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14381, 14])).
% 5.85/5.86 tff(14383,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(X4!53))))) = succ(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14382])).
% 5.85/5.86 tff(14384,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(X4!53))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14383, 33])).
% 5.85/5.86 tff(14385,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14384])).
% 5.85/5.86 tff(14386,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14385, 30])).
% 5.85/5.86 tff(14387,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14386])).
% 5.85/5.86 tff(14388,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14387, 39])).
% 5.85/5.86 tff(14389,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14388])).
% 5.85/5.86 tff(14390,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14389, 53])).
% 5.85/5.86 tff(14391,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14390])).
% 5.85/5.86 tff(14392,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14391, 45])).
% 5.85/5.86 tff(14393,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14392])).
% 5.85/5.86 tff(14394,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14393, 28])).
% 5.85/5.86 tff(14395,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14394])).
% 5.85/5.86 tff(14396,plain,
% 5.85/5.86 (NSX4!21 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[651, 14395, 42])).
% 5.85/5.86 tff(14397,plain,
% 5.85/5.86 (pred(NSX4!21) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14396])).
% 5.85/5.86 tff(14398,plain,
% 5.85/5.86 (pred(NSX4!21) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14397, 22])).
% 5.85/5.86 tff(14399,plain,
% 5.85/5.86 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14398, 14374])).
% 5.85/5.86 tff(14400,plain,
% 5.85/5.86 (Y5!50 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[656, 14399, 57])).
% 5.85/5.86 tff(14401,plain,
% 5.85/5.86 (pred(Y5!50) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14400])).
% 5.85/5.86 tff(14402,plain,
% 5.85/5.86 (pred(Y5!50) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14401, 22])).
% 5.85/5.86 tff(14403,plain,
% 5.85/5.86 (pred(pred(Y5!50)) = pred(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14402])).
% 5.85/5.86 tff(14404,plain,
% 5.85/5.86 (pred(pred(Y5!50)) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14403, 21])).
% 5.85/5.86 tff(14405,plain,
% 5.85/5.86 (pred(pred(pred(Y5!50))) = pred(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14404])).
% 5.85/5.86 tff(14406,plain,
% 5.85/5.86 (pred(pred(pred(Y5!50))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14405, 20])).
% 5.85/5.86 tff(14407,plain,
% 5.85/5.86 (pred(pred(pred(pred(Y5!50)))) = pred(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14406])).
% 5.85/5.86 tff(14408,plain,
% 5.85/5.86 (pred(pred(pred(pred(Y5!50)))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14407, 19])).
% 5.85/5.86 tff(14409,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14408])).
% 5.85/5.86 tff(14410,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(Y5!50))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14409, 18])).
% 5.85/5.86 tff(14411,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14410])).
% 5.85/5.86 tff(14412,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14411, 17])).
% 5.85/5.86 tff(14413,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14412])).
% 5.85/5.86 tff(14414,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14413, 16])).
% 5.85/5.86 tff(14415,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14414])).
% 5.85/5.86 tff(14416,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14415, 15])).
% 5.85/5.86 tff(14417,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14416])).
% 5.85/5.86 tff(14418,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14417, 25])).
% 5.85/5.86 tff(14419,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14418])).
% 5.85/5.86 tff(14420,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14419, 24])).
% 5.85/5.86 tff(14421,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14420])).
% 5.85/5.86 tff(14422,plain,
% 5.85/5.86 (NPY5!18 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[694, 14421, 23])).
% 5.85/5.86 tff(14423,plain,
% 5.85/5.86 (succ(NPY5!18) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14422])).
% 5.85/5.86 tff(14424,plain,
% 5.85/5.86 (succ(NPY5!18) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14423, 58])).
% 5.85/5.86 tff(14425,plain,
% 5.85/5.86 (succ(Y5!50) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14400])).
% 5.85/5.86 tff(14426,plain,
% 5.85/5.86 (succ(Y5!50) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14425, 58])).
% 5.85/5.86 tff(14427,plain,
% 5.85/5.86 (succ(succ(Y5!50)) = succ(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14426])).
% 5.85/5.86 tff(14428,plain,
% 5.85/5.86 (succ(succ(Y5!50)) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14427, 36])).
% 5.85/5.86 tff(14429,plain,
% 5.85/5.86 (succ(succ(succ(Y5!50))) = succ(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14428])).
% 5.85/5.86 tff(14430,plain,
% 5.85/5.86 (succ(succ(succ(Y5!50))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14429, 48])).
% 5.85/5.86 tff(14431,plain,
% 5.85/5.86 (succ(succ(succ(succ(Y5!50)))) = succ(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14430])).
% 5.85/5.86 tff(14432,plain,
% 5.85/5.86 (succ(succ(succ(succ(Y5!50)))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14431, 14])).
% 5.85/5.86 tff(14433,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14432])).
% 5.85/5.86 tff(14434,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(Y5!50))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14433, 33])).
% 5.85/5.86 tff(14435,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14434])).
% 5.85/5.86 tff(14436,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14435, 30])).
% 5.85/5.86 tff(14437,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14436])).
% 5.85/5.86 tff(14438,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14437, 39])).
% 5.85/5.86 tff(14439,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14438])).
% 5.85/5.86 tff(14440,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14439, 53])).
% 5.85/5.86 tff(14441,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14440])).
% 5.85/5.86 tff(14442,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14441, 45])).
% 5.85/5.86 tff(14443,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14442])).
% 5.85/5.86 tff(14444,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14443, 28])).
% 5.85/5.86 tff(14445,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14444])).
% 5.85/5.86 tff(14446,plain,
% 5.85/5.86 (NSY5!16 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[717, 14445, 42])).
% 5.85/5.86 tff(14447,plain,
% 5.85/5.86 (pred(NSY5!16) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14446])).
% 5.85/5.86 tff(14448,plain,
% 5.85/5.86 (pred(NSY5!16) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14447, 22])).
% 5.85/5.86 tff(14449,plain,
% 5.85/5.86 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14448, 14424])).
% 5.85/5.86 tff(14450,plain,
% 5.85/5.86 (sum(pred(NSY5!16), succ(NPY5!18)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14449, 57])).
% 5.85/5.86 tff(14451,plain,
% 5.85/5.86 (sum(pred(Y4!52), succ(X4!53)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14294, 14376])).
% 5.85/5.86 tff(14452,plain,
% 5.85/5.86 (sum(pred(Y4!52), succ(X4!53)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14451, 57])).
% 5.85/5.86 tff(14453,plain,
% 5.85/5.86 (sum(pred(X4!53), succ(Y4!52)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14350, 14318])).
% 5.85/5.86 tff(14454,plain,
% 5.85/5.86 (sum(pred(X4!53), succ(Y4!52)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14453, 57])).
% 5.85/5.86 tff(14455,plain,
% 5.85/5.86 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n0, n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14454, 14452])).
% 5.85/5.86 tff(14456,plain,
% 5.85/5.86 (X5!51 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[553, 14455, 59])).
% 5.85/5.86 tff(14457,plain,
% 5.85/5.86 (pred(X5!51) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14456])).
% 5.85/5.86 tff(14458,plain,
% 5.85/5.86 (pred(X5!51) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14457, 22])).
% 5.85/5.86 tff(14459,plain,
% 5.85/5.86 (pred(pred(X5!51)) = pred(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14458])).
% 5.85/5.86 tff(14460,plain,
% 5.85/5.86 (pred(pred(X5!51)) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14459, 21])).
% 5.85/5.86 tff(14461,plain,
% 5.85/5.86 (pred(pred(pred(X5!51))) = pred(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14460])).
% 5.85/5.86 tff(14462,plain,
% 5.85/5.86 (pred(pred(pred(X5!51))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14461, 20])).
% 5.85/5.86 tff(14463,plain,
% 5.85/5.86 (pred(pred(pred(pred(X5!51)))) = pred(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14462])).
% 5.85/5.86 tff(14464,plain,
% 5.85/5.86 (pred(pred(pred(pred(X5!51)))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14463, 19])).
% 5.85/5.86 tff(14465,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(X5!51))))) = pred(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14464])).
% 5.85/5.86 tff(14466,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(X5!51))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14465, 18])).
% 5.85/5.86 tff(14467,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14466])).
% 5.85/5.86 tff(14468,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14467, 17])).
% 5.85/5.86 tff(14469,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14468])).
% 5.85/5.86 tff(14470,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14469, 16])).
% 5.85/5.86 tff(14471,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14470])).
% 5.85/5.86 tff(14472,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14471, 15])).
% 5.85/5.86 tff(14473,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14472])).
% 5.85/5.86 tff(14474,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14473, 25])).
% 5.85/5.86 tff(14475,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14474])).
% 5.85/5.86 tff(14476,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14475, 24])).
% 5.85/5.86 tff(14477,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14476])).
% 5.85/5.86 tff(14478,plain,
% 5.85/5.86 (NPX5!19 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[742, 14477, 23])).
% 5.85/5.86 tff(14479,plain,
% 5.85/5.86 (succ(NPX5!19) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14478])).
% 5.85/5.86 tff(14480,plain,
% 5.85/5.86 (succ(NPX5!19) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14479, 58])).
% 5.85/5.86 tff(14481,plain,
% 5.85/5.86 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n1, n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14480, 14450])).
% 5.85/5.86 tff(14482,plain,
% 5.85/5.86 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14481, 56])).
% 5.85/5.86 tff(14483,plain,
% 5.85/5.86 (succ(X5!51) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14456])).
% 5.85/5.86 tff(14484,plain,
% 5.85/5.86 (succ(X5!51) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14483, 58])).
% 5.85/5.86 tff(14485,plain,
% 5.85/5.86 (succ(succ(X5!51)) = succ(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14484])).
% 5.85/5.86 tff(14486,plain,
% 5.85/5.86 (succ(succ(X5!51)) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14485, 36])).
% 5.85/5.86 tff(14487,plain,
% 5.85/5.86 (succ(succ(succ(X5!51))) = succ(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14486])).
% 5.85/5.86 tff(14488,plain,
% 5.85/5.86 (succ(succ(succ(X5!51))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14487, 48])).
% 5.85/5.86 tff(14489,plain,
% 5.85/5.86 (succ(succ(succ(succ(X5!51)))) = succ(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14488])).
% 5.85/5.86 tff(14490,plain,
% 5.85/5.86 (succ(succ(succ(succ(X5!51)))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14489, 14])).
% 5.85/5.86 tff(14491,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(X5!51))))) = succ(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14490])).
% 5.85/5.86 tff(14492,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(X5!51))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14491, 33])).
% 5.85/5.86 tff(14493,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14492])).
% 5.85/5.86 tff(14494,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14493, 30])).
% 5.85/5.86 tff(14495,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14494])).
% 5.85/5.86 tff(14496,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14495, 39])).
% 5.85/5.86 tff(14497,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14496])).
% 5.85/5.86 tff(14498,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14497, 53])).
% 5.85/5.86 tff(14499,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14498])).
% 5.85/5.86 tff(14500,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14499, 45])).
% 5.85/5.86 tff(14501,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14500])).
% 5.85/5.86 tff(14502,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14501, 28])).
% 5.85/5.86 tff(14503,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14502])).
% 5.85/5.86 tff(14504,plain,
% 5.85/5.86 (NSX5!17 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[767, 14503, 42])).
% 5.85/5.86 tff(14505,plain,
% 5.85/5.86 (pred(NSX5!17) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14504])).
% 5.85/5.86 tff(14506,plain,
% 5.85/5.86 (pred(NSX5!17) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14505, 22])).
% 5.85/5.86 tff(14507,plain,
% 5.85/5.86 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14506, 14482])).
% 5.85/5.86 tff(14508,plain,
% 5.85/5.86 (Y6!48 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[772, 14507, 57])).
% 5.85/5.86 tff(14509,plain,
% 5.85/5.86 (pred(Y6!48) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14508])).
% 5.85/5.86 tff(14510,plain,
% 5.85/5.86 (pred(Y6!48) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14509, 22])).
% 5.85/5.86 tff(14511,plain,
% 5.85/5.86 (pred(pred(Y6!48)) = pred(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14510])).
% 5.85/5.86 tff(14512,plain,
% 5.85/5.86 (pred(pred(Y6!48)) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14511, 21])).
% 5.85/5.86 tff(14513,plain,
% 5.85/5.86 (pred(pred(pred(Y6!48))) = pred(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14512])).
% 5.85/5.86 tff(14514,plain,
% 5.85/5.86 (pred(pred(pred(Y6!48))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14513, 20])).
% 5.85/5.86 tff(14515,plain,
% 5.85/5.86 (pred(pred(pred(pred(Y6!48)))) = pred(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14514])).
% 5.85/5.86 tff(14516,plain,
% 5.85/5.86 (pred(pred(pred(pred(Y6!48)))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14515, 19])).
% 5.85/5.86 tff(14517,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14516])).
% 5.85/5.86 tff(14518,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(Y6!48))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14517, 18])).
% 5.85/5.86 tff(14519,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14518])).
% 5.85/5.86 tff(14520,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14519, 17])).
% 5.85/5.86 tff(14521,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14520])).
% 5.85/5.86 tff(14522,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14521, 16])).
% 5.85/5.86 tff(14523,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14522])).
% 5.85/5.86 tff(14524,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14523, 15])).
% 5.85/5.86 tff(14525,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14524])).
% 5.85/5.86 tff(14526,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14525, 25])).
% 5.85/5.86 tff(14527,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14526])).
% 5.85/5.86 tff(14528,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14527, 24])).
% 5.85/5.86 tff(14529,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14528])).
% 5.85/5.86 tff(14530,plain,
% 5.85/5.86 (NPY6!14 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[1465, 14529, 23])).
% 5.85/5.86 tff(14531,plain,
% 5.85/5.86 (succ(NPY6!14) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14530])).
% 5.85/5.86 tff(14532,plain,
% 5.85/5.86 (succ(NPY6!14) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14531, 58])).
% 5.85/5.86 tff(14533,plain,
% 5.85/5.86 (succ(Y6!48) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14508])).
% 5.85/5.86 tff(14534,plain,
% 5.85/5.86 (succ(Y6!48) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14533, 58])).
% 5.85/5.86 tff(14535,plain,
% 5.85/5.86 (succ(succ(Y6!48)) = succ(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14534])).
% 5.85/5.86 tff(14536,plain,
% 5.85/5.86 (succ(succ(Y6!48)) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14535, 36])).
% 5.85/5.86 tff(14537,plain,
% 5.85/5.86 (succ(succ(succ(Y6!48))) = succ(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14536])).
% 5.85/5.86 tff(14538,plain,
% 5.85/5.86 (succ(succ(succ(Y6!48))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14537, 48])).
% 5.85/5.86 tff(14539,plain,
% 5.85/5.86 (succ(succ(succ(succ(Y6!48)))) = succ(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14538])).
% 5.85/5.86 tff(14540,plain,
% 5.85/5.86 (succ(succ(succ(succ(Y6!48)))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14539, 14])).
% 5.85/5.86 tff(14541,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14540])).
% 5.85/5.86 tff(14542,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(Y6!48))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14541, 33])).
% 5.85/5.86 tff(14543,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14542])).
% 5.85/5.86 tff(14544,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14543, 30])).
% 5.85/5.86 tff(14545,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14544])).
% 5.85/5.86 tff(14546,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14545, 39])).
% 5.85/5.86 tff(14547,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14546])).
% 5.85/5.86 tff(14548,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14547, 53])).
% 5.85/5.86 tff(14549,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14548])).
% 5.85/5.86 tff(14550,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14549, 45])).
% 5.85/5.86 tff(14551,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14550])).
% 5.85/5.86 tff(14552,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14551, 28])).
% 5.85/5.86 tff(14553,plain,
% 5.85/5.86 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14552])).
% 5.85/5.86 tff(14554,plain,
% 5.85/5.86 (NSY6!12 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[1490, 14553, 42])).
% 5.85/5.86 tff(14555,plain,
% 5.85/5.86 (pred(NSY6!12) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14554])).
% 5.85/5.86 tff(14556,plain,
% 5.85/5.86 (pred(NSY6!12) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14555, 22])).
% 5.85/5.86 tff(14557,plain,
% 5.85/5.86 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14556, 14532])).
% 5.85/5.86 tff(14558,plain,
% 5.85/5.86 (sum(pred(NSY6!12), succ(NPY6!14)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14557, 57])).
% 5.85/5.86 tff(14559,plain,
% 5.85/5.86 (sum(pred(Y5!50), succ(X5!51)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14402, 14484])).
% 5.85/5.86 tff(14560,plain,
% 5.85/5.86 (sum(pred(Y5!50), succ(X5!51)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14559, 57])).
% 5.85/5.86 tff(14561,plain,
% 5.85/5.86 (sum(pred(X5!51), succ(Y5!50)) = sum(n10, n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14458, 14426])).
% 5.85/5.86 tff(14562,plain,
% 5.85/5.86 (sum(pred(X5!51), succ(Y5!50)) = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[14561, 57])).
% 5.85/5.86 tff(14563,plain,
% 5.85/5.86 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n0, n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14562, 14560])).
% 5.85/5.86 tff(14564,plain,
% 5.85/5.86 (X6!49 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[669, 14563, 59])).
% 5.85/5.86 tff(14565,plain,
% 5.85/5.86 (pred(X6!49) = pred(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14564])).
% 5.85/5.86 tff(14566,plain,
% 5.85/5.86 (pred(X6!49) = n10),
% 5.85/5.86 inference(transitivity,[status(thm)],[14565, 22])).
% 5.85/5.86 tff(14567,plain,
% 5.85/5.86 (pred(pred(X6!49)) = pred(n10)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14566])).
% 5.85/5.86 tff(14568,plain,
% 5.85/5.86 (pred(pred(X6!49)) = n9),
% 5.85/5.86 inference(transitivity,[status(thm)],[14567, 21])).
% 5.85/5.86 tff(14569,plain,
% 5.85/5.86 (pred(pred(pred(X6!49))) = pred(n9)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14568])).
% 5.85/5.86 tff(14570,plain,
% 5.85/5.86 (pred(pred(pred(X6!49))) = n8),
% 5.85/5.86 inference(transitivity,[status(thm)],[14569, 20])).
% 5.85/5.86 tff(14571,plain,
% 5.85/5.86 (pred(pred(pred(pred(X6!49)))) = pred(n8)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14570])).
% 5.85/5.86 tff(14572,plain,
% 5.85/5.86 (pred(pred(pred(pred(X6!49)))) = n7),
% 5.85/5.86 inference(transitivity,[status(thm)],[14571, 19])).
% 5.85/5.86 tff(14573,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(X6!49))))) = pred(n7)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14572])).
% 5.85/5.86 tff(14574,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(X6!49))))) = n6),
% 5.85/5.86 inference(transitivity,[status(thm)],[14573, 18])).
% 5.85/5.86 tff(14575,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n6)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14574])).
% 5.85/5.86 tff(14576,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n5),
% 5.85/5.86 inference(transitivity,[status(thm)],[14575, 17])).
% 5.85/5.86 tff(14577,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n5)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14576])).
% 5.85/5.86 tff(14578,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n4),
% 5.85/5.86 inference(transitivity,[status(thm)],[14577, 16])).
% 5.85/5.86 tff(14579,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n4)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14578])).
% 5.85/5.86 tff(14580,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n3),
% 5.85/5.86 inference(transitivity,[status(thm)],[14579, 15])).
% 5.85/5.86 tff(14581,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n3)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14580])).
% 5.85/5.86 tff(14582,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n2),
% 5.85/5.86 inference(transitivity,[status(thm)],[14581, 25])).
% 5.85/5.86 tff(14583,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n2)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14582])).
% 5.85/5.86 tff(14584,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14583, 24])).
% 5.85/5.86 tff(14585,plain,
% 5.85/5.86 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n1)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14584])).
% 5.85/5.86 tff(14586,plain,
% 5.85/5.86 (NPX6!15 = n0),
% 5.85/5.86 inference(transitivity,[status(thm)],[1523, 14585, 23])).
% 5.85/5.86 tff(14587,plain,
% 5.85/5.86 (succ(NPX6!15) = succ(n0)),
% 5.85/5.86 inference(monotonicity,[status(thm)],[14586])).
% 5.85/5.86 tff(14588,plain,
% 5.85/5.86 (succ(NPX6!15) = n1),
% 5.85/5.86 inference(transitivity,[status(thm)],[14587, 58])).
% 5.85/5.87 tff(14589,plain,
% 5.85/5.87 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n1, n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14588, 14558])).
% 5.85/5.87 tff(14590,plain,
% 5.85/5.87 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14589, 56])).
% 5.85/5.87 tff(14591,plain,
% 5.85/5.87 (succ(X6!49) = succ(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14564])).
% 5.85/5.87 tff(14592,plain,
% 5.85/5.87 (succ(X6!49) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14591, 58])).
% 5.85/5.87 tff(14593,plain,
% 5.85/5.87 (succ(succ(X6!49)) = succ(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14592])).
% 5.85/5.87 tff(14594,plain,
% 5.85/5.87 (succ(succ(X6!49)) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14593, 36])).
% 5.85/5.87 tff(14595,plain,
% 5.85/5.87 (succ(succ(succ(X6!49))) = succ(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14594])).
% 5.85/5.87 tff(14596,plain,
% 5.85/5.87 (succ(succ(succ(X6!49))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14595, 48])).
% 5.85/5.87 tff(14597,plain,
% 5.85/5.87 (succ(succ(succ(succ(X6!49)))) = succ(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14596])).
% 5.85/5.87 tff(14598,plain,
% 5.85/5.87 (succ(succ(succ(succ(X6!49)))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14597, 14])).
% 5.85/5.87 tff(14599,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(X6!49))))) = succ(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14598])).
% 5.85/5.87 tff(14600,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(X6!49))))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14599, 33])).
% 5.85/5.87 tff(14601,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14600])).
% 5.85/5.87 tff(14602,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14601, 30])).
% 5.85/5.87 tff(14603,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14602])).
% 5.85/5.87 tff(14604,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14603, 39])).
% 5.85/5.87 tff(14605,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14604])).
% 5.85/5.87 tff(14606,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14605, 53])).
% 5.85/5.87 tff(14607,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14606])).
% 5.85/5.87 tff(14608,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14607, 45])).
% 5.85/5.87 tff(14609,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14608])).
% 5.85/5.87 tff(14610,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14609, 28])).
% 5.85/5.87 tff(14611,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14610])).
% 5.85/5.87 tff(14612,plain,
% 5.85/5.87 (NSX6!13 = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[1550, 14611, 42])).
% 5.85/5.87 tff(14613,plain,
% 5.85/5.87 (pred(NSX6!13) = pred(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14612])).
% 5.85/5.87 tff(14614,plain,
% 5.85/5.87 (pred(NSX6!13) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14613, 22])).
% 5.85/5.87 tff(14615,plain,
% 5.85/5.87 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n10, n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14614, 14590])).
% 5.85/5.87 tff(14616,plain,
% 5.85/5.87 (sum(n10, n1) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.85/5.87 inference(symmetry,[status(thm)],[14615])).
% 5.85/5.87 tff(14617,plain,
% 5.85/5.87 (sum(pred(Y6!48), succ(X6!49)) = sum(n10, n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14510, 14592])).
% 5.85/5.87 tff(14618,plain,
% 5.85/5.87 (sum(pred(Y6!48), succ(X6!49)) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14617, 57])).
% 5.85/5.87 tff(14619,plain,
% 5.85/5.87 (sum(pred(X6!49), succ(Y6!48)) = sum(n10, n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14566, 14534])).
% 5.85/5.87 tff(14620,plain,
% 5.85/5.87 (sum(pred(X6!49), succ(Y6!48)) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14619, 57])).
% 5.85/5.87 tff(14621,plain,
% 5.85/5.87 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n0, n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14620, 14618])).
% 5.85/5.87 tff(14622,plain,
% 5.85/5.87 (X7!47 = Y7!46),
% 5.85/5.87 inference(transitivity,[status(thm)],[785, 14621, 59, 5850, 14616, 794])).
% 5.85/5.87 tff(14623,plain,
% 5.85/5.87 ($false),
% 5.85/5.87 inference(unit_resolution,[status(thm)],[792, 14622])).
% 5.85/5.87 tff(14624,plain,((~(Y0!60 = n7)) | (X7!47 = Y7!46) | (~(X0!61 = n4))), inference(lemma,lemma(discharge,[]))).
% 5.85/5.87 tff(14625,plain,
% 5.85/5.87 (~(Y0!60 = n7)),
% 5.85/5.87 inference(unit_resolution,[status(thm)],[14624, 11930, 792])).
% 5.85/5.87 tff(14626,assumption,(Y0!60 = n2), introduced(assumption)).
% 5.85/5.87 tff(14627,plain,
% 5.85/5.87 (pred(Y0!60) = pred(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14626])).
% 5.85/5.87 tff(14628,plain,
% 5.85/5.87 (pred(Y0!60) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14627, 24])).
% 5.85/5.87 tff(14629,plain,
% 5.85/5.87 (pred(pred(Y0!60)) = pred(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14628])).
% 5.85/5.87 tff(14630,plain,
% 5.85/5.87 (pred(pred(Y0!60)) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14629, 23])).
% 5.85/5.87 tff(14631,plain,
% 5.85/5.87 (pred(pred(pred(Y0!60))) = pred(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14630])).
% 5.85/5.87 tff(14632,plain,
% 5.85/5.87 (pred(pred(pred(Y0!60))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14631, 22])).
% 5.85/5.87 tff(14633,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y0!60)))) = pred(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14632])).
% 5.85/5.87 tff(14634,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y0!60)))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14633, 21])).
% 5.85/5.87 tff(14635,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14634])).
% 5.85/5.87 tff(14636,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y0!60))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14635, 20])).
% 5.85/5.87 tff(14637,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14636])).
% 5.85/5.87 tff(14638,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14637, 19])).
% 5.85/5.87 tff(14639,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14638])).
% 5.85/5.87 tff(14640,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14639, 18])).
% 5.85/5.87 tff(14641,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14640])).
% 5.85/5.87 tff(14642,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14641, 17])).
% 5.85/5.87 tff(14643,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14642])).
% 5.85/5.87 tff(14644,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14643, 16])).
% 5.85/5.87 tff(14645,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14644])).
% 5.85/5.87 tff(14646,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14645, 15])).
% 5.85/5.87 tff(14647,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14646])).
% 5.85/5.87 tff(14648,plain,
% 5.85/5.87 (NPY0!38 = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[118, 14647, 25])).
% 5.85/5.87 tff(14649,plain,
% 5.85/5.87 (succ(NPY0!38) = succ(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14648])).
% 5.85/5.87 tff(14650,plain,
% 5.85/5.87 (succ(NPY0!38) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14649, 48])).
% 5.85/5.87 tff(14651,plain,
% 5.85/5.87 (succ(Y0!60) = succ(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14626])).
% 5.85/5.87 tff(14652,plain,
% 5.85/5.87 (succ(Y0!60) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14651, 48])).
% 5.85/5.87 tff(14653,plain,
% 5.85/5.87 (succ(succ(Y0!60)) = succ(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14652])).
% 5.85/5.87 tff(14654,plain,
% 5.85/5.87 (succ(succ(Y0!60)) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14653, 14])).
% 5.85/5.87 tff(14655,plain,
% 5.85/5.87 (succ(succ(succ(Y0!60))) = succ(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14654])).
% 5.85/5.87 tff(14656,plain,
% 5.85/5.87 (succ(succ(succ(Y0!60))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14655, 33])).
% 5.85/5.87 tff(14657,plain,
% 5.85/5.87 (succ(succ(succ(succ(Y0!60)))) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14656])).
% 5.85/5.87 tff(14658,plain,
% 5.85/5.87 (succ(succ(succ(succ(Y0!60)))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14657, 30])).
% 5.85/5.87 tff(14659,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14658])).
% 5.85/5.87 tff(14660,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(Y0!60))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14659, 39])).
% 5.85/5.87 tff(14661,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14660])).
% 5.85/5.87 tff(14662,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14661, 53])).
% 5.85/5.87 tff(14663,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14662])).
% 5.85/5.87 tff(14664,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14663, 45])).
% 5.85/5.87 tff(14665,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14664])).
% 5.85/5.87 tff(14666,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14665, 28])).
% 5.85/5.87 tff(14667,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14666])).
% 5.85/5.87 tff(14668,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14667, 42])).
% 5.85/5.87 tff(14669,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14668])).
% 5.85/5.87 tff(14670,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14669, 58])).
% 5.85/5.87 tff(14671,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14670])).
% 5.85/5.87 tff(14672,plain,
% 5.85/5.87 (NSY0!36 = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[141, 14671, 36])).
% 5.85/5.87 tff(14673,plain,
% 5.85/5.87 (pred(NSY0!36) = pred(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14672])).
% 5.85/5.87 tff(14674,plain,
% 5.85/5.87 (pred(NSY0!36) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14673, 24])).
% 5.85/5.87 tff(14675,plain,
% 5.85/5.87 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n1, n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14674, 14650])).
% 5.85/5.87 tff(14676,plain,
% 5.85/5.87 (sum(pred(NSY0!36), succ(NPY0!38)) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14675, 47])).
% 5.85/5.87 tff(14677,plain,
% 5.85/5.87 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n7, n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[874, 14676])).
% 5.85/5.87 tff(14678,plain,
% 5.85/5.87 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14677, 5147])).
% 5.85/5.87 tff(14679,plain,
% 5.85/5.87 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n5, n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[900, 14678])).
% 5.85/5.87 tff(14680,plain,
% 5.85/5.87 (Y1!58 = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[196, 14679, 4537])).
% 5.85/5.87 tff(14681,plain,
% 5.85/5.87 (pred(Y1!58) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14680])).
% 5.85/5.87 tff(14682,plain,
% 5.85/5.87 (pred(Y1!58) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14681, 16])).
% 5.85/5.87 tff(14683,plain,
% 5.85/5.87 (pred(pred(Y1!58)) = pred(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14682])).
% 5.85/5.87 tff(14684,plain,
% 5.85/5.87 (pred(pred(Y1!58)) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14683, 15])).
% 5.85/5.87 tff(14685,plain,
% 5.85/5.87 (pred(pred(pred(Y1!58))) = pred(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14684])).
% 5.85/5.87 tff(14686,plain,
% 5.85/5.87 (pred(pred(pred(Y1!58))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14685, 25])).
% 5.85/5.87 tff(14687,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y1!58)))) = pred(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14686])).
% 5.85/5.87 tff(14688,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y1!58)))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14687, 24])).
% 5.85/5.87 tff(14689,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14688])).
% 5.85/5.87 tff(14690,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y1!58))))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14689, 23])).
% 5.85/5.87 tff(14691,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14690])).
% 5.85/5.87 tff(14692,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14691, 22])).
% 5.85/5.87 tff(14693,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14692])).
% 5.85/5.87 tff(14694,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14693, 21])).
% 5.85/5.87 tff(14695,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14694])).
% 5.85/5.87 tff(14696,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14695, 20])).
% 5.85/5.87 tff(14697,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14696])).
% 5.85/5.87 tff(14698,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14697, 19])).
% 5.85/5.87 tff(14699,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14698])).
% 5.85/5.87 tff(14700,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14699, 18])).
% 5.85/5.87 tff(14701,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14700])).
% 5.85/5.87 tff(14702,plain,
% 5.85/5.87 (NPY1!34 = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[232, 14701, 17])).
% 5.85/5.87 tff(14703,plain,
% 5.85/5.87 (succ(NPY1!34) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14702])).
% 5.85/5.87 tff(14704,plain,
% 5.85/5.87 (succ(NPY1!34) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14703, 30])).
% 5.85/5.87 tff(14705,plain,
% 5.85/5.87 (succ(Y1!58) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14680])).
% 5.85/5.87 tff(14706,plain,
% 5.85/5.87 (succ(Y1!58) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14705, 30])).
% 5.85/5.87 tff(14707,plain,
% 5.85/5.87 (succ(succ(Y1!58)) = succ(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14706])).
% 5.85/5.87 tff(14708,plain,
% 5.85/5.87 (succ(succ(Y1!58)) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14707, 39])).
% 5.85/5.87 tff(14709,plain,
% 5.85/5.87 (succ(succ(succ(Y1!58))) = succ(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14708])).
% 5.85/5.87 tff(14710,plain,
% 5.85/5.87 (succ(succ(succ(Y1!58))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14709, 53])).
% 5.85/5.87 tff(14711,plain,
% 5.85/5.87 (succ(succ(succ(succ(Y1!58)))) = succ(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14710])).
% 5.85/5.87 tff(14712,plain,
% 5.85/5.87 (succ(succ(succ(succ(Y1!58)))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14711, 45])).
% 5.85/5.87 tff(14713,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14712])).
% 5.85/5.87 tff(14714,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(Y1!58))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14713, 28])).
% 5.85/5.87 tff(14715,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14714])).
% 5.85/5.87 tff(14716,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14715, 42])).
% 5.85/5.87 tff(14717,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14716])).
% 5.85/5.87 tff(14718,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14717, 58])).
% 5.85/5.87 tff(14719,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14718])).
% 5.85/5.87 tff(14720,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14719, 36])).
% 5.85/5.87 tff(14721,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14720])).
% 5.85/5.87 tff(14722,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14721, 48])).
% 5.85/5.87 tff(14723,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14722])).
% 5.85/5.87 tff(14724,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14723, 14])).
% 5.85/5.87 tff(14725,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14724])).
% 5.85/5.87 tff(14726,plain,
% 5.85/5.87 (NSY1!32 = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[255, 14725, 33])).
% 5.85/5.87 tff(14727,plain,
% 5.85/5.87 (pred(NSY1!32) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14726])).
% 5.85/5.87 tff(14728,plain,
% 5.85/5.87 (pred(NSY1!32) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14727, 16])).
% 5.85/5.87 tff(14729,plain,
% 5.85/5.87 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n4, n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14728, 14704])).
% 5.85/5.87 tff(14730,plain,
% 5.85/5.87 (sum(pred(NSY1!32), succ(NPY1!34)) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14729, 12])).
% 5.85/5.87 tff(14731,plain,
% 5.85/5.87 (sum(pred(Y0!60), succ(X0!61)) = sum(n1, n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14628, 878])).
% 5.85/5.87 tff(14732,plain,
% 5.85/5.87 (sum(pred(Y0!60), succ(X0!61)) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14731, 791])).
% 5.85/5.87 tff(14733,plain,
% 5.85/5.87 (sum(pred(X0!61), succ(Y0!60)) = sum(n5, n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[852, 14652])).
% 5.85/5.87 tff(14734,plain,
% 5.85/5.87 (sum(pred(X0!61), succ(Y0!60)) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14733, 13964])).
% 5.85/5.87 tff(14735,plain,
% 5.85/5.87 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n8, n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14734, 14732])).
% 5.85/5.87 tff(14736,plain,
% 5.85/5.87 (X1!59 = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[93, 14735, 31])).
% 5.85/5.87 tff(14737,plain,
% 5.85/5.87 (pred(X1!59) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14736])).
% 5.85/5.87 tff(14738,plain,
% 5.85/5.87 (pred(X1!59) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14737, 16])).
% 5.85/5.87 tff(14739,plain,
% 5.85/5.87 (pred(pred(X1!59)) = pred(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14738])).
% 5.85/5.87 tff(14740,plain,
% 5.85/5.87 (pred(pred(X1!59)) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14739, 15])).
% 5.85/5.87 tff(14741,plain,
% 5.85/5.87 (pred(pred(pred(X1!59))) = pred(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14740])).
% 5.85/5.87 tff(14742,plain,
% 5.85/5.87 (pred(pred(pred(X1!59))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14741, 25])).
% 5.85/5.87 tff(14743,plain,
% 5.85/5.87 (pred(pred(pred(pred(X1!59)))) = pred(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14742])).
% 5.85/5.87 tff(14744,plain,
% 5.85/5.87 (pred(pred(pred(pred(X1!59)))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14743, 24])).
% 5.85/5.87 tff(14745,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(X1!59))))) = pred(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14744])).
% 5.85/5.87 tff(14746,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(X1!59))))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14745, 23])).
% 5.85/5.87 tff(14747,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14746])).
% 5.85/5.87 tff(14748,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14747, 22])).
% 5.85/5.87 tff(14749,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14748])).
% 5.85/5.87 tff(14750,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14749, 21])).
% 5.85/5.87 tff(14751,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14750])).
% 5.85/5.87 tff(14752,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14751, 20])).
% 5.85/5.87 tff(14753,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14752])).
% 5.85/5.87 tff(14754,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14753, 19])).
% 5.85/5.87 tff(14755,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14754])).
% 5.85/5.87 tff(14756,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14755, 18])).
% 5.85/5.87 tff(14757,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14756])).
% 5.85/5.87 tff(14758,plain,
% 5.85/5.87 (NPX1!35 = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[280, 14757, 17])).
% 5.85/5.87 tff(14759,plain,
% 5.85/5.87 (succ(NPX1!35) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14758])).
% 5.85/5.87 tff(14760,plain,
% 5.85/5.87 (succ(NPX1!35) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14759, 30])).
% 5.85/5.87 tff(14761,plain,
% 5.85/5.87 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n6, n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14760, 14730])).
% 5.85/5.87 tff(14762,plain,
% 5.85/5.87 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14761, 674])).
% 5.85/5.87 tff(14763,plain,
% 5.85/5.87 (succ(X1!59) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14736])).
% 5.85/5.87 tff(14764,plain,
% 5.85/5.87 (succ(X1!59) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14763, 30])).
% 5.85/5.87 tff(14765,plain,
% 5.85/5.87 (succ(succ(X1!59)) = succ(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14764])).
% 5.85/5.87 tff(14766,plain,
% 5.85/5.87 (succ(succ(X1!59)) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14765, 39])).
% 5.85/5.87 tff(14767,plain,
% 5.85/5.87 (succ(succ(succ(X1!59))) = succ(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14766])).
% 5.85/5.87 tff(14768,plain,
% 5.85/5.87 (succ(succ(succ(X1!59))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14767, 53])).
% 5.85/5.87 tff(14769,plain,
% 5.85/5.87 (succ(succ(succ(succ(X1!59)))) = succ(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14768])).
% 5.85/5.87 tff(14770,plain,
% 5.85/5.87 (succ(succ(succ(succ(X1!59)))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14769, 45])).
% 5.85/5.87 tff(14771,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(X1!59))))) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14770])).
% 5.85/5.87 tff(14772,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(X1!59))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14771, 28])).
% 5.85/5.87 tff(14773,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14772])).
% 5.85/5.87 tff(14774,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14773, 42])).
% 5.85/5.87 tff(14775,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14774])).
% 5.85/5.87 tff(14776,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14775, 58])).
% 5.85/5.87 tff(14777,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14776])).
% 5.85/5.87 tff(14778,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14777, 36])).
% 5.85/5.87 tff(14779,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14778])).
% 5.85/5.87 tff(14780,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14779, 48])).
% 5.85/5.87 tff(14781,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14780])).
% 5.85/5.87 tff(14782,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14781, 14])).
% 5.85/5.87 tff(14783,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14782])).
% 5.85/5.87 tff(14784,plain,
% 5.85/5.87 (NSX1!33 = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[305, 14783, 33])).
% 5.85/5.87 tff(14785,plain,
% 5.85/5.87 (pred(NSX1!33) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14784])).
% 5.85/5.87 tff(14786,plain,
% 5.85/5.87 (pred(NSX1!33) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14785, 16])).
% 5.85/5.87 tff(14787,plain,
% 5.85/5.87 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n4, n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14786, 14762])).
% 5.85/5.87 tff(14788,plain,
% 5.85/5.87 (Y2!56 = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[310, 14787, 673])).
% 5.85/5.87 tff(14789,plain,
% 5.85/5.87 (pred(Y2!56) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14788])).
% 5.85/5.87 tff(14790,plain,
% 5.85/5.87 (pred(Y2!56) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14789, 20])).
% 5.85/5.87 tff(14791,plain,
% 5.85/5.87 (pred(pred(Y2!56)) = pred(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14790])).
% 5.85/5.87 tff(14792,plain,
% 5.85/5.87 (pred(pred(Y2!56)) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14791, 19])).
% 5.85/5.87 tff(14793,plain,
% 5.85/5.87 (pred(pred(pred(Y2!56))) = pred(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14792])).
% 5.85/5.87 tff(14794,plain,
% 5.85/5.87 (pred(pred(pred(Y2!56))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14793, 18])).
% 5.85/5.87 tff(14795,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y2!56)))) = pred(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14794])).
% 5.85/5.87 tff(14796,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y2!56)))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14795, 17])).
% 5.85/5.87 tff(14797,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14796])).
% 5.85/5.87 tff(14798,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y2!56))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14797, 16])).
% 5.85/5.87 tff(14799,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14798])).
% 5.85/5.87 tff(14800,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14799, 15])).
% 5.85/5.87 tff(14801,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14800])).
% 5.85/5.87 tff(14802,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14801, 25])).
% 5.85/5.87 tff(14803,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14802])).
% 5.85/5.87 tff(14804,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14803, 24])).
% 5.85/5.87 tff(14805,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14804])).
% 5.85/5.87 tff(14806,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14805, 23])).
% 5.85/5.87 tff(14807,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14806])).
% 5.85/5.87 tff(14808,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14807, 22])).
% 5.85/5.87 tff(14809,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14808])).
% 5.85/5.87 tff(14810,plain,
% 5.85/5.87 (NPY2!30 = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[347, 14809, 21])).
% 5.85/5.87 tff(14811,plain,
% 5.85/5.87 (succ(NPY2!30) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14810])).
% 5.85/5.87 tff(14812,plain,
% 5.85/5.87 (succ(NPY2!30) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14811, 28])).
% 5.85/5.87 tff(14813,plain,
% 5.85/5.87 (succ(Y2!56) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14788])).
% 5.85/5.87 tff(14814,plain,
% 5.85/5.87 (succ(Y2!56) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14813, 28])).
% 5.85/5.87 tff(14815,plain,
% 5.85/5.87 (succ(succ(Y2!56)) = succ(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14814])).
% 5.85/5.87 tff(14816,plain,
% 5.85/5.87 (succ(succ(Y2!56)) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14815, 42])).
% 5.85/5.87 tff(14817,plain,
% 5.85/5.87 (succ(succ(succ(Y2!56))) = succ(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14816])).
% 5.85/5.87 tff(14818,plain,
% 5.85/5.87 (succ(succ(succ(Y2!56))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14817, 58])).
% 5.85/5.87 tff(14819,plain,
% 5.85/5.87 (succ(succ(succ(succ(Y2!56)))) = succ(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14818])).
% 5.85/5.87 tff(14820,plain,
% 5.85/5.87 (succ(succ(succ(succ(Y2!56)))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14819, 36])).
% 5.85/5.87 tff(14821,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14820])).
% 5.85/5.87 tff(14822,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(Y2!56))))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14821, 48])).
% 5.85/5.87 tff(14823,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14822])).
% 5.85/5.87 tff(14824,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14823, 14])).
% 5.85/5.87 tff(14825,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14824])).
% 5.85/5.87 tff(14826,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14825, 33])).
% 5.85/5.87 tff(14827,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14826])).
% 5.85/5.87 tff(14828,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14827, 30])).
% 5.85/5.87 tff(14829,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14828])).
% 5.85/5.87 tff(14830,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14829, 39])).
% 5.85/5.87 tff(14831,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14830])).
% 5.85/5.87 tff(14832,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14831, 53])).
% 5.85/5.87 tff(14833,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14832])).
% 5.85/5.87 tff(14834,plain,
% 5.85/5.87 (NSY2!28 = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[370, 14833, 45])).
% 5.85/5.87 tff(14835,plain,
% 5.85/5.87 (pred(NSY2!28) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14834])).
% 5.85/5.87 tff(14836,plain,
% 5.85/5.87 (pred(NSY2!28) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14835, 20])).
% 5.85/5.87 tff(14837,plain,
% 5.85/5.87 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n8, n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14836, 14812])).
% 5.85/5.87 tff(14838,plain,
% 5.85/5.87 (sum(pred(NSY2!28), succ(NPY2!30)) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14837, 27])).
% 5.85/5.87 tff(14839,plain,
% 5.85/5.87 (sum(pred(Y1!58), succ(X1!59)) = sum(n4, n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14682, 14764])).
% 5.85/5.87 tff(14840,plain,
% 5.85/5.87 (sum(pred(Y1!58), succ(X1!59)) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14839, 12])).
% 5.85/5.87 tff(14841,plain,
% 5.85/5.87 (sum(pred(X1!59), succ(Y1!58)) = sum(n4, n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14738, 14706])).
% 5.85/5.87 tff(14842,plain,
% 5.85/5.87 (sum(pred(X1!59), succ(Y1!58)) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14841, 12])).
% 5.85/5.87 tff(14843,plain,
% 5.85/5.87 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n10, n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14842, 14840])).
% 5.85/5.87 tff(14844,plain,
% 5.85/5.87 (X2!57 = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[209, 14843, 29])).
% 5.85/5.87 tff(14845,plain,
% 5.85/5.87 (pred(X2!57) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14844])).
% 5.85/5.87 tff(14846,plain,
% 5.85/5.87 (pred(X2!57) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14845, 20])).
% 5.85/5.87 tff(14847,plain,
% 5.85/5.87 (pred(pred(X2!57)) = pred(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14846])).
% 5.85/5.87 tff(14848,plain,
% 5.85/5.87 (pred(pred(X2!57)) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14847, 19])).
% 5.85/5.87 tff(14849,plain,
% 5.85/5.87 (pred(pred(pred(X2!57))) = pred(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14848])).
% 5.85/5.87 tff(14850,plain,
% 5.85/5.87 (pred(pred(pred(X2!57))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14849, 18])).
% 5.85/5.87 tff(14851,plain,
% 5.85/5.87 (pred(pred(pred(pred(X2!57)))) = pred(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14850])).
% 5.85/5.87 tff(14852,plain,
% 5.85/5.87 (pred(pred(pred(pred(X2!57)))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14851, 17])).
% 5.85/5.87 tff(14853,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(X2!57))))) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14852])).
% 5.85/5.87 tff(14854,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(X2!57))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14853, 16])).
% 5.85/5.87 tff(14855,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14854])).
% 5.85/5.87 tff(14856,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14855, 15])).
% 5.85/5.87 tff(14857,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14856])).
% 5.85/5.87 tff(14858,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14857, 25])).
% 5.85/5.87 tff(14859,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14858])).
% 5.85/5.87 tff(14860,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14859, 24])).
% 5.85/5.87 tff(14861,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14860])).
% 5.85/5.87 tff(14862,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14861, 23])).
% 5.85/5.87 tff(14863,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14862])).
% 5.85/5.87 tff(14864,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14863, 22])).
% 5.85/5.87 tff(14865,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14864])).
% 5.85/5.87 tff(14866,plain,
% 5.85/5.87 (NPX2!31 = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[395, 14865, 21])).
% 5.85/5.87 tff(14867,plain,
% 5.85/5.87 (succ(NPX2!31) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14866])).
% 5.85/5.87 tff(14868,plain,
% 5.85/5.87 (succ(NPX2!31) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14867, 28])).
% 5.85/5.87 tff(14869,plain,
% 5.85/5.87 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n10, n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14868, 14838])).
% 5.85/5.87 tff(14870,plain,
% 5.85/5.87 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14869, 69])).
% 5.85/5.87 tff(14871,plain,
% 5.85/5.87 (succ(X2!57) = succ(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14844])).
% 5.85/5.87 tff(14872,plain,
% 5.85/5.87 (succ(X2!57) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14871, 28])).
% 5.85/5.87 tff(14873,plain,
% 5.85/5.87 (succ(succ(X2!57)) = succ(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14872])).
% 5.85/5.87 tff(14874,plain,
% 5.85/5.87 (succ(succ(X2!57)) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14873, 42])).
% 5.85/5.87 tff(14875,plain,
% 5.85/5.87 (succ(succ(succ(X2!57))) = succ(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14874])).
% 5.85/5.87 tff(14876,plain,
% 5.85/5.87 (succ(succ(succ(X2!57))) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14875, 58])).
% 5.85/5.87 tff(14877,plain,
% 5.85/5.87 (succ(succ(succ(succ(X2!57)))) = succ(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14876])).
% 5.85/5.87 tff(14878,plain,
% 5.85/5.87 (succ(succ(succ(succ(X2!57)))) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14877, 36])).
% 5.85/5.87 tff(14879,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(X2!57))))) = succ(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14878])).
% 5.85/5.87 tff(14880,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(X2!57))))) = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[14879, 48])).
% 5.85/5.87 tff(14881,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14880])).
% 5.85/5.87 tff(14882,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14881, 14])).
% 5.85/5.87 tff(14883,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14882])).
% 5.85/5.87 tff(14884,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14883, 33])).
% 5.85/5.87 tff(14885,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14884])).
% 5.85/5.87 tff(14886,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14885, 30])).
% 5.85/5.87 tff(14887,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14886])).
% 5.85/5.87 tff(14888,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14887, 39])).
% 5.85/5.87 tff(14889,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14888])).
% 5.85/5.87 tff(14890,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14889, 53])).
% 5.85/5.87 tff(14891,plain,
% 5.85/5.87 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14890])).
% 5.85/5.87 tff(14892,plain,
% 5.85/5.87 (NSX2!29 = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[420, 14891, 45])).
% 5.85/5.87 tff(14893,plain,
% 5.85/5.87 (pred(NSX2!29) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14892])).
% 5.85/5.87 tff(14894,plain,
% 5.85/5.87 (pred(NSX2!29) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14893, 20])).
% 5.85/5.87 tff(14895,plain,
% 5.85/5.87 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n8, n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14894, 14870])).
% 5.85/5.87 tff(14896,plain,
% 5.85/5.87 (Y3!54 = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[425, 14895, 98])).
% 5.85/5.87 tff(14897,plain,
% 5.85/5.87 (pred(Y3!54) = pred(n3)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14896])).
% 5.85/5.87 tff(14898,plain,
% 5.85/5.87 (pred(Y3!54) = n2),
% 5.85/5.87 inference(transitivity,[status(thm)],[14897, 25])).
% 5.85/5.87 tff(14899,plain,
% 5.85/5.87 (pred(pred(Y3!54)) = pred(n2)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14898])).
% 5.85/5.87 tff(14900,plain,
% 5.85/5.87 (pred(pred(Y3!54)) = n1),
% 5.85/5.87 inference(transitivity,[status(thm)],[14899, 24])).
% 5.85/5.87 tff(14901,plain,
% 5.85/5.87 (pred(pred(pred(Y3!54))) = pred(n1)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14900])).
% 5.85/5.87 tff(14902,plain,
% 5.85/5.87 (pred(pred(pred(Y3!54))) = n0),
% 5.85/5.87 inference(transitivity,[status(thm)],[14901, 23])).
% 5.85/5.87 tff(14903,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y3!54)))) = pred(n0)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14902])).
% 5.85/5.87 tff(14904,plain,
% 5.85/5.87 (pred(pred(pred(pred(Y3!54)))) = n10),
% 5.85/5.87 inference(transitivity,[status(thm)],[14903, 22])).
% 5.85/5.87 tff(14905,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n10)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14904])).
% 5.85/5.87 tff(14906,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(Y3!54))))) = n9),
% 5.85/5.87 inference(transitivity,[status(thm)],[14905, 21])).
% 5.85/5.87 tff(14907,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n9)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14906])).
% 5.85/5.87 tff(14908,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n8),
% 5.85/5.87 inference(transitivity,[status(thm)],[14907, 20])).
% 5.85/5.87 tff(14909,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n8)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14908])).
% 5.85/5.87 tff(14910,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n7),
% 5.85/5.87 inference(transitivity,[status(thm)],[14909, 19])).
% 5.85/5.87 tff(14911,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n7)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14910])).
% 5.85/5.87 tff(14912,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n6),
% 5.85/5.87 inference(transitivity,[status(thm)],[14911, 18])).
% 5.85/5.87 tff(14913,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n6)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14912])).
% 5.85/5.87 tff(14914,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n5),
% 5.85/5.87 inference(transitivity,[status(thm)],[14913, 17])).
% 5.85/5.87 tff(14915,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n5)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14914])).
% 5.85/5.87 tff(14916,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n4),
% 5.85/5.87 inference(transitivity,[status(thm)],[14915, 16])).
% 5.85/5.87 tff(14917,plain,
% 5.85/5.87 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n4)),
% 5.85/5.87 inference(monotonicity,[status(thm)],[14916])).
% 5.85/5.87 tff(14918,plain,
% 5.85/5.87 (NPY3!26 = n3),
% 5.85/5.87 inference(transitivity,[status(thm)],[462, 14917, 15])).
% 5.85/5.88 tff(14919,plain,
% 5.85/5.88 (succ(NPY3!26) = succ(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14918])).
% 5.85/5.88 tff(14920,plain,
% 5.85/5.88 (succ(NPY3!26) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[14919, 14])).
% 5.85/5.88 tff(14921,plain,
% 5.85/5.88 (succ(Y3!54) = succ(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14896])).
% 5.85/5.88 tff(14922,plain,
% 5.85/5.88 (succ(Y3!54) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[14921, 14])).
% 5.85/5.88 tff(14923,plain,
% 5.85/5.88 (succ(succ(Y3!54)) = succ(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14922])).
% 5.85/5.88 tff(14924,plain,
% 5.85/5.88 (succ(succ(Y3!54)) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[14923, 33])).
% 5.85/5.88 tff(14925,plain,
% 5.85/5.88 (succ(succ(succ(Y3!54))) = succ(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14924])).
% 5.85/5.88 tff(14926,plain,
% 5.85/5.88 (succ(succ(succ(Y3!54))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[14925, 30])).
% 5.85/5.88 tff(14927,plain,
% 5.85/5.88 (succ(succ(succ(succ(Y3!54)))) = succ(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14926])).
% 5.85/5.88 tff(14928,plain,
% 5.85/5.88 (succ(succ(succ(succ(Y3!54)))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[14927, 39])).
% 5.85/5.88 tff(14929,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14928])).
% 5.85/5.88 tff(14930,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(Y3!54))))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[14929, 53])).
% 5.85/5.88 tff(14931,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14930])).
% 5.85/5.88 tff(14932,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[14931, 45])).
% 5.85/5.88 tff(14933,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14932])).
% 5.85/5.88 tff(14934,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[14933, 28])).
% 5.85/5.88 tff(14935,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14934])).
% 5.85/5.88 tff(14936,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[14935, 42])).
% 5.85/5.88 tff(14937,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14936])).
% 5.85/5.88 tff(14938,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[14937, 58])).
% 5.85/5.88 tff(14939,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14938])).
% 5.85/5.88 tff(14940,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[14939, 36])).
% 5.85/5.88 tff(14941,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14940])).
% 5.85/5.88 tff(14942,plain,
% 5.85/5.88 (NSY3!24 = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[485, 14941, 48])).
% 5.85/5.88 tff(14943,plain,
% 5.85/5.88 (pred(NSY3!24) = pred(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14942])).
% 5.85/5.88 tff(14944,plain,
% 5.85/5.88 (pred(NSY3!24) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[14943, 25])).
% 5.85/5.88 tff(14945,plain,
% 5.85/5.88 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n2, n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14944, 14920])).
% 5.85/5.88 tff(14946,plain,
% 5.85/5.88 (sum(pred(NSY3!24), succ(NPY3!26)) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[14945, 13])).
% 5.85/5.88 tff(14947,plain,
% 5.85/5.88 (sum(pred(Y2!56), succ(X2!57)) = sum(n8, n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14790, 14872])).
% 5.85/5.88 tff(14948,plain,
% 5.85/5.88 (sum(pred(Y2!56), succ(X2!57)) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[14947, 27])).
% 5.85/5.88 tff(14949,plain,
% 5.85/5.88 (sum(pred(X2!57), succ(Y2!56)) = sum(n8, n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14846, 14814])).
% 5.85/5.88 tff(14950,plain,
% 5.85/5.88 (sum(pred(X2!57), succ(Y2!56)) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[14949, 27])).
% 5.85/5.88 tff(14951,plain,
% 5.85/5.88 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n7, n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14950, 14948])).
% 5.85/5.88 tff(14952,plain,
% 5.85/5.88 (X3!55 = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[323, 14951, 26])).
% 5.85/5.88 tff(14953,plain,
% 5.85/5.88 (pred(X3!55) = pred(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14952])).
% 5.85/5.88 tff(14954,plain,
% 5.85/5.88 (pred(X3!55) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[14953, 25])).
% 5.85/5.88 tff(14955,plain,
% 5.85/5.88 (pred(pred(X3!55)) = pred(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14954])).
% 5.85/5.88 tff(14956,plain,
% 5.85/5.88 (pred(pred(X3!55)) = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[14955, 24])).
% 5.85/5.88 tff(14957,plain,
% 5.85/5.88 (pred(pred(pred(X3!55))) = pred(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14956])).
% 5.85/5.88 tff(14958,plain,
% 5.85/5.88 (pred(pred(pred(X3!55))) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[14957, 23])).
% 5.85/5.88 tff(14959,plain,
% 5.85/5.88 (pred(pred(pred(pred(X3!55)))) = pred(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14958])).
% 5.85/5.88 tff(14960,plain,
% 5.85/5.88 (pred(pred(pred(pred(X3!55)))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[14959, 22])).
% 5.85/5.88 tff(14961,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(X3!55))))) = pred(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14960])).
% 5.85/5.88 tff(14962,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(X3!55))))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[14961, 21])).
% 5.85/5.88 tff(14963,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14962])).
% 5.85/5.88 tff(14964,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[14963, 20])).
% 5.85/5.88 tff(14965,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14964])).
% 5.85/5.88 tff(14966,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[14965, 19])).
% 5.85/5.88 tff(14967,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14966])).
% 5.85/5.88 tff(14968,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[14967, 18])).
% 5.85/5.88 tff(14969,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14968])).
% 5.85/5.88 tff(14970,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[14969, 17])).
% 5.85/5.88 tff(14971,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14970])).
% 5.85/5.88 tff(14972,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[14971, 16])).
% 5.85/5.88 tff(14973,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14972])).
% 5.85/5.88 tff(14974,plain,
% 5.85/5.88 (NPX3!27 = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[510, 14973, 15])).
% 5.85/5.88 tff(14975,plain,
% 5.85/5.88 (succ(NPX3!27) = succ(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14974])).
% 5.85/5.88 tff(14976,plain,
% 5.85/5.88 (succ(NPX3!27) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[14975, 14])).
% 5.85/5.88 tff(14977,plain,
% 5.85/5.88 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n4, n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14976, 14946])).
% 5.85/5.88 tff(14978,plain,
% 5.85/5.88 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[14977, 12])).
% 5.85/5.88 tff(14979,plain,
% 5.85/5.88 (succ(X3!55) = succ(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14952])).
% 5.85/5.88 tff(14980,plain,
% 5.85/5.88 (succ(X3!55) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[14979, 14])).
% 5.85/5.88 tff(14981,plain,
% 5.85/5.88 (succ(succ(X3!55)) = succ(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14980])).
% 5.85/5.88 tff(14982,plain,
% 5.85/5.88 (succ(succ(X3!55)) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[14981, 33])).
% 5.85/5.88 tff(14983,plain,
% 5.85/5.88 (succ(succ(succ(X3!55))) = succ(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14982])).
% 5.85/5.88 tff(14984,plain,
% 5.85/5.88 (succ(succ(succ(X3!55))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[14983, 30])).
% 5.85/5.88 tff(14985,plain,
% 5.85/5.88 (succ(succ(succ(succ(X3!55)))) = succ(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14984])).
% 5.85/5.88 tff(14986,plain,
% 5.85/5.88 (succ(succ(succ(succ(X3!55)))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[14985, 39])).
% 5.85/5.88 tff(14987,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(X3!55))))) = succ(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14986])).
% 5.85/5.88 tff(14988,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(X3!55))))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[14987, 53])).
% 5.85/5.88 tff(14989,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14988])).
% 5.85/5.88 tff(14990,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[14989, 45])).
% 5.85/5.88 tff(14991,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14990])).
% 5.85/5.88 tff(14992,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[14991, 28])).
% 5.85/5.88 tff(14993,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14992])).
% 5.85/5.88 tff(14994,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[14993, 42])).
% 5.85/5.88 tff(14995,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14994])).
% 5.85/5.88 tff(14996,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[14995, 58])).
% 5.85/5.88 tff(14997,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14996])).
% 5.85/5.88 tff(14998,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[14997, 36])).
% 5.85/5.88 tff(14999,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14998])).
% 5.85/5.88 tff(15000,plain,
% 5.85/5.88 (NSX3!25 = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[535, 14999, 48])).
% 5.85/5.88 tff(15001,plain,
% 5.85/5.88 (pred(NSX3!25) = pred(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15000])).
% 5.85/5.88 tff(15002,plain,
% 5.85/5.88 (pred(NSX3!25) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15001, 25])).
% 5.85/5.88 tff(15003,plain,
% 5.85/5.88 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n2, n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15002, 14978])).
% 5.85/5.88 tff(15004,plain,
% 5.85/5.88 (Y4!52 = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[540, 15003, 327])).
% 5.85/5.88 tff(15005,plain,
% 5.85/5.88 (pred(Y4!52) = pred(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15004])).
% 5.85/5.88 tff(15006,plain,
% 5.85/5.88 (pred(Y4!52) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15005, 23])).
% 5.85/5.88 tff(15007,plain,
% 5.85/5.88 (pred(pred(Y4!52)) = pred(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15006])).
% 5.85/5.88 tff(15008,plain,
% 5.85/5.88 (pred(pred(Y4!52)) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[15007, 22])).
% 5.85/5.88 tff(15009,plain,
% 5.85/5.88 (pred(pred(pred(Y4!52))) = pred(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15008])).
% 5.85/5.88 tff(15010,plain,
% 5.85/5.88 (pred(pred(pred(Y4!52))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[15009, 21])).
% 5.85/5.88 tff(15011,plain,
% 5.85/5.88 (pred(pred(pred(pred(Y4!52)))) = pred(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15010])).
% 5.85/5.88 tff(15012,plain,
% 5.85/5.88 (pred(pred(pred(pred(Y4!52)))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[15011, 20])).
% 5.85/5.88 tff(15013,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15012])).
% 5.85/5.88 tff(15014,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(Y4!52))))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[15013, 19])).
% 5.85/5.88 tff(15015,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15014])).
% 5.85/5.88 tff(15016,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15015, 18])).
% 5.85/5.88 tff(15017,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15016])).
% 5.85/5.88 tff(15018,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[15017, 17])).
% 5.85/5.88 tff(15019,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15018])).
% 5.85/5.88 tff(15020,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[15019, 16])).
% 5.85/5.88 tff(15021,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15020])).
% 5.85/5.88 tff(15022,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[15021, 15])).
% 5.85/5.88 tff(15023,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15022])).
% 5.85/5.88 tff(15024,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15023, 25])).
% 5.85/5.88 tff(15025,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15024])).
% 5.85/5.88 tff(15026,plain,
% 5.85/5.88 (NPY4!22 = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[578, 15025, 24])).
% 5.85/5.88 tff(15027,plain,
% 5.85/5.88 (succ(NPY4!22) = succ(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15026])).
% 5.85/5.88 tff(15028,plain,
% 5.85/5.88 (succ(NPY4!22) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15027, 36])).
% 5.85/5.88 tff(15029,plain,
% 5.85/5.88 (succ(Y4!52) = succ(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15004])).
% 5.85/5.88 tff(15030,plain,
% 5.85/5.88 (succ(Y4!52) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15029, 36])).
% 5.85/5.88 tff(15031,plain,
% 5.85/5.88 (succ(succ(Y4!52)) = succ(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15030])).
% 5.85/5.88 tff(15032,plain,
% 5.85/5.88 (succ(succ(Y4!52)) = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[15031, 48])).
% 5.85/5.88 tff(15033,plain,
% 5.85/5.88 (succ(succ(succ(Y4!52))) = succ(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15032])).
% 5.85/5.88 tff(15034,plain,
% 5.85/5.88 (succ(succ(succ(Y4!52))) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[15033, 14])).
% 5.85/5.88 tff(15035,plain,
% 5.85/5.88 (succ(succ(succ(succ(Y4!52)))) = succ(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15034])).
% 5.85/5.88 tff(15036,plain,
% 5.85/5.88 (succ(succ(succ(succ(Y4!52)))) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[15035, 33])).
% 5.85/5.88 tff(15037,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15036])).
% 5.85/5.88 tff(15038,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(Y4!52))))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15037, 30])).
% 5.85/5.88 tff(15039,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15038])).
% 5.85/5.88 tff(15040,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[15039, 39])).
% 5.85/5.88 tff(15041,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15040])).
% 5.85/5.88 tff(15042,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[15041, 53])).
% 5.85/5.88 tff(15043,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15042])).
% 5.85/5.88 tff(15044,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[15043, 45])).
% 5.85/5.88 tff(15045,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15044])).
% 5.85/5.88 tff(15046,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[15045, 28])).
% 5.85/5.88 tff(15047,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15046])).
% 5.85/5.88 tff(15048,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15047, 42])).
% 5.85/5.88 tff(15049,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15048])).
% 5.85/5.88 tff(15050,plain,
% 5.85/5.88 (NSY4!20 = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[601, 15049, 58])).
% 5.85/5.88 tff(15051,plain,
% 5.85/5.88 (pred(NSY4!20) = pred(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15050])).
% 5.85/5.88 tff(15052,plain,
% 5.85/5.88 (pred(NSY4!20) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15051, 23])).
% 5.85/5.88 tff(15053,plain,
% 5.85/5.88 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n0, n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15052, 15028])).
% 5.85/5.88 tff(15054,plain,
% 5.85/5.88 (sum(pred(NSY4!20), succ(NPY4!22)) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15053, 35])).
% 5.85/5.88 tff(15055,plain,
% 5.85/5.88 (sum(pred(Y3!54), succ(X3!55)) = sum(n2, n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14898, 14980])).
% 5.85/5.88 tff(15056,plain,
% 5.85/5.88 (sum(pred(Y3!54), succ(X3!55)) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15055, 13])).
% 5.85/5.88 tff(15057,plain,
% 5.85/5.88 (sum(pred(X3!55), succ(Y3!54)) = sum(n2, n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[14954, 14922])).
% 5.85/5.88 tff(15058,plain,
% 5.85/5.88 (sum(pred(X3!55), succ(Y3!54)) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15057, 13])).
% 5.85/5.88 tff(15059,plain,
% 5.85/5.88 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n6, n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15058, 15056])).
% 5.85/5.88 tff(15060,plain,
% 5.85/5.88 (X4!53 = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[438, 15059, 37])).
% 5.85/5.88 tff(15061,plain,
% 5.85/5.88 (pred(X4!53) = pred(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15060])).
% 5.85/5.88 tff(15062,plain,
% 5.85/5.88 (pred(X4!53) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15061, 23])).
% 5.85/5.88 tff(15063,plain,
% 5.85/5.88 (pred(pred(X4!53)) = pred(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15062])).
% 5.85/5.88 tff(15064,plain,
% 5.85/5.88 (pred(pred(X4!53)) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[15063, 22])).
% 5.85/5.88 tff(15065,plain,
% 5.85/5.88 (pred(pred(pred(X4!53))) = pred(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15064])).
% 5.85/5.88 tff(15066,plain,
% 5.85/5.88 (pred(pred(pred(X4!53))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[15065, 21])).
% 5.85/5.88 tff(15067,plain,
% 5.85/5.88 (pred(pred(pred(pred(X4!53)))) = pred(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15066])).
% 5.85/5.88 tff(15068,plain,
% 5.85/5.88 (pred(pred(pred(pred(X4!53)))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[15067, 20])).
% 5.85/5.88 tff(15069,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(X4!53))))) = pred(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15068])).
% 5.85/5.88 tff(15070,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(X4!53))))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[15069, 19])).
% 5.85/5.88 tff(15071,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15070])).
% 5.85/5.88 tff(15072,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15071, 18])).
% 5.85/5.88 tff(15073,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15072])).
% 5.85/5.88 tff(15074,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[15073, 17])).
% 5.85/5.88 tff(15075,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15074])).
% 5.85/5.88 tff(15076,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[15075, 16])).
% 5.85/5.88 tff(15077,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15076])).
% 5.85/5.88 tff(15078,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[15077, 15])).
% 5.85/5.88 tff(15079,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15078])).
% 5.85/5.88 tff(15080,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15079, 25])).
% 5.85/5.88 tff(15081,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15080])).
% 5.85/5.88 tff(15082,plain,
% 5.85/5.88 (NPX4!23 = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[626, 15081, 24])).
% 5.85/5.88 tff(15083,plain,
% 5.85/5.88 (succ(NPX4!23) = succ(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15082])).
% 5.85/5.88 tff(15084,plain,
% 5.85/5.88 (succ(NPX4!23) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15083, 36])).
% 5.85/5.88 tff(15085,plain,
% 5.85/5.88 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n2, n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15084, 15054])).
% 5.85/5.88 tff(15086,plain,
% 5.85/5.88 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[15085, 34])).
% 5.85/5.88 tff(15087,plain,
% 5.85/5.88 (succ(X4!53) = succ(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15060])).
% 5.85/5.88 tff(15088,plain,
% 5.85/5.88 (succ(X4!53) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15087, 36])).
% 5.85/5.88 tff(15089,plain,
% 5.85/5.88 (succ(succ(X4!53)) = succ(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15088])).
% 5.85/5.88 tff(15090,plain,
% 5.85/5.88 (succ(succ(X4!53)) = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[15089, 48])).
% 5.85/5.88 tff(15091,plain,
% 5.85/5.88 (succ(succ(succ(X4!53))) = succ(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15090])).
% 5.85/5.88 tff(15092,plain,
% 5.85/5.88 (succ(succ(succ(X4!53))) = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[15091, 14])).
% 5.85/5.88 tff(15093,plain,
% 5.85/5.88 (succ(succ(succ(succ(X4!53)))) = succ(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15092])).
% 5.85/5.88 tff(15094,plain,
% 5.85/5.88 (succ(succ(succ(succ(X4!53)))) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[15093, 33])).
% 5.85/5.88 tff(15095,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(X4!53))))) = succ(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15094])).
% 5.85/5.88 tff(15096,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(X4!53))))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15095, 30])).
% 5.85/5.88 tff(15097,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15096])).
% 5.85/5.88 tff(15098,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[15097, 39])).
% 5.85/5.88 tff(15099,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15098])).
% 5.85/5.88 tff(15100,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[15099, 53])).
% 5.85/5.88 tff(15101,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15100])).
% 5.85/5.88 tff(15102,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[15101, 45])).
% 5.85/5.88 tff(15103,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15102])).
% 5.85/5.88 tff(15104,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[15103, 28])).
% 5.85/5.88 tff(15105,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15104])).
% 5.85/5.88 tff(15106,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15105, 42])).
% 5.85/5.88 tff(15107,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15106])).
% 5.85/5.88 tff(15108,plain,
% 5.85/5.88 (NSX4!21 = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[651, 15107, 58])).
% 5.85/5.88 tff(15109,plain,
% 5.85/5.88 (pred(NSX4!21) = pred(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15108])).
% 5.85/5.88 tff(15110,plain,
% 5.85/5.88 (pred(NSX4!21) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15109, 23])).
% 5.85/5.88 tff(15111,plain,
% 5.85/5.88 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n0, n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15110, 15086])).
% 5.85/5.88 tff(15112,plain,
% 5.85/5.88 (Y5!50 = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[656, 15111, 442])).
% 5.85/5.88 tff(15113,plain,
% 5.85/5.88 (pred(Y5!50) = pred(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15112])).
% 5.85/5.88 tff(15114,plain,
% 5.85/5.88 (pred(Y5!50) = n3),
% 5.85/5.88 inference(transitivity,[status(thm)],[15113, 15])).
% 5.85/5.88 tff(15115,plain,
% 5.85/5.88 (pred(pred(Y5!50)) = pred(n3)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15114])).
% 5.85/5.88 tff(15116,plain,
% 5.85/5.88 (pred(pred(Y5!50)) = n2),
% 5.85/5.88 inference(transitivity,[status(thm)],[15115, 25])).
% 5.85/5.88 tff(15117,plain,
% 5.85/5.88 (pred(pred(pred(Y5!50))) = pred(n2)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15116])).
% 5.85/5.88 tff(15118,plain,
% 5.85/5.88 (pred(pred(pred(Y5!50))) = n1),
% 5.85/5.88 inference(transitivity,[status(thm)],[15117, 24])).
% 5.85/5.88 tff(15119,plain,
% 5.85/5.88 (pred(pred(pred(pred(Y5!50)))) = pred(n1)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15118])).
% 5.85/5.88 tff(15120,plain,
% 5.85/5.88 (pred(pred(pred(pred(Y5!50)))) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15119, 23])).
% 5.85/5.88 tff(15121,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n0)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15120])).
% 5.85/5.88 tff(15122,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(Y5!50))))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[15121, 22])).
% 5.85/5.88 tff(15123,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15122])).
% 5.85/5.88 tff(15124,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[15123, 21])).
% 5.85/5.88 tff(15125,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15124])).
% 5.85/5.88 tff(15126,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[15125, 20])).
% 5.85/5.88 tff(15127,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15126])).
% 5.85/5.88 tff(15128,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[15127, 19])).
% 5.85/5.88 tff(15129,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15128])).
% 5.85/5.88 tff(15130,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15129, 18])).
% 5.85/5.88 tff(15131,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15130])).
% 5.85/5.88 tff(15132,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[15131, 17])).
% 5.85/5.88 tff(15133,plain,
% 5.85/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15132])).
% 5.85/5.88 tff(15134,plain,
% 5.85/5.88 (NPY5!18 = n4),
% 5.85/5.88 inference(transitivity,[status(thm)],[694, 15133, 16])).
% 5.85/5.88 tff(15135,plain,
% 5.85/5.88 (succ(NPY5!18) = succ(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15134])).
% 5.85/5.88 tff(15136,plain,
% 5.85/5.88 (succ(NPY5!18) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[15135, 33])).
% 5.85/5.88 tff(15137,plain,
% 5.85/5.88 (succ(Y5!50) = succ(n4)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15112])).
% 5.85/5.88 tff(15138,plain,
% 5.85/5.88 (succ(Y5!50) = n5),
% 5.85/5.88 inference(transitivity,[status(thm)],[15137, 33])).
% 5.85/5.88 tff(15139,plain,
% 5.85/5.88 (succ(succ(Y5!50)) = succ(n5)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15138])).
% 5.85/5.88 tff(15140,plain,
% 5.85/5.88 (succ(succ(Y5!50)) = n6),
% 5.85/5.88 inference(transitivity,[status(thm)],[15139, 30])).
% 5.85/5.88 tff(15141,plain,
% 5.85/5.88 (succ(succ(succ(Y5!50))) = succ(n6)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15140])).
% 5.85/5.88 tff(15142,plain,
% 5.85/5.88 (succ(succ(succ(Y5!50))) = n7),
% 5.85/5.88 inference(transitivity,[status(thm)],[15141, 39])).
% 5.85/5.88 tff(15143,plain,
% 5.85/5.88 (succ(succ(succ(succ(Y5!50)))) = succ(n7)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15142])).
% 5.85/5.88 tff(15144,plain,
% 5.85/5.88 (succ(succ(succ(succ(Y5!50)))) = n8),
% 5.85/5.88 inference(transitivity,[status(thm)],[15143, 53])).
% 5.85/5.88 tff(15145,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n8)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15144])).
% 5.85/5.88 tff(15146,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(Y5!50))))) = n9),
% 5.85/5.88 inference(transitivity,[status(thm)],[15145, 45])).
% 5.85/5.88 tff(15147,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n9)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15146])).
% 5.85/5.88 tff(15148,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n10),
% 5.85/5.88 inference(transitivity,[status(thm)],[15147, 28])).
% 5.85/5.88 tff(15149,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n10)),
% 5.85/5.88 inference(monotonicity,[status(thm)],[15148])).
% 5.85/5.88 tff(15150,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n0),
% 5.85/5.88 inference(transitivity,[status(thm)],[15149, 42])).
% 5.85/5.88 tff(15151,plain,
% 5.85/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n0)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15150])).
% 5.95/5.88 tff(15152,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n1),
% 5.95/5.88 inference(transitivity,[status(thm)],[15151, 58])).
% 5.95/5.88 tff(15153,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n1)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15152])).
% 5.95/5.88 tff(15154,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n2),
% 5.95/5.88 inference(transitivity,[status(thm)],[15153, 36])).
% 5.95/5.88 tff(15155,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15154])).
% 5.95/5.88 tff(15156,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n3),
% 5.95/5.88 inference(transitivity,[status(thm)],[15155, 48])).
% 5.95/5.88 tff(15157,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n3)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15156])).
% 5.95/5.88 tff(15158,plain,
% 5.95/5.88 (NSY5!16 = n4),
% 5.95/5.88 inference(transitivity,[status(thm)],[717, 15157, 14])).
% 5.95/5.88 tff(15159,plain,
% 5.95/5.88 (pred(NSY5!16) = pred(n4)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15158])).
% 5.95/5.88 tff(15160,plain,
% 5.95/5.88 (pred(NSY5!16) = n3),
% 5.95/5.88 inference(transitivity,[status(thm)],[15159, 15])).
% 5.95/5.88 tff(15161,plain,
% 5.95/5.88 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n3, n5)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15160, 15136])).
% 5.95/5.88 tff(15162,plain,
% 5.95/5.88 (sum(pred(NSY5!16), succ(NPY5!18)) = n8),
% 5.95/5.88 inference(transitivity,[status(thm)],[15161, 32])).
% 5.95/5.88 tff(15163,plain,
% 5.95/5.88 (sum(pred(Y4!52), succ(X4!53)) = sum(n0, n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15006, 15088])).
% 5.95/5.88 tff(15164,plain,
% 5.95/5.88 (sum(pred(Y4!52), succ(X4!53)) = n2),
% 5.95/5.88 inference(transitivity,[status(thm)],[15163, 35])).
% 5.95/5.88 tff(15165,plain,
% 5.95/5.88 (sum(pred(X4!53), succ(Y4!52)) = sum(n0, n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15062, 15030])).
% 5.95/5.88 tff(15166,plain,
% 5.95/5.88 (sum(pred(X4!53), succ(Y4!52)) = n2),
% 5.95/5.88 inference(transitivity,[status(thm)],[15165, 35])).
% 5.95/5.88 tff(15167,plain,
% 5.95/5.88 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n2, n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15166, 15164])).
% 5.95/5.88 tff(15168,plain,
% 5.95/5.88 (X5!51 = n4),
% 5.95/5.88 inference(transitivity,[status(thm)],[553, 15167, 34])).
% 5.95/5.88 tff(15169,plain,
% 5.95/5.88 (pred(X5!51) = pred(n4)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15168])).
% 5.95/5.88 tff(15170,plain,
% 5.95/5.88 (pred(X5!51) = n3),
% 5.95/5.88 inference(transitivity,[status(thm)],[15169, 15])).
% 5.95/5.88 tff(15171,plain,
% 5.95/5.88 (pred(pred(X5!51)) = pred(n3)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15170])).
% 5.95/5.88 tff(15172,plain,
% 5.95/5.88 (pred(pred(X5!51)) = n2),
% 5.95/5.88 inference(transitivity,[status(thm)],[15171, 25])).
% 5.95/5.88 tff(15173,plain,
% 5.95/5.88 (pred(pred(pred(X5!51))) = pred(n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15172])).
% 5.95/5.88 tff(15174,plain,
% 5.95/5.88 (pred(pred(pred(X5!51))) = n1),
% 5.95/5.88 inference(transitivity,[status(thm)],[15173, 24])).
% 5.95/5.88 tff(15175,plain,
% 5.95/5.88 (pred(pred(pred(pred(X5!51)))) = pred(n1)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15174])).
% 5.95/5.88 tff(15176,plain,
% 5.95/5.88 (pred(pred(pred(pred(X5!51)))) = n0),
% 5.95/5.88 inference(transitivity,[status(thm)],[15175, 23])).
% 5.95/5.88 tff(15177,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(X5!51))))) = pred(n0)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15176])).
% 5.95/5.88 tff(15178,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(X5!51))))) = n10),
% 5.95/5.88 inference(transitivity,[status(thm)],[15177, 22])).
% 5.95/5.88 tff(15179,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n10)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15178])).
% 5.95/5.88 tff(15180,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n9),
% 5.95/5.88 inference(transitivity,[status(thm)],[15179, 21])).
% 5.95/5.88 tff(15181,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n9)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15180])).
% 5.95/5.88 tff(15182,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n8),
% 5.95/5.88 inference(transitivity,[status(thm)],[15181, 20])).
% 5.95/5.88 tff(15183,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n8)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15182])).
% 5.95/5.88 tff(15184,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n7),
% 5.95/5.88 inference(transitivity,[status(thm)],[15183, 19])).
% 5.95/5.88 tff(15185,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n7)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15184])).
% 5.95/5.88 tff(15186,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n6),
% 5.95/5.88 inference(transitivity,[status(thm)],[15185, 18])).
% 5.95/5.88 tff(15187,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n6)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15186])).
% 5.95/5.88 tff(15188,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n5),
% 5.95/5.88 inference(transitivity,[status(thm)],[15187, 17])).
% 5.95/5.88 tff(15189,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n5)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15188])).
% 5.95/5.88 tff(15190,plain,
% 5.95/5.88 (NPX5!19 = n4),
% 5.95/5.88 inference(transitivity,[status(thm)],[742, 15189, 16])).
% 5.95/5.88 tff(15191,plain,
% 5.95/5.88 (succ(NPX5!19) = succ(n4)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15190])).
% 5.95/5.88 tff(15192,plain,
% 5.95/5.88 (succ(NPX5!19) = n5),
% 5.95/5.88 inference(transitivity,[status(thm)],[15191, 33])).
% 5.95/5.88 tff(15193,plain,
% 5.95/5.88 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n5, n8)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15192, 15162])).
% 5.95/5.88 tff(15194,plain,
% 5.95/5.88 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n2),
% 5.95/5.88 inference(transitivity,[status(thm)],[15193, 558])).
% 5.95/5.88 tff(15195,plain,
% 5.95/5.88 (succ(X5!51) = succ(n4)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15168])).
% 5.95/5.88 tff(15196,plain,
% 5.95/5.88 (succ(X5!51) = n5),
% 5.95/5.88 inference(transitivity,[status(thm)],[15195, 33])).
% 5.95/5.88 tff(15197,plain,
% 5.95/5.88 (succ(succ(X5!51)) = succ(n5)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15196])).
% 5.95/5.88 tff(15198,plain,
% 5.95/5.88 (succ(succ(X5!51)) = n6),
% 5.95/5.88 inference(transitivity,[status(thm)],[15197, 30])).
% 5.95/5.88 tff(15199,plain,
% 5.95/5.88 (succ(succ(succ(X5!51))) = succ(n6)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15198])).
% 5.95/5.88 tff(15200,plain,
% 5.95/5.88 (succ(succ(succ(X5!51))) = n7),
% 5.95/5.88 inference(transitivity,[status(thm)],[15199, 39])).
% 5.95/5.88 tff(15201,plain,
% 5.95/5.88 (succ(succ(succ(succ(X5!51)))) = succ(n7)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15200])).
% 5.95/5.88 tff(15202,plain,
% 5.95/5.88 (succ(succ(succ(succ(X5!51)))) = n8),
% 5.95/5.88 inference(transitivity,[status(thm)],[15201, 53])).
% 5.95/5.88 tff(15203,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(X5!51))))) = succ(n8)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15202])).
% 5.95/5.88 tff(15204,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(X5!51))))) = n9),
% 5.95/5.88 inference(transitivity,[status(thm)],[15203, 45])).
% 5.95/5.88 tff(15205,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n9)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15204])).
% 5.95/5.88 tff(15206,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n10),
% 5.95/5.88 inference(transitivity,[status(thm)],[15205, 28])).
% 5.95/5.88 tff(15207,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n10)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15206])).
% 5.95/5.88 tff(15208,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n0),
% 5.95/5.88 inference(transitivity,[status(thm)],[15207, 42])).
% 5.95/5.88 tff(15209,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n0)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15208])).
% 5.95/5.88 tff(15210,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n1),
% 5.95/5.88 inference(transitivity,[status(thm)],[15209, 58])).
% 5.95/5.88 tff(15211,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n1)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15210])).
% 5.95/5.88 tff(15212,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n2),
% 5.95/5.88 inference(transitivity,[status(thm)],[15211, 36])).
% 5.95/5.88 tff(15213,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15212])).
% 5.95/5.88 tff(15214,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n3),
% 5.95/5.88 inference(transitivity,[status(thm)],[15213, 48])).
% 5.95/5.88 tff(15215,plain,
% 5.95/5.88 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n3)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15214])).
% 5.95/5.88 tff(15216,plain,
% 5.95/5.88 (NSX5!17 = n4),
% 5.95/5.88 inference(transitivity,[status(thm)],[767, 15215, 14])).
% 5.95/5.88 tff(15217,plain,
% 5.95/5.88 (pred(NSX5!17) = pred(n4)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15216])).
% 5.95/5.88 tff(15218,plain,
% 5.95/5.88 (pred(NSX5!17) = n3),
% 5.95/5.88 inference(transitivity,[status(thm)],[15217, 15])).
% 5.95/5.88 tff(15219,plain,
% 5.95/5.88 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n3, n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15218, 15194])).
% 5.95/5.88 tff(15220,plain,
% 5.95/5.88 (Y6!48 = n5),
% 5.95/5.88 inference(transitivity,[status(thm)],[772, 15219, 557])).
% 5.95/5.88 tff(15221,plain,
% 5.95/5.88 (pred(Y6!48) = pred(n5)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15220])).
% 5.95/5.88 tff(15222,plain,
% 5.95/5.88 (pred(Y6!48) = n4),
% 5.95/5.88 inference(transitivity,[status(thm)],[15221, 16])).
% 5.95/5.88 tff(15223,plain,
% 5.95/5.88 (pred(pred(Y6!48)) = pred(n4)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15222])).
% 5.95/5.88 tff(15224,plain,
% 5.95/5.88 (pred(pred(Y6!48)) = n3),
% 5.95/5.88 inference(transitivity,[status(thm)],[15223, 15])).
% 5.95/5.88 tff(15225,plain,
% 5.95/5.88 (pred(pred(pred(Y6!48))) = pred(n3)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15224])).
% 5.95/5.88 tff(15226,plain,
% 5.95/5.88 (pred(pred(pred(Y6!48))) = n2),
% 5.95/5.88 inference(transitivity,[status(thm)],[15225, 25])).
% 5.95/5.88 tff(15227,plain,
% 5.95/5.88 (pred(pred(pred(pred(Y6!48)))) = pred(n2)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15226])).
% 5.95/5.88 tff(15228,plain,
% 5.95/5.88 (pred(pred(pred(pred(Y6!48)))) = n1),
% 5.95/5.88 inference(transitivity,[status(thm)],[15227, 24])).
% 5.95/5.88 tff(15229,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n1)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15228])).
% 5.95/5.88 tff(15230,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(Y6!48))))) = n0),
% 5.95/5.88 inference(transitivity,[status(thm)],[15229, 23])).
% 5.95/5.88 tff(15231,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n0)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15230])).
% 5.95/5.88 tff(15232,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n10),
% 5.95/5.88 inference(transitivity,[status(thm)],[15231, 22])).
% 5.95/5.88 tff(15233,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n10)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15232])).
% 5.95/5.88 tff(15234,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n9),
% 5.95/5.88 inference(transitivity,[status(thm)],[15233, 21])).
% 5.95/5.88 tff(15235,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n9)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15234])).
% 5.95/5.88 tff(15236,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n8),
% 5.95/5.88 inference(transitivity,[status(thm)],[15235, 20])).
% 5.95/5.88 tff(15237,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n8)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15236])).
% 5.95/5.88 tff(15238,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n7),
% 5.95/5.88 inference(transitivity,[status(thm)],[15237, 19])).
% 5.95/5.88 tff(15239,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n7)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15238])).
% 5.95/5.88 tff(15240,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n6),
% 5.95/5.88 inference(transitivity,[status(thm)],[15239, 18])).
% 5.95/5.88 tff(15241,plain,
% 5.95/5.88 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n6)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15240])).
% 5.95/5.88 tff(15242,plain,
% 5.95/5.88 (NPY6!14 = n5),
% 5.95/5.88 inference(transitivity,[status(thm)],[1465, 15241, 17])).
% 5.95/5.88 tff(15243,plain,
% 5.95/5.88 (succ(NPY6!14) = succ(n5)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15242])).
% 5.95/5.88 tff(15244,plain,
% 5.95/5.88 (succ(NPY6!14) = n6),
% 5.95/5.88 inference(transitivity,[status(thm)],[15243, 30])).
% 5.95/5.88 tff(15245,plain,
% 5.95/5.88 (succ(Y6!48) = succ(n5)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15220])).
% 5.95/5.88 tff(15246,plain,
% 5.95/5.88 (succ(Y6!48) = n6),
% 5.95/5.88 inference(transitivity,[status(thm)],[15245, 30])).
% 5.95/5.88 tff(15247,plain,
% 5.95/5.88 (succ(succ(Y6!48)) = succ(n6)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15246])).
% 5.95/5.88 tff(15248,plain,
% 5.95/5.88 (succ(succ(Y6!48)) = n7),
% 5.95/5.88 inference(transitivity,[status(thm)],[15247, 39])).
% 5.95/5.88 tff(15249,plain,
% 5.95/5.88 (succ(succ(succ(Y6!48))) = succ(n7)),
% 5.95/5.88 inference(monotonicity,[status(thm)],[15248])).
% 5.95/5.88 tff(15250,plain,
% 5.95/5.88 (succ(succ(succ(Y6!48))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15249, 53])).
% 5.95/5.89 tff(15251,plain,
% 5.95/5.89 (succ(succ(succ(succ(Y6!48)))) = succ(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15250])).
% 5.95/5.89 tff(15252,plain,
% 5.95/5.89 (succ(succ(succ(succ(Y6!48)))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15251, 45])).
% 5.95/5.89 tff(15253,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15252])).
% 5.95/5.89 tff(15254,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(Y6!48))))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15253, 28])).
% 5.95/5.89 tff(15255,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15254])).
% 5.95/5.89 tff(15256,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15255, 42])).
% 5.95/5.89 tff(15257,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15256])).
% 5.95/5.89 tff(15258,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15257, 58])).
% 5.95/5.89 tff(15259,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15258])).
% 5.95/5.89 tff(15260,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15259, 36])).
% 5.95/5.89 tff(15261,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15260])).
% 5.95/5.89 tff(15262,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15261, 48])).
% 5.95/5.89 tff(15263,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15262])).
% 5.95/5.89 tff(15264,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15263, 14])).
% 5.95/5.89 tff(15265,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15264])).
% 5.95/5.89 tff(15266,plain,
% 5.95/5.89 (NSY6!12 = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[1490, 15265, 33])).
% 5.95/5.89 tff(15267,plain,
% 5.95/5.89 (pred(NSY6!12) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15266])).
% 5.95/5.89 tff(15268,plain,
% 5.95/5.89 (pred(NSY6!12) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15267, 16])).
% 5.95/5.89 tff(15269,plain,
% 5.95/5.89 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n4, n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15268, 15244])).
% 5.95/5.89 tff(15270,plain,
% 5.95/5.89 (sum(pred(NSY6!12), succ(NPY6!14)) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15269, 12])).
% 5.95/5.89 tff(15271,plain,
% 5.95/5.89 (sum(pred(Y5!50), succ(X5!51)) = sum(n3, n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15114, 15196])).
% 5.95/5.89 tff(15272,plain,
% 5.95/5.89 (sum(pred(Y5!50), succ(X5!51)) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15271, 32])).
% 5.95/5.89 tff(15273,plain,
% 5.95/5.89 (sum(pred(X5!51), succ(Y5!50)) = sum(n3, n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15170, 15138])).
% 5.95/5.89 tff(15274,plain,
% 5.95/5.89 (sum(pred(X5!51), succ(Y5!50)) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15273, 32])).
% 5.95/5.89 tff(15275,plain,
% 5.95/5.89 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n8, n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15274, 15272])).
% 5.95/5.89 tff(15276,plain,
% 5.95/5.89 (X6!49 = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[669, 15275, 31])).
% 5.95/5.89 tff(15277,plain,
% 5.95/5.89 (pred(X6!49) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15276])).
% 5.95/5.89 tff(15278,plain,
% 5.95/5.89 (pred(X6!49) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15277, 16])).
% 5.95/5.89 tff(15279,plain,
% 5.95/5.89 (pred(pred(X6!49)) = pred(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15278])).
% 5.95/5.89 tff(15280,plain,
% 5.95/5.89 (pred(pred(X6!49)) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15279, 15])).
% 5.95/5.89 tff(15281,plain,
% 5.95/5.89 (pred(pred(pred(X6!49))) = pred(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15280])).
% 5.95/5.89 tff(15282,plain,
% 5.95/5.89 (pred(pred(pred(X6!49))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15281, 25])).
% 5.95/5.89 tff(15283,plain,
% 5.95/5.89 (pred(pred(pred(pred(X6!49)))) = pred(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15282])).
% 5.95/5.89 tff(15284,plain,
% 5.95/5.89 (pred(pred(pred(pred(X6!49)))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15283, 24])).
% 5.95/5.89 tff(15285,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(X6!49))))) = pred(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15284])).
% 5.95/5.89 tff(15286,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(X6!49))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15285, 23])).
% 5.95/5.89 tff(15287,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15286])).
% 5.95/5.89 tff(15288,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15287, 22])).
% 5.95/5.89 tff(15289,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15288])).
% 5.95/5.89 tff(15290,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15289, 21])).
% 5.95/5.89 tff(15291,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15290])).
% 5.95/5.89 tff(15292,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15291, 20])).
% 5.95/5.89 tff(15293,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15292])).
% 5.95/5.89 tff(15294,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15293, 19])).
% 5.95/5.89 tff(15295,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15294])).
% 5.95/5.89 tff(15296,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15295, 18])).
% 5.95/5.89 tff(15297,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15296])).
% 5.95/5.89 tff(15298,plain,
% 5.95/5.89 (NPX6!15 = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[1523, 15297, 17])).
% 5.95/5.89 tff(15299,plain,
% 5.95/5.89 (succ(NPX6!15) = succ(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15298])).
% 5.95/5.89 tff(15300,plain,
% 5.95/5.89 (succ(NPX6!15) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15299, 30])).
% 5.95/5.89 tff(15301,plain,
% 5.95/5.89 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n6, n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15300, 15270])).
% 5.95/5.89 tff(15302,plain,
% 5.95/5.89 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15301, 674])).
% 5.95/5.89 tff(15303,plain,
% 5.95/5.89 (succ(X6!49) = succ(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15276])).
% 5.95/5.89 tff(15304,plain,
% 5.95/5.89 (succ(X6!49) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15303, 30])).
% 5.95/5.89 tff(15305,plain,
% 5.95/5.89 (succ(succ(X6!49)) = succ(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15304])).
% 5.95/5.89 tff(15306,plain,
% 5.95/5.89 (succ(succ(X6!49)) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15305, 39])).
% 5.95/5.89 tff(15307,plain,
% 5.95/5.89 (succ(succ(succ(X6!49))) = succ(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15306])).
% 5.95/5.89 tff(15308,plain,
% 5.95/5.89 (succ(succ(succ(X6!49))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15307, 53])).
% 5.95/5.89 tff(15309,plain,
% 5.95/5.89 (succ(succ(succ(succ(X6!49)))) = succ(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15308])).
% 5.95/5.89 tff(15310,plain,
% 5.95/5.89 (succ(succ(succ(succ(X6!49)))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15309, 45])).
% 5.95/5.89 tff(15311,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(X6!49))))) = succ(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15310])).
% 5.95/5.89 tff(15312,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(X6!49))))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15311, 28])).
% 5.95/5.89 tff(15313,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15312])).
% 5.95/5.89 tff(15314,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15313, 42])).
% 5.95/5.89 tff(15315,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15314])).
% 5.95/5.89 tff(15316,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15315, 58])).
% 5.95/5.89 tff(15317,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15316])).
% 5.95/5.89 tff(15318,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15317, 36])).
% 5.95/5.89 tff(15319,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15318])).
% 5.95/5.89 tff(15320,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15319, 48])).
% 5.95/5.89 tff(15321,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15320])).
% 5.95/5.89 tff(15322,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15321, 14])).
% 5.95/5.89 tff(15323,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15322])).
% 5.95/5.89 tff(15324,plain,
% 5.95/5.89 (NSX6!13 = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[1550, 15323, 33])).
% 5.95/5.89 tff(15325,plain,
% 5.95/5.89 (pred(NSX6!13) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15324])).
% 5.95/5.89 tff(15326,plain,
% 5.95/5.89 (pred(NSX6!13) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15325, 16])).
% 5.95/5.89 tff(15327,plain,
% 5.95/5.89 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n4, n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15326, 15302])).
% 5.95/5.89 tff(15328,plain,
% 5.95/5.89 (sum(n4, n5) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.95/5.89 inference(symmetry,[status(thm)],[15327])).
% 5.95/5.89 tff(15329,plain,
% 5.95/5.89 (sum(pred(Y6!48), succ(X6!49)) = sum(n4, n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15222, 15304])).
% 5.95/5.89 tff(15330,plain,
% 5.95/5.89 (sum(pred(Y6!48), succ(X6!49)) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15329, 12])).
% 5.95/5.89 tff(15331,plain,
% 5.95/5.89 (sum(pred(X6!49), succ(Y6!48)) = sum(n4, n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15278, 15246])).
% 5.95/5.89 tff(15332,plain,
% 5.95/5.89 (sum(pred(X6!49), succ(Y6!48)) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15331, 12])).
% 5.95/5.89 tff(15333,plain,
% 5.95/5.89 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n10, n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15332, 15330])).
% 5.95/5.89 tff(15334,plain,
% 5.95/5.89 (X7!47 = Y7!46),
% 5.95/5.89 inference(transitivity,[status(thm)],[785, 15333, 29, 10596, 15328, 794])).
% 5.95/5.89 tff(15335,plain,
% 5.95/5.89 ($false),
% 5.95/5.89 inference(unit_resolution,[status(thm)],[792, 15334])).
% 5.95/5.89 tff(15336,plain,((~(X0!61 = n6)) | (X7!47 = Y7!46) | (~(Y0!60 = n2))), inference(lemma,lemma(discharge,[]))).
% 5.95/5.89 tff(15337,plain,
% 5.95/5.89 (~(X0!61 = n6)),
% 5.95/5.89 inference(unit_resolution,[status(thm)],[15336, 14626, 792])).
% 5.95/5.89 tff(15338,plain,
% 5.95/5.89 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n8, n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[169, 14676])).
% 5.95/5.89 tff(15339,plain,
% 5.95/5.89 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15338, 5918])).
% 5.95/5.89 tff(15340,plain,
% 5.95/5.89 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n6, n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[194, 15339])).
% 5.95/5.89 tff(15341,plain,
% 5.95/5.89 (Y1!58 = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[196, 15340, 7901])).
% 5.95/5.89 tff(15342,plain,
% 5.95/5.89 (pred(Y1!58) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15341])).
% 5.95/5.89 tff(15343,plain,
% 5.95/5.89 (pred(Y1!58) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15342, 18])).
% 5.95/5.89 tff(15344,plain,
% 5.95/5.89 (pred(pred(Y1!58)) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15343])).
% 5.95/5.89 tff(15345,plain,
% 5.95/5.89 (pred(pred(Y1!58)) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15344, 17])).
% 5.95/5.89 tff(15346,plain,
% 5.95/5.89 (pred(pred(pred(Y1!58))) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15345])).
% 5.95/5.89 tff(15347,plain,
% 5.95/5.89 (pred(pred(pred(Y1!58))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15346, 16])).
% 5.95/5.89 tff(15348,plain,
% 5.95/5.89 (pred(pred(pred(pred(Y1!58)))) = pred(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15347])).
% 5.95/5.89 tff(15349,plain,
% 5.95/5.89 (pred(pred(pred(pred(Y1!58)))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15348, 15])).
% 5.95/5.89 tff(15350,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15349])).
% 5.95/5.89 tff(15351,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(Y1!58))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15350, 25])).
% 5.95/5.89 tff(15352,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15351])).
% 5.95/5.89 tff(15353,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15352, 24])).
% 5.95/5.89 tff(15354,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15353])).
% 5.95/5.89 tff(15355,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15354, 23])).
% 5.95/5.89 tff(15356,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15355])).
% 5.95/5.89 tff(15357,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15356, 22])).
% 5.95/5.89 tff(15358,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15357])).
% 5.95/5.89 tff(15359,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15358, 21])).
% 5.95/5.89 tff(15360,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15359])).
% 5.95/5.89 tff(15361,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15360, 20])).
% 5.95/5.89 tff(15362,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15361])).
% 5.95/5.89 tff(15363,plain,
% 5.95/5.89 (NPY1!34 = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[232, 15362, 19])).
% 5.95/5.89 tff(15364,plain,
% 5.95/5.89 (succ(NPY1!34) = succ(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15363])).
% 5.95/5.89 tff(15365,plain,
% 5.95/5.89 (succ(NPY1!34) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15364, 53])).
% 5.95/5.89 tff(15366,plain,
% 5.95/5.89 (succ(Y1!58) = succ(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15341])).
% 5.95/5.89 tff(15367,plain,
% 5.95/5.89 (succ(Y1!58) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15366, 53])).
% 5.95/5.89 tff(15368,plain,
% 5.95/5.89 (succ(succ(Y1!58)) = succ(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15367])).
% 5.95/5.89 tff(15369,plain,
% 5.95/5.89 (succ(succ(Y1!58)) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15368, 45])).
% 5.95/5.89 tff(15370,plain,
% 5.95/5.89 (succ(succ(succ(Y1!58))) = succ(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15369])).
% 5.95/5.89 tff(15371,plain,
% 5.95/5.89 (succ(succ(succ(Y1!58))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15370, 28])).
% 5.95/5.89 tff(15372,plain,
% 5.95/5.89 (succ(succ(succ(succ(Y1!58)))) = succ(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15371])).
% 5.95/5.89 tff(15373,plain,
% 5.95/5.89 (succ(succ(succ(succ(Y1!58)))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15372, 42])).
% 5.95/5.89 tff(15374,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15373])).
% 5.95/5.89 tff(15375,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(Y1!58))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15374, 58])).
% 5.95/5.89 tff(15376,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15375])).
% 5.95/5.89 tff(15377,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15376, 36])).
% 5.95/5.89 tff(15378,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15377])).
% 5.95/5.89 tff(15379,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15378, 48])).
% 5.95/5.89 tff(15380,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15379])).
% 5.95/5.89 tff(15381,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15380, 14])).
% 5.95/5.89 tff(15382,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15381])).
% 5.95/5.89 tff(15383,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15382, 33])).
% 5.95/5.89 tff(15384,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15383])).
% 5.95/5.89 tff(15385,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15384, 30])).
% 5.95/5.89 tff(15386,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15385])).
% 5.95/5.89 tff(15387,plain,
% 5.95/5.89 (NSY1!32 = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[255, 15386, 39])).
% 5.95/5.89 tff(15388,plain,
% 5.95/5.89 (pred(NSY1!32) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15387])).
% 5.95/5.89 tff(15389,plain,
% 5.95/5.89 (pred(NSY1!32) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15388, 18])).
% 5.95/5.89 tff(15390,plain,
% 5.95/5.89 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n6, n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15389, 15365])).
% 5.95/5.89 tff(15391,plain,
% 5.95/5.89 (sum(pred(NSY1!32), succ(NPY1!34)) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15390, 52])).
% 5.95/5.89 tff(15392,plain,
% 5.95/5.89 (sum(n1, n8) = n9),
% 5.95/5.89 inference(and_elim,[status(thm)],[9])).
% 5.95/5.89 tff(15393,plain,
% 5.95/5.89 (sum(pred(Y0!60), succ(X0!61)) = sum(n1, n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[14628, 75])).
% 5.95/5.89 tff(15394,plain,
% 5.95/5.89 (sum(pred(Y0!60), succ(X0!61)) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15393, 15392])).
% 5.95/5.89 tff(15395,plain,
% 5.95/5.89 (sum(pred(X0!61), succ(Y0!60)) = sum(n6, n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[89, 14652])).
% 5.95/5.89 tff(15396,plain,
% 5.95/5.89 (sum(pred(X0!61), succ(Y0!60)) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15395, 97])).
% 5.95/5.89 tff(15397,plain,
% 5.95/5.89 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n9, n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15396, 15394])).
% 5.95/5.89 tff(15398,plain,
% 5.95/5.89 (X1!59 = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[93, 15397, 54])).
% 5.95/5.89 tff(15399,plain,
% 5.95/5.89 (pred(X1!59) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15398])).
% 5.95/5.89 tff(15400,plain,
% 5.95/5.89 (pred(X1!59) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15399, 18])).
% 5.95/5.89 tff(15401,plain,
% 5.95/5.89 (pred(pred(X1!59)) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15400])).
% 5.95/5.89 tff(15402,plain,
% 5.95/5.89 (pred(pred(X1!59)) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15401, 17])).
% 5.95/5.89 tff(15403,plain,
% 5.95/5.89 (pred(pred(pred(X1!59))) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15402])).
% 5.95/5.89 tff(15404,plain,
% 5.95/5.89 (pred(pred(pred(X1!59))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15403, 16])).
% 5.95/5.89 tff(15405,plain,
% 5.95/5.89 (pred(pred(pred(pred(X1!59)))) = pred(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15404])).
% 5.95/5.89 tff(15406,plain,
% 5.95/5.89 (pred(pred(pred(pred(X1!59)))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15405, 15])).
% 5.95/5.89 tff(15407,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(X1!59))))) = pred(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15406])).
% 5.95/5.89 tff(15408,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(X1!59))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15407, 25])).
% 5.95/5.89 tff(15409,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15408])).
% 5.95/5.89 tff(15410,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15409, 24])).
% 5.95/5.89 tff(15411,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15410])).
% 5.95/5.89 tff(15412,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15411, 23])).
% 5.95/5.89 tff(15413,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15412])).
% 5.95/5.89 tff(15414,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15413, 22])).
% 5.95/5.89 tff(15415,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15414])).
% 5.95/5.89 tff(15416,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15415, 21])).
% 5.95/5.89 tff(15417,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15416])).
% 5.95/5.89 tff(15418,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15417, 20])).
% 5.95/5.89 tff(15419,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15418])).
% 5.95/5.89 tff(15420,plain,
% 5.95/5.89 (NPX1!35 = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[280, 15419, 19])).
% 5.95/5.89 tff(15421,plain,
% 5.95/5.89 (succ(NPX1!35) = succ(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15420])).
% 5.95/5.89 tff(15422,plain,
% 5.95/5.89 (succ(NPX1!35) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15421, 53])).
% 5.95/5.89 tff(15423,plain,
% 5.95/5.89 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n8, n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15422, 15391])).
% 5.95/5.89 tff(15424,plain,
% 5.95/5.89 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15423, 64])).
% 5.95/5.89 tff(15425,plain,
% 5.95/5.89 (succ(X1!59) = succ(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15398])).
% 5.95/5.89 tff(15426,plain,
% 5.95/5.89 (succ(X1!59) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15425, 53])).
% 5.95/5.89 tff(15427,plain,
% 5.95/5.89 (succ(succ(X1!59)) = succ(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15426])).
% 5.95/5.89 tff(15428,plain,
% 5.95/5.89 (succ(succ(X1!59)) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15427, 45])).
% 5.95/5.89 tff(15429,plain,
% 5.95/5.89 (succ(succ(succ(X1!59))) = succ(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15428])).
% 5.95/5.89 tff(15430,plain,
% 5.95/5.89 (succ(succ(succ(X1!59))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15429, 28])).
% 5.95/5.89 tff(15431,plain,
% 5.95/5.89 (succ(succ(succ(succ(X1!59)))) = succ(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15430])).
% 5.95/5.89 tff(15432,plain,
% 5.95/5.89 (succ(succ(succ(succ(X1!59)))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15431, 42])).
% 5.95/5.89 tff(15433,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(X1!59))))) = succ(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15432])).
% 5.95/5.89 tff(15434,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(X1!59))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15433, 58])).
% 5.95/5.89 tff(15435,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15434])).
% 5.95/5.89 tff(15436,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15435, 36])).
% 5.95/5.89 tff(15437,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15436])).
% 5.95/5.89 tff(15438,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15437, 48])).
% 5.95/5.89 tff(15439,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15438])).
% 5.95/5.89 tff(15440,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15439, 14])).
% 5.95/5.89 tff(15441,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15440])).
% 5.95/5.89 tff(15442,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15441, 33])).
% 5.95/5.89 tff(15443,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15442])).
% 5.95/5.89 tff(15444,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15443, 30])).
% 5.95/5.89 tff(15445,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15444])).
% 5.95/5.89 tff(15446,plain,
% 5.95/5.89 (NSX1!33 = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[305, 15445, 39])).
% 5.95/5.89 tff(15447,plain,
% 5.95/5.89 (pred(NSX1!33) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15446])).
% 5.95/5.89 tff(15448,plain,
% 5.95/5.89 (pred(NSX1!33) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15447, 18])).
% 5.95/5.89 tff(15449,plain,
% 5.95/5.89 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n6, n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15448, 15424])).
% 5.95/5.89 tff(15450,plain,
% 5.95/5.89 (Y2!56 = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[310, 15449, 788])).
% 5.95/5.89 tff(15451,plain,
% 5.95/5.89 (pred(Y2!56) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15450])).
% 5.95/5.89 tff(15452,plain,
% 5.95/5.89 (pred(Y2!56) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15451, 17])).
% 5.95/5.89 tff(15453,plain,
% 5.95/5.89 (pred(pred(Y2!56)) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15452])).
% 5.95/5.89 tff(15454,plain,
% 5.95/5.89 (pred(pred(Y2!56)) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15453, 16])).
% 5.95/5.89 tff(15455,plain,
% 5.95/5.89 (pred(pred(pred(Y2!56))) = pred(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15454])).
% 5.95/5.89 tff(15456,plain,
% 5.95/5.89 (pred(pred(pred(Y2!56))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15455, 15])).
% 5.95/5.89 tff(15457,plain,
% 5.95/5.89 (pred(pred(pred(pred(Y2!56)))) = pred(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15456])).
% 5.95/5.89 tff(15458,plain,
% 5.95/5.89 (pred(pred(pred(pred(Y2!56)))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15457, 25])).
% 5.95/5.89 tff(15459,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15458])).
% 5.95/5.89 tff(15460,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(Y2!56))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15459, 24])).
% 5.95/5.89 tff(15461,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15460])).
% 5.95/5.89 tff(15462,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15461, 23])).
% 5.95/5.89 tff(15463,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15462])).
% 5.95/5.89 tff(15464,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15463, 22])).
% 5.95/5.89 tff(15465,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15464])).
% 5.95/5.89 tff(15466,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15465, 21])).
% 5.95/5.89 tff(15467,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15466])).
% 5.95/5.89 tff(15468,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15467, 20])).
% 5.95/5.89 tff(15469,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15468])).
% 5.95/5.89 tff(15470,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15469, 19])).
% 5.95/5.89 tff(15471,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15470])).
% 5.95/5.89 tff(15472,plain,
% 5.95/5.89 (NPY2!30 = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[347, 15471, 18])).
% 5.95/5.89 tff(15473,plain,
% 5.95/5.89 (succ(NPY2!30) = succ(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15472])).
% 5.95/5.89 tff(15474,plain,
% 5.95/5.89 (succ(NPY2!30) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15473, 39])).
% 5.95/5.89 tff(15475,plain,
% 5.95/5.89 (succ(Y2!56) = succ(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15450])).
% 5.95/5.89 tff(15476,plain,
% 5.95/5.89 (succ(Y2!56) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15475, 39])).
% 5.95/5.89 tff(15477,plain,
% 5.95/5.89 (succ(succ(Y2!56)) = succ(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15476])).
% 5.95/5.89 tff(15478,plain,
% 5.95/5.89 (succ(succ(Y2!56)) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15477, 53])).
% 5.95/5.89 tff(15479,plain,
% 5.95/5.89 (succ(succ(succ(Y2!56))) = succ(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15478])).
% 5.95/5.89 tff(15480,plain,
% 5.95/5.89 (succ(succ(succ(Y2!56))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15479, 45])).
% 5.95/5.89 tff(15481,plain,
% 5.95/5.89 (succ(succ(succ(succ(Y2!56)))) = succ(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15480])).
% 5.95/5.89 tff(15482,plain,
% 5.95/5.89 (succ(succ(succ(succ(Y2!56)))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15481, 28])).
% 5.95/5.89 tff(15483,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15482])).
% 5.95/5.89 tff(15484,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(Y2!56))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15483, 42])).
% 5.95/5.89 tff(15485,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15484])).
% 5.95/5.89 tff(15486,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15485, 58])).
% 5.95/5.89 tff(15487,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15486])).
% 5.95/5.89 tff(15488,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15487, 36])).
% 5.95/5.89 tff(15489,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15488])).
% 5.95/5.89 tff(15490,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15489, 48])).
% 5.95/5.89 tff(15491,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15490])).
% 5.95/5.89 tff(15492,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15491, 14])).
% 5.95/5.89 tff(15493,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15492])).
% 5.95/5.89 tff(15494,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15493, 33])).
% 5.95/5.89 tff(15495,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15494])).
% 5.95/5.89 tff(15496,plain,
% 5.95/5.89 (NSY2!28 = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[370, 15495, 30])).
% 5.95/5.89 tff(15497,plain,
% 5.95/5.89 (pred(NSY2!28) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15496])).
% 5.95/5.89 tff(15498,plain,
% 5.95/5.89 (pred(NSY2!28) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15497, 17])).
% 5.95/5.89 tff(15499,plain,
% 5.95/5.89 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n5, n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15498, 15474])).
% 5.95/5.89 tff(15500,plain,
% 5.95/5.89 (sum(pred(NSY2!28), succ(NPY2!30)) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15499, 50])).
% 5.95/5.89 tff(15501,plain,
% 5.95/5.89 (sum(pred(Y1!58), succ(X1!59)) = sum(n6, n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15343, 15426])).
% 5.95/5.89 tff(15502,plain,
% 5.95/5.89 (sum(pred(Y1!58), succ(X1!59)) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15501, 52])).
% 5.95/5.89 tff(15503,plain,
% 5.95/5.89 (sum(pred(X1!59), succ(Y1!58)) = sum(n6, n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15400, 15367])).
% 5.95/5.89 tff(15504,plain,
% 5.95/5.89 (sum(pred(X1!59), succ(Y1!58)) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15503, 52])).
% 5.95/5.89 tff(15505,plain,
% 5.95/5.89 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n3, n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15504, 15502])).
% 5.95/5.89 tff(15506,plain,
% 5.95/5.89 (X2!57 = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[209, 15505, 51])).
% 5.95/5.89 tff(15507,plain,
% 5.95/5.89 (pred(X2!57) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15506])).
% 5.95/5.89 tff(15508,plain,
% 5.95/5.89 (pred(X2!57) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15507, 17])).
% 5.95/5.89 tff(15509,plain,
% 5.95/5.89 (pred(pred(X2!57)) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15508])).
% 5.95/5.89 tff(15510,plain,
% 5.95/5.89 (pred(pred(X2!57)) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15509, 16])).
% 5.95/5.89 tff(15511,plain,
% 5.95/5.89 (pred(pred(pred(X2!57))) = pred(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15510])).
% 5.95/5.89 tff(15512,plain,
% 5.95/5.89 (pred(pred(pred(X2!57))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15511, 15])).
% 5.95/5.89 tff(15513,plain,
% 5.95/5.89 (pred(pred(pred(pred(X2!57)))) = pred(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15512])).
% 5.95/5.89 tff(15514,plain,
% 5.95/5.89 (pred(pred(pred(pred(X2!57)))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15513, 25])).
% 5.95/5.89 tff(15515,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(X2!57))))) = pred(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15514])).
% 5.95/5.89 tff(15516,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(X2!57))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15515, 24])).
% 5.95/5.89 tff(15517,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15516])).
% 5.95/5.89 tff(15518,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15517, 23])).
% 5.95/5.89 tff(15519,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15518])).
% 5.95/5.89 tff(15520,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15519, 22])).
% 5.95/5.89 tff(15521,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15520])).
% 5.95/5.89 tff(15522,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15521, 21])).
% 5.95/5.89 tff(15523,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15522])).
% 5.95/5.89 tff(15524,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15523, 20])).
% 5.95/5.89 tff(15525,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15524])).
% 5.95/5.89 tff(15526,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15525, 19])).
% 5.95/5.89 tff(15527,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15526])).
% 5.95/5.89 tff(15528,plain,
% 5.95/5.89 (NPX2!31 = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[395, 15527, 18])).
% 5.95/5.89 tff(15529,plain,
% 5.95/5.89 (succ(NPX2!31) = succ(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15528])).
% 5.95/5.89 tff(15530,plain,
% 5.95/5.89 (succ(NPX2!31) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15529, 39])).
% 5.95/5.89 tff(15531,plain,
% 5.95/5.89 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n7, n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15530, 15500])).
% 5.95/5.89 tff(15532,plain,
% 5.95/5.89 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15531, 787])).
% 5.95/5.89 tff(15533,plain,
% 5.95/5.89 (succ(X2!57) = succ(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15506])).
% 5.95/5.89 tff(15534,plain,
% 5.95/5.89 (succ(X2!57) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15533, 39])).
% 5.95/5.89 tff(15535,plain,
% 5.95/5.89 (succ(succ(X2!57)) = succ(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15534])).
% 5.95/5.89 tff(15536,plain,
% 5.95/5.89 (succ(succ(X2!57)) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15535, 53])).
% 5.95/5.89 tff(15537,plain,
% 5.95/5.89 (succ(succ(succ(X2!57))) = succ(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15536])).
% 5.95/5.89 tff(15538,plain,
% 5.95/5.89 (succ(succ(succ(X2!57))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15537, 45])).
% 5.95/5.89 tff(15539,plain,
% 5.95/5.89 (succ(succ(succ(succ(X2!57)))) = succ(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15538])).
% 5.95/5.89 tff(15540,plain,
% 5.95/5.89 (succ(succ(succ(succ(X2!57)))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15539, 28])).
% 5.95/5.89 tff(15541,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(X2!57))))) = succ(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15540])).
% 5.95/5.89 tff(15542,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(X2!57))))) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15541, 42])).
% 5.95/5.89 tff(15543,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15542])).
% 5.95/5.89 tff(15544,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15543, 58])).
% 5.95/5.89 tff(15545,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15544])).
% 5.95/5.89 tff(15546,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[15545, 36])).
% 5.95/5.89 tff(15547,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15546])).
% 5.95/5.89 tff(15548,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15547, 48])).
% 5.95/5.89 tff(15549,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n3)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15548])).
% 5.95/5.89 tff(15550,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15549, 14])).
% 5.95/5.89 tff(15551,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15550])).
% 5.95/5.89 tff(15552,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15551, 33])).
% 5.95/5.89 tff(15553,plain,
% 5.95/5.89 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15552])).
% 5.95/5.89 tff(15554,plain,
% 5.95/5.89 (NSX2!29 = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[420, 15553, 30])).
% 5.95/5.89 tff(15555,plain,
% 5.95/5.89 (pred(NSX2!29) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15554])).
% 5.95/5.89 tff(15556,plain,
% 5.95/5.89 (pred(NSX2!29) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15555, 17])).
% 5.95/5.89 tff(15557,plain,
% 5.95/5.89 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n5, n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15556, 15532])).
% 5.95/5.89 tff(15558,plain,
% 5.95/5.89 (Y3!54 = n2),
% 5.95/5.89 inference(transitivity,[status(thm)],[425, 15557, 558])).
% 5.95/5.89 tff(15559,plain,
% 5.95/5.89 (pred(Y3!54) = pred(n2)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15558])).
% 5.95/5.89 tff(15560,plain,
% 5.95/5.89 (pred(Y3!54) = n1),
% 5.95/5.89 inference(transitivity,[status(thm)],[15559, 24])).
% 5.95/5.89 tff(15561,plain,
% 5.95/5.89 (pred(pred(Y3!54)) = pred(n1)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15560])).
% 5.95/5.89 tff(15562,plain,
% 5.95/5.89 (pred(pred(Y3!54)) = n0),
% 5.95/5.89 inference(transitivity,[status(thm)],[15561, 23])).
% 5.95/5.89 tff(15563,plain,
% 5.95/5.89 (pred(pred(pred(Y3!54))) = pred(n0)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15562])).
% 5.95/5.89 tff(15564,plain,
% 5.95/5.89 (pred(pred(pred(Y3!54))) = n10),
% 5.95/5.89 inference(transitivity,[status(thm)],[15563, 22])).
% 5.95/5.89 tff(15565,plain,
% 5.95/5.89 (pred(pred(pred(pred(Y3!54)))) = pred(n10)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15564])).
% 5.95/5.89 tff(15566,plain,
% 5.95/5.89 (pred(pred(pred(pred(Y3!54)))) = n9),
% 5.95/5.89 inference(transitivity,[status(thm)],[15565, 21])).
% 5.95/5.89 tff(15567,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n9)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15566])).
% 5.95/5.89 tff(15568,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(Y3!54))))) = n8),
% 5.95/5.89 inference(transitivity,[status(thm)],[15567, 20])).
% 5.95/5.89 tff(15569,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n8)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15568])).
% 5.95/5.89 tff(15570,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n7),
% 5.95/5.89 inference(transitivity,[status(thm)],[15569, 19])).
% 5.95/5.89 tff(15571,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n7)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15570])).
% 5.95/5.89 tff(15572,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n6),
% 5.95/5.89 inference(transitivity,[status(thm)],[15571, 18])).
% 5.95/5.89 tff(15573,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n6)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15572])).
% 5.95/5.89 tff(15574,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n5),
% 5.95/5.89 inference(transitivity,[status(thm)],[15573, 17])).
% 5.95/5.89 tff(15575,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n5)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15574])).
% 5.95/5.89 tff(15576,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n4),
% 5.95/5.89 inference(transitivity,[status(thm)],[15575, 16])).
% 5.95/5.89 tff(15577,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n4)),
% 5.95/5.89 inference(monotonicity,[status(thm)],[15576])).
% 5.95/5.89 tff(15578,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n3),
% 5.95/5.89 inference(transitivity,[status(thm)],[15577, 15])).
% 5.95/5.89 tff(15579,plain,
% 5.95/5.89 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15578])).
% 5.95/5.90 tff(15580,plain,
% 5.95/5.90 (NPY3!26 = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[462, 15579, 25])).
% 5.95/5.90 tff(15581,plain,
% 5.95/5.90 (succ(NPY3!26) = succ(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15580])).
% 5.95/5.90 tff(15582,plain,
% 5.95/5.90 (succ(NPY3!26) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15581, 48])).
% 5.95/5.90 tff(15583,plain,
% 5.95/5.90 (succ(Y3!54) = succ(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15558])).
% 5.95/5.90 tff(15584,plain,
% 5.95/5.90 (succ(Y3!54) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15583, 48])).
% 5.95/5.90 tff(15585,plain,
% 5.95/5.90 (succ(succ(Y3!54)) = succ(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15584])).
% 5.95/5.90 tff(15586,plain,
% 5.95/5.90 (succ(succ(Y3!54)) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15585, 14])).
% 5.95/5.90 tff(15587,plain,
% 5.95/5.90 (succ(succ(succ(Y3!54))) = succ(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15586])).
% 5.95/5.90 tff(15588,plain,
% 5.95/5.90 (succ(succ(succ(Y3!54))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15587, 33])).
% 5.95/5.90 tff(15589,plain,
% 5.95/5.90 (succ(succ(succ(succ(Y3!54)))) = succ(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15588])).
% 5.95/5.90 tff(15590,plain,
% 5.95/5.90 (succ(succ(succ(succ(Y3!54)))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15589, 30])).
% 5.95/5.90 tff(15591,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15590])).
% 5.95/5.90 tff(15592,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(Y3!54))))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15591, 39])).
% 5.95/5.90 tff(15593,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15592])).
% 5.95/5.90 tff(15594,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[15593, 53])).
% 5.95/5.90 tff(15595,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15594])).
% 5.95/5.90 tff(15596,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15595, 45])).
% 5.95/5.90 tff(15597,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15596])).
% 5.95/5.90 tff(15598,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[15597, 28])).
% 5.95/5.90 tff(15599,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15598])).
% 5.95/5.90 tff(15600,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15599, 42])).
% 5.95/5.90 tff(15601,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15600])).
% 5.95/5.90 tff(15602,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15601, 58])).
% 5.95/5.90 tff(15603,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15602])).
% 5.95/5.90 tff(15604,plain,
% 5.95/5.90 (NSY3!24 = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[485, 15603, 36])).
% 5.95/5.90 tff(15605,plain,
% 5.95/5.90 (pred(NSY3!24) = pred(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15604])).
% 5.95/5.90 tff(15606,plain,
% 5.95/5.90 (pred(NSY3!24) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15605, 24])).
% 5.95/5.90 tff(15607,plain,
% 5.95/5.90 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n1, n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15606, 15582])).
% 5.95/5.90 tff(15608,plain,
% 5.95/5.90 (sum(pred(NSY3!24), succ(NPY3!26)) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15607, 47])).
% 5.95/5.90 tff(15609,plain,
% 5.95/5.90 (sum(pred(Y2!56), succ(X2!57)) = sum(n5, n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15452, 15534])).
% 5.95/5.90 tff(15610,plain,
% 5.95/5.90 (sum(pred(Y2!56), succ(X2!57)) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15609, 50])).
% 5.95/5.90 tff(15611,plain,
% 5.95/5.90 (sum(pred(X2!57), succ(Y2!56)) = sum(n5, n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15508, 15476])).
% 5.95/5.90 tff(15612,plain,
% 5.95/5.90 (sum(pred(X2!57), succ(Y2!56)) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15611, 50])).
% 5.95/5.90 tff(15613,plain,
% 5.95/5.90 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n1, n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15612, 15610])).
% 5.95/5.90 tff(15614,plain,
% 5.95/5.90 (X3!55 = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[323, 15613, 49])).
% 5.95/5.90 tff(15615,plain,
% 5.95/5.90 (pred(X3!55) = pred(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15614])).
% 5.95/5.90 tff(15616,plain,
% 5.95/5.90 (pred(X3!55) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15615, 24])).
% 5.95/5.90 tff(15617,plain,
% 5.95/5.90 (pred(pred(X3!55)) = pred(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15616])).
% 5.95/5.90 tff(15618,plain,
% 5.95/5.90 (pred(pred(X3!55)) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15617, 23])).
% 5.95/5.90 tff(15619,plain,
% 5.95/5.90 (pred(pred(pred(X3!55))) = pred(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15618])).
% 5.95/5.90 tff(15620,plain,
% 5.95/5.90 (pred(pred(pred(X3!55))) = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[15619, 22])).
% 5.95/5.90 tff(15621,plain,
% 5.95/5.90 (pred(pred(pred(pred(X3!55)))) = pred(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15620])).
% 5.95/5.90 tff(15622,plain,
% 5.95/5.90 (pred(pred(pred(pred(X3!55)))) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15621, 21])).
% 5.95/5.90 tff(15623,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(X3!55))))) = pred(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15622])).
% 5.95/5.90 tff(15624,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(X3!55))))) = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[15623, 20])).
% 5.95/5.90 tff(15625,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15624])).
% 5.95/5.90 tff(15626,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15625, 19])).
% 5.95/5.90 tff(15627,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15626])).
% 5.95/5.90 tff(15628,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15627, 18])).
% 5.95/5.90 tff(15629,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15628])).
% 5.95/5.90 tff(15630,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15629, 17])).
% 5.95/5.90 tff(15631,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15630])).
% 5.95/5.90 tff(15632,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15631, 16])).
% 5.95/5.90 tff(15633,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15632])).
% 5.95/5.90 tff(15634,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15633, 15])).
% 5.95/5.90 tff(15635,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15634])).
% 5.95/5.90 tff(15636,plain,
% 5.95/5.90 (NPX3!27 = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[510, 15635, 25])).
% 5.95/5.90 tff(15637,plain,
% 5.95/5.90 (succ(NPX3!27) = succ(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15636])).
% 5.95/5.90 tff(15638,plain,
% 5.95/5.90 (succ(NPX3!27) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15637, 48])).
% 5.95/5.90 tff(15639,plain,
% 5.95/5.90 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n3, n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15638, 15608])).
% 5.95/5.90 tff(15640,plain,
% 5.95/5.90 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15639, 786])).
% 5.95/5.90 tff(15641,plain,
% 5.95/5.90 (succ(X3!55) = succ(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15614])).
% 5.95/5.90 tff(15642,plain,
% 5.95/5.90 (succ(X3!55) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15641, 48])).
% 5.95/5.90 tff(15643,plain,
% 5.95/5.90 (succ(succ(X3!55)) = succ(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15642])).
% 5.95/5.90 tff(15644,plain,
% 5.95/5.90 (succ(succ(X3!55)) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15643, 14])).
% 5.95/5.90 tff(15645,plain,
% 5.95/5.90 (succ(succ(succ(X3!55))) = succ(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15644])).
% 5.95/5.90 tff(15646,plain,
% 5.95/5.90 (succ(succ(succ(X3!55))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15645, 33])).
% 5.95/5.90 tff(15647,plain,
% 5.95/5.90 (succ(succ(succ(succ(X3!55)))) = succ(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15646])).
% 5.95/5.90 tff(15648,plain,
% 5.95/5.90 (succ(succ(succ(succ(X3!55)))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15647, 30])).
% 5.95/5.90 tff(15649,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(X3!55))))) = succ(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15648])).
% 5.95/5.90 tff(15650,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(X3!55))))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15649, 39])).
% 5.95/5.90 tff(15651,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15650])).
% 5.95/5.90 tff(15652,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[15651, 53])).
% 5.95/5.90 tff(15653,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15652])).
% 5.95/5.90 tff(15654,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15653, 45])).
% 5.95/5.90 tff(15655,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15654])).
% 5.95/5.90 tff(15656,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[15655, 28])).
% 5.95/5.90 tff(15657,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15656])).
% 5.95/5.90 tff(15658,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15657, 42])).
% 5.95/5.90 tff(15659,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15658])).
% 5.95/5.90 tff(15660,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15659, 58])).
% 5.95/5.90 tff(15661,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15660])).
% 5.95/5.90 tff(15662,plain,
% 5.95/5.90 (NSX3!25 = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[535, 15661, 36])).
% 5.95/5.90 tff(15663,plain,
% 5.95/5.90 (pred(NSX3!25) = pred(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15662])).
% 5.95/5.90 tff(15664,plain,
% 5.95/5.90 (pred(NSX3!25) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15663, 24])).
% 5.95/5.90 tff(15665,plain,
% 5.95/5.90 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n1, n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15664, 15640])).
% 5.95/5.90 tff(15666,plain,
% 5.95/5.90 (Y4!52 = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[540, 15665, 791])).
% 5.95/5.90 tff(15667,plain,
% 5.95/5.90 (pred(Y4!52) = pred(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15666])).
% 5.95/5.90 tff(15668,plain,
% 5.95/5.90 (pred(Y4!52) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15667, 19])).
% 5.95/5.90 tff(15669,plain,
% 5.95/5.90 (pred(pred(Y4!52)) = pred(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15668])).
% 5.95/5.90 tff(15670,plain,
% 5.95/5.90 (pred(pred(Y4!52)) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15669, 18])).
% 5.95/5.90 tff(15671,plain,
% 5.95/5.90 (pred(pred(pred(Y4!52))) = pred(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15670])).
% 5.95/5.90 tff(15672,plain,
% 5.95/5.90 (pred(pred(pred(Y4!52))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15671, 17])).
% 5.95/5.90 tff(15673,plain,
% 5.95/5.90 (pred(pred(pred(pred(Y4!52)))) = pred(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15672])).
% 5.95/5.90 tff(15674,plain,
% 5.95/5.90 (pred(pred(pred(pred(Y4!52)))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15673, 16])).
% 5.95/5.90 tff(15675,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15674])).
% 5.95/5.90 tff(15676,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(Y4!52))))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15675, 15])).
% 5.95/5.90 tff(15677,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15676])).
% 5.95/5.90 tff(15678,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[15677, 25])).
% 5.95/5.90 tff(15679,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15678])).
% 5.95/5.90 tff(15680,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15679, 24])).
% 5.95/5.90 tff(15681,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15680])).
% 5.95/5.90 tff(15682,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15681, 23])).
% 5.95/5.90 tff(15683,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15682])).
% 5.95/5.90 tff(15684,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[15683, 22])).
% 5.95/5.90 tff(15685,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15684])).
% 5.95/5.90 tff(15686,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15685, 21])).
% 5.95/5.90 tff(15687,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15686])).
% 5.95/5.90 tff(15688,plain,
% 5.95/5.90 (NPY4!22 = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[578, 15687, 20])).
% 5.95/5.90 tff(15689,plain,
% 5.95/5.90 (succ(NPY4!22) = succ(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15688])).
% 5.95/5.90 tff(15690,plain,
% 5.95/5.90 (succ(NPY4!22) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15689, 45])).
% 5.95/5.90 tff(15691,plain,
% 5.95/5.90 (succ(Y4!52) = succ(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15666])).
% 5.95/5.90 tff(15692,plain,
% 5.95/5.90 (succ(Y4!52) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15691, 45])).
% 5.95/5.90 tff(15693,plain,
% 5.95/5.90 (succ(succ(Y4!52)) = succ(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15692])).
% 5.95/5.90 tff(15694,plain,
% 5.95/5.90 (succ(succ(Y4!52)) = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[15693, 28])).
% 5.95/5.90 tff(15695,plain,
% 5.95/5.90 (succ(succ(succ(Y4!52))) = succ(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15694])).
% 5.95/5.90 tff(15696,plain,
% 5.95/5.90 (succ(succ(succ(Y4!52))) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15695, 42])).
% 5.95/5.90 tff(15697,plain,
% 5.95/5.90 (succ(succ(succ(succ(Y4!52)))) = succ(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15696])).
% 5.95/5.90 tff(15698,plain,
% 5.95/5.90 (succ(succ(succ(succ(Y4!52)))) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15697, 58])).
% 5.95/5.90 tff(15699,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15698])).
% 5.95/5.90 tff(15700,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(Y4!52))))) = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[15699, 36])).
% 5.95/5.90 tff(15701,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15700])).
% 5.95/5.90 tff(15702,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15701, 48])).
% 5.95/5.90 tff(15703,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15702])).
% 5.95/5.90 tff(15704,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15703, 14])).
% 5.95/5.90 tff(15705,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15704])).
% 5.95/5.90 tff(15706,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15705, 33])).
% 5.95/5.90 tff(15707,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15706])).
% 5.95/5.90 tff(15708,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15707, 30])).
% 5.95/5.90 tff(15709,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15708])).
% 5.95/5.90 tff(15710,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15709, 39])).
% 5.95/5.90 tff(15711,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15710])).
% 5.95/5.90 tff(15712,plain,
% 5.95/5.90 (NSY4!20 = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[601, 15711, 53])).
% 5.95/5.90 tff(15713,plain,
% 5.95/5.90 (pred(NSY4!20) = pred(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15712])).
% 5.95/5.90 tff(15714,plain,
% 5.95/5.90 (pred(NSY4!20) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15713, 19])).
% 5.95/5.90 tff(15715,plain,
% 5.95/5.90 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n7, n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15714, 15690])).
% 5.95/5.90 tff(15716,plain,
% 5.95/5.90 (sum(pred(NSY4!20), succ(NPY4!22)) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15715, 44])).
% 5.95/5.90 tff(15717,plain,
% 5.95/5.90 (sum(pred(Y3!54), succ(X3!55)) = sum(n1, n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15560, 15642])).
% 5.95/5.90 tff(15718,plain,
% 5.95/5.90 (sum(pred(Y3!54), succ(X3!55)) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15717, 47])).
% 5.95/5.90 tff(15719,plain,
% 5.95/5.90 (sum(pred(X3!55), succ(Y3!54)) = sum(n1, n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15616, 15584])).
% 5.95/5.90 tff(15720,plain,
% 5.95/5.90 (sum(pred(X3!55), succ(Y3!54)) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15719, 47])).
% 5.95/5.90 tff(15721,plain,
% 5.95/5.90 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n4, n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15720, 15718])).
% 5.95/5.90 tff(15722,plain,
% 5.95/5.90 (X4!53 = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[438, 15721, 46])).
% 5.95/5.90 tff(15723,plain,
% 5.95/5.90 (pred(X4!53) = pred(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15722])).
% 5.95/5.90 tff(15724,plain,
% 5.95/5.90 (pred(X4!53) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15723, 19])).
% 5.95/5.90 tff(15725,plain,
% 5.95/5.90 (pred(pred(X4!53)) = pred(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15724])).
% 5.95/5.90 tff(15726,plain,
% 5.95/5.90 (pred(pred(X4!53)) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15725, 18])).
% 5.95/5.90 tff(15727,plain,
% 5.95/5.90 (pred(pred(pred(X4!53))) = pred(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15726])).
% 5.95/5.90 tff(15728,plain,
% 5.95/5.90 (pred(pred(pred(X4!53))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15727, 17])).
% 5.95/5.90 tff(15729,plain,
% 5.95/5.90 (pred(pred(pred(pred(X4!53)))) = pred(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15728])).
% 5.95/5.90 tff(15730,plain,
% 5.95/5.90 (pred(pred(pred(pred(X4!53)))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15729, 16])).
% 5.95/5.90 tff(15731,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(X4!53))))) = pred(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15730])).
% 5.95/5.90 tff(15732,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(X4!53))))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15731, 15])).
% 5.95/5.90 tff(15733,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15732])).
% 5.95/5.90 tff(15734,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[15733, 25])).
% 5.95/5.90 tff(15735,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15734])).
% 5.95/5.90 tff(15736,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15735, 24])).
% 5.95/5.90 tff(15737,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15736])).
% 5.95/5.90 tff(15738,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15737, 23])).
% 5.95/5.90 tff(15739,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15738])).
% 5.95/5.90 tff(15740,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[15739, 22])).
% 5.95/5.90 tff(15741,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15740])).
% 5.95/5.90 tff(15742,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15741, 21])).
% 5.95/5.90 tff(15743,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15742])).
% 5.95/5.90 tff(15744,plain,
% 5.95/5.90 (NPX4!23 = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[626, 15743, 20])).
% 5.95/5.90 tff(15745,plain,
% 5.95/5.90 (succ(NPX4!23) = succ(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15744])).
% 5.95/5.90 tff(15746,plain,
% 5.95/5.90 (succ(NPX4!23) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15745, 45])).
% 5.95/5.90 tff(15747,plain,
% 5.95/5.90 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n9, n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15746, 15716])).
% 5.95/5.90 tff(15748,plain,
% 5.95/5.90 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15747, 790])).
% 5.95/5.90 tff(15749,plain,
% 5.95/5.90 (succ(X4!53) = succ(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15722])).
% 5.95/5.90 tff(15750,plain,
% 5.95/5.90 (succ(X4!53) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15749, 45])).
% 5.95/5.90 tff(15751,plain,
% 5.95/5.90 (succ(succ(X4!53)) = succ(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15750])).
% 5.95/5.90 tff(15752,plain,
% 5.95/5.90 (succ(succ(X4!53)) = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[15751, 28])).
% 5.95/5.90 tff(15753,plain,
% 5.95/5.90 (succ(succ(succ(X4!53))) = succ(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15752])).
% 5.95/5.90 tff(15754,plain,
% 5.95/5.90 (succ(succ(succ(X4!53))) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15753, 42])).
% 5.95/5.90 tff(15755,plain,
% 5.95/5.90 (succ(succ(succ(succ(X4!53)))) = succ(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15754])).
% 5.95/5.90 tff(15756,plain,
% 5.95/5.90 (succ(succ(succ(succ(X4!53)))) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15755, 58])).
% 5.95/5.90 tff(15757,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(X4!53))))) = succ(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15756])).
% 5.95/5.90 tff(15758,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(X4!53))))) = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[15757, 36])).
% 5.95/5.90 tff(15759,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15758])).
% 5.95/5.90 tff(15760,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15759, 48])).
% 5.95/5.90 tff(15761,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15760])).
% 5.95/5.90 tff(15762,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15761, 14])).
% 5.95/5.90 tff(15763,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15762])).
% 5.95/5.90 tff(15764,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15763, 33])).
% 5.95/5.90 tff(15765,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15764])).
% 5.95/5.90 tff(15766,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15765, 30])).
% 5.95/5.90 tff(15767,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15766])).
% 5.95/5.90 tff(15768,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15767, 39])).
% 5.95/5.90 tff(15769,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15768])).
% 5.95/5.90 tff(15770,plain,
% 5.95/5.90 (NSX4!21 = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[651, 15769, 53])).
% 5.95/5.90 tff(15771,plain,
% 5.95/5.90 (pred(NSX4!21) = pred(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15770])).
% 5.95/5.90 tff(15772,plain,
% 5.95/5.90 (pred(NSX4!21) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15771, 19])).
% 5.95/5.90 tff(15773,plain,
% 5.95/5.90 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n7, n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15772, 15748])).
% 5.95/5.90 tff(15774,plain,
% 5.95/5.90 (Y5!50 = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[656, 15773, 789])).
% 5.95/5.90 tff(15775,plain,
% 5.95/5.90 (pred(Y5!50) = pred(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15774])).
% 5.95/5.90 tff(15776,plain,
% 5.95/5.90 (pred(Y5!50) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15775, 21])).
% 5.95/5.90 tff(15777,plain,
% 5.95/5.90 (pred(pred(Y5!50)) = pred(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15776])).
% 5.95/5.90 tff(15778,plain,
% 5.95/5.90 (pred(pred(Y5!50)) = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[15777, 20])).
% 5.95/5.90 tff(15779,plain,
% 5.95/5.90 (pred(pred(pred(Y5!50))) = pred(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15778])).
% 5.95/5.90 tff(15780,plain,
% 5.95/5.90 (pred(pred(pred(Y5!50))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15779, 19])).
% 5.95/5.90 tff(15781,plain,
% 5.95/5.90 (pred(pred(pred(pred(Y5!50)))) = pred(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15780])).
% 5.95/5.90 tff(15782,plain,
% 5.95/5.90 (pred(pred(pred(pred(Y5!50)))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15781, 18])).
% 5.95/5.90 tff(15783,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15782])).
% 5.95/5.90 tff(15784,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(Y5!50))))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15783, 17])).
% 5.95/5.90 tff(15785,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15784])).
% 5.95/5.90 tff(15786,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15785, 16])).
% 5.95/5.90 tff(15787,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15786])).
% 5.95/5.90 tff(15788,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15787, 15])).
% 5.95/5.90 tff(15789,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15788])).
% 5.95/5.90 tff(15790,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[15789, 25])).
% 5.95/5.90 tff(15791,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15790])).
% 5.95/5.90 tff(15792,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15791, 24])).
% 5.95/5.90 tff(15793,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15792])).
% 5.95/5.90 tff(15794,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15793, 23])).
% 5.95/5.90 tff(15795,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15794])).
% 5.95/5.90 tff(15796,plain,
% 5.95/5.90 (NPY5!18 = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[694, 15795, 22])).
% 5.95/5.90 tff(15797,plain,
% 5.95/5.90 (succ(NPY5!18) = succ(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15796])).
% 5.95/5.90 tff(15798,plain,
% 5.95/5.90 (succ(NPY5!18) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15797, 42])).
% 5.95/5.90 tff(15799,plain,
% 5.95/5.90 (succ(Y5!50) = succ(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15774])).
% 5.95/5.90 tff(15800,plain,
% 5.95/5.90 (succ(Y5!50) = n0),
% 5.95/5.90 inference(transitivity,[status(thm)],[15799, 42])).
% 5.95/5.90 tff(15801,plain,
% 5.95/5.90 (succ(succ(Y5!50)) = succ(n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15800])).
% 5.95/5.90 tff(15802,plain,
% 5.95/5.90 (succ(succ(Y5!50)) = n1),
% 5.95/5.90 inference(transitivity,[status(thm)],[15801, 58])).
% 5.95/5.90 tff(15803,plain,
% 5.95/5.90 (succ(succ(succ(Y5!50))) = succ(n1)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15802])).
% 5.95/5.90 tff(15804,plain,
% 5.95/5.90 (succ(succ(succ(Y5!50))) = n2),
% 5.95/5.90 inference(transitivity,[status(thm)],[15803, 36])).
% 5.95/5.90 tff(15805,plain,
% 5.95/5.90 (succ(succ(succ(succ(Y5!50)))) = succ(n2)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15804])).
% 5.95/5.90 tff(15806,plain,
% 5.95/5.90 (succ(succ(succ(succ(Y5!50)))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15805, 48])).
% 5.95/5.90 tff(15807,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n3)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15806])).
% 5.95/5.90 tff(15808,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(Y5!50))))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15807, 14])).
% 5.95/5.90 tff(15809,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15808])).
% 5.95/5.90 tff(15810,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15809, 33])).
% 5.95/5.90 tff(15811,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15810])).
% 5.95/5.90 tff(15812,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15811, 30])).
% 5.95/5.90 tff(15813,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15812])).
% 5.95/5.90 tff(15814,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15813, 39])).
% 5.95/5.90 tff(15815,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15814])).
% 5.95/5.90 tff(15816,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[15815, 53])).
% 5.95/5.90 tff(15817,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15816])).
% 5.95/5.90 tff(15818,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15817, 45])).
% 5.95/5.90 tff(15819,plain,
% 5.95/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15818])).
% 5.95/5.90 tff(15820,plain,
% 5.95/5.90 (NSY5!16 = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[717, 15819, 28])).
% 5.95/5.90 tff(15821,plain,
% 5.95/5.90 (pred(NSY5!16) = pred(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15820])).
% 5.95/5.90 tff(15822,plain,
% 5.95/5.90 (pred(NSY5!16) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15821, 21])).
% 5.95/5.90 tff(15823,plain,
% 5.95/5.90 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n9, n0)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15822, 15798])).
% 5.95/5.90 tff(15824,plain,
% 5.95/5.90 (sum(pred(NSY5!16), succ(NPY5!18)) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15823, 41])).
% 5.95/5.90 tff(15825,plain,
% 5.95/5.90 (sum(pred(Y4!52), succ(X4!53)) = sum(n7, n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15668, 15750])).
% 5.95/5.90 tff(15826,plain,
% 5.95/5.90 (sum(pred(Y4!52), succ(X4!53)) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15825, 44])).
% 5.95/5.90 tff(15827,plain,
% 5.95/5.90 (sum(pred(X4!53), succ(Y4!52)) = sum(n7, n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15724, 15692])).
% 5.95/5.90 tff(15828,plain,
% 5.95/5.90 (sum(pred(X4!53), succ(Y4!52)) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15827, 44])).
% 5.95/5.90 tff(15829,plain,
% 5.95/5.90 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n5, n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15828, 15826])).
% 5.95/5.90 tff(15830,plain,
% 5.95/5.90 (X5!51 = n10),
% 5.95/5.90 inference(transitivity,[status(thm)],[553, 15829, 43])).
% 5.95/5.90 tff(15831,plain,
% 5.95/5.90 (pred(X5!51) = pred(n10)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15830])).
% 5.95/5.90 tff(15832,plain,
% 5.95/5.90 (pred(X5!51) = n9),
% 5.95/5.90 inference(transitivity,[status(thm)],[15831, 21])).
% 5.95/5.90 tff(15833,plain,
% 5.95/5.90 (pred(pred(X5!51)) = pred(n9)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15832])).
% 5.95/5.90 tff(15834,plain,
% 5.95/5.90 (pred(pred(X5!51)) = n8),
% 5.95/5.90 inference(transitivity,[status(thm)],[15833, 20])).
% 5.95/5.90 tff(15835,plain,
% 5.95/5.90 (pred(pred(pred(X5!51))) = pred(n8)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15834])).
% 5.95/5.90 tff(15836,plain,
% 5.95/5.90 (pred(pred(pred(X5!51))) = n7),
% 5.95/5.90 inference(transitivity,[status(thm)],[15835, 19])).
% 5.95/5.90 tff(15837,plain,
% 5.95/5.90 (pred(pred(pred(pred(X5!51)))) = pred(n7)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15836])).
% 5.95/5.90 tff(15838,plain,
% 5.95/5.90 (pred(pred(pred(pred(X5!51)))) = n6),
% 5.95/5.90 inference(transitivity,[status(thm)],[15837, 18])).
% 5.95/5.90 tff(15839,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(X5!51))))) = pred(n6)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15838])).
% 5.95/5.90 tff(15840,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(X5!51))))) = n5),
% 5.95/5.90 inference(transitivity,[status(thm)],[15839, 17])).
% 5.95/5.90 tff(15841,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n5)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15840])).
% 5.95/5.90 tff(15842,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n4),
% 5.95/5.90 inference(transitivity,[status(thm)],[15841, 16])).
% 5.95/5.90 tff(15843,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n4)),
% 5.95/5.90 inference(monotonicity,[status(thm)],[15842])).
% 5.95/5.90 tff(15844,plain,
% 5.95/5.90 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n3),
% 5.95/5.90 inference(transitivity,[status(thm)],[15843, 15])).
% 5.97/5.90 tff(15845,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n3)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15844])).
% 5.97/5.90 tff(15846,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n2),
% 5.97/5.90 inference(transitivity,[status(thm)],[15845, 25])).
% 5.97/5.90 tff(15847,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n2)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15846])).
% 5.97/5.90 tff(15848,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n1),
% 5.97/5.90 inference(transitivity,[status(thm)],[15847, 24])).
% 5.97/5.90 tff(15849,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n1)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15848])).
% 5.97/5.90 tff(15850,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n0),
% 5.97/5.90 inference(transitivity,[status(thm)],[15849, 23])).
% 5.97/5.90 tff(15851,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n0)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15850])).
% 5.97/5.90 tff(15852,plain,
% 5.97/5.90 (NPX5!19 = n10),
% 5.97/5.90 inference(transitivity,[status(thm)],[742, 15851, 22])).
% 5.97/5.90 tff(15853,plain,
% 5.97/5.90 (succ(NPX5!19) = succ(n10)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15852])).
% 5.97/5.90 tff(15854,plain,
% 5.97/5.90 (succ(NPX5!19) = n0),
% 5.97/5.90 inference(transitivity,[status(thm)],[15853, 42])).
% 5.97/5.90 tff(15855,plain,
% 5.97/5.90 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n0, n9)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15854, 15824])).
% 5.97/5.90 tff(15856,plain,
% 5.97/5.90 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n9),
% 5.97/5.90 inference(transitivity,[status(thm)],[15855, 40])).
% 5.97/5.90 tff(15857,plain,
% 5.97/5.90 (succ(X5!51) = succ(n10)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15830])).
% 5.97/5.90 tff(15858,plain,
% 5.97/5.90 (succ(X5!51) = n0),
% 5.97/5.90 inference(transitivity,[status(thm)],[15857, 42])).
% 5.97/5.90 tff(15859,plain,
% 5.97/5.90 (succ(succ(X5!51)) = succ(n0)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15858])).
% 5.97/5.90 tff(15860,plain,
% 5.97/5.90 (succ(succ(X5!51)) = n1),
% 5.97/5.90 inference(transitivity,[status(thm)],[15859, 58])).
% 5.97/5.90 tff(15861,plain,
% 5.97/5.90 (succ(succ(succ(X5!51))) = succ(n1)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15860])).
% 5.97/5.90 tff(15862,plain,
% 5.97/5.90 (succ(succ(succ(X5!51))) = n2),
% 5.97/5.90 inference(transitivity,[status(thm)],[15861, 36])).
% 5.97/5.90 tff(15863,plain,
% 5.97/5.90 (succ(succ(succ(succ(X5!51)))) = succ(n2)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15862])).
% 5.97/5.90 tff(15864,plain,
% 5.97/5.90 (succ(succ(succ(succ(X5!51)))) = n3),
% 5.97/5.90 inference(transitivity,[status(thm)],[15863, 48])).
% 5.97/5.90 tff(15865,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(X5!51))))) = succ(n3)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15864])).
% 5.97/5.90 tff(15866,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(X5!51))))) = n4),
% 5.97/5.90 inference(transitivity,[status(thm)],[15865, 14])).
% 5.97/5.90 tff(15867,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n4)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15866])).
% 5.97/5.90 tff(15868,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n5),
% 5.97/5.90 inference(transitivity,[status(thm)],[15867, 33])).
% 5.97/5.90 tff(15869,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n5)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15868])).
% 5.97/5.90 tff(15870,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n6),
% 5.97/5.90 inference(transitivity,[status(thm)],[15869, 30])).
% 5.97/5.90 tff(15871,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n6)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15870])).
% 5.97/5.90 tff(15872,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n7),
% 5.97/5.90 inference(transitivity,[status(thm)],[15871, 39])).
% 5.97/5.90 tff(15873,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n7)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15872])).
% 5.97/5.90 tff(15874,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n8),
% 5.97/5.90 inference(transitivity,[status(thm)],[15873, 53])).
% 5.97/5.90 tff(15875,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n8)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15874])).
% 5.97/5.90 tff(15876,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n9),
% 5.97/5.90 inference(transitivity,[status(thm)],[15875, 45])).
% 5.97/5.90 tff(15877,plain,
% 5.97/5.90 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n9)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15876])).
% 5.97/5.90 tff(15878,plain,
% 5.97/5.90 (NSX5!17 = n10),
% 5.97/5.90 inference(transitivity,[status(thm)],[767, 15877, 28])).
% 5.97/5.90 tff(15879,plain,
% 5.97/5.90 (pred(NSX5!17) = pred(n10)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15878])).
% 5.97/5.90 tff(15880,plain,
% 5.97/5.90 (pred(NSX5!17) = n9),
% 5.97/5.90 inference(transitivity,[status(thm)],[15879, 21])).
% 5.97/5.90 tff(15881,plain,
% 5.97/5.90 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n9, n9)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15880, 15856])).
% 5.97/5.90 tff(15882,plain,
% 5.97/5.90 (Y6!48 = n7),
% 5.97/5.90 inference(transitivity,[status(thm)],[772, 15881, 54])).
% 5.97/5.90 tff(15883,plain,
% 5.97/5.90 (pred(Y6!48) = pred(n7)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15882])).
% 5.97/5.90 tff(15884,plain,
% 5.97/5.90 (pred(Y6!48) = n6),
% 5.97/5.90 inference(transitivity,[status(thm)],[15883, 18])).
% 5.97/5.90 tff(15885,plain,
% 5.97/5.90 (pred(pred(Y6!48)) = pred(n6)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15884])).
% 5.97/5.90 tff(15886,plain,
% 5.97/5.90 (pred(pred(Y6!48)) = n5),
% 5.97/5.90 inference(transitivity,[status(thm)],[15885, 17])).
% 5.97/5.90 tff(15887,plain,
% 5.97/5.90 (pred(pred(pred(Y6!48))) = pred(n5)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15886])).
% 5.97/5.90 tff(15888,plain,
% 5.97/5.90 (pred(pred(pred(Y6!48))) = n4),
% 5.97/5.90 inference(transitivity,[status(thm)],[15887, 16])).
% 5.97/5.90 tff(15889,plain,
% 5.97/5.90 (pred(pred(pred(pred(Y6!48)))) = pred(n4)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15888])).
% 5.97/5.90 tff(15890,plain,
% 5.97/5.90 (pred(pred(pred(pred(Y6!48)))) = n3),
% 5.97/5.90 inference(transitivity,[status(thm)],[15889, 15])).
% 5.97/5.90 tff(15891,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n3)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15890])).
% 5.97/5.90 tff(15892,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(Y6!48))))) = n2),
% 5.97/5.90 inference(transitivity,[status(thm)],[15891, 25])).
% 5.97/5.90 tff(15893,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n2)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15892])).
% 5.97/5.90 tff(15894,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n1),
% 5.97/5.90 inference(transitivity,[status(thm)],[15893, 24])).
% 5.97/5.90 tff(15895,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n1)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15894])).
% 5.97/5.90 tff(15896,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n0),
% 5.97/5.90 inference(transitivity,[status(thm)],[15895, 23])).
% 5.97/5.90 tff(15897,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n0)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15896])).
% 5.97/5.90 tff(15898,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n10),
% 5.97/5.90 inference(transitivity,[status(thm)],[15897, 22])).
% 5.97/5.90 tff(15899,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n10)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15898])).
% 5.97/5.90 tff(15900,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n9),
% 5.97/5.90 inference(transitivity,[status(thm)],[15899, 21])).
% 5.97/5.90 tff(15901,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n9)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15900])).
% 5.97/5.90 tff(15902,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n8),
% 5.97/5.90 inference(transitivity,[status(thm)],[15901, 20])).
% 5.97/5.90 tff(15903,plain,
% 5.97/5.90 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n8)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15902])).
% 5.97/5.90 tff(15904,plain,
% 5.97/5.90 (NPY6!14 = n7),
% 5.97/5.90 inference(transitivity,[status(thm)],[1465, 15903, 19])).
% 5.97/5.90 tff(15905,plain,
% 5.97/5.90 (succ(NPY6!14) = succ(n7)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15904])).
% 5.97/5.90 tff(15906,plain,
% 5.97/5.90 (succ(NPY6!14) = n8),
% 5.97/5.90 inference(transitivity,[status(thm)],[15905, 53])).
% 5.97/5.90 tff(15907,plain,
% 5.97/5.90 (succ(Y6!48) = succ(n7)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15882])).
% 5.97/5.90 tff(15908,plain,
% 5.97/5.90 (succ(Y6!48) = n8),
% 5.97/5.90 inference(transitivity,[status(thm)],[15907, 53])).
% 5.97/5.90 tff(15909,plain,
% 5.97/5.90 (succ(succ(Y6!48)) = succ(n8)),
% 5.97/5.90 inference(monotonicity,[status(thm)],[15908])).
% 5.97/5.90 tff(15910,plain,
% 5.97/5.90 (succ(succ(Y6!48)) = n9),
% 5.97/5.90 inference(transitivity,[status(thm)],[15909, 45])).
% 5.97/5.91 tff(15911,plain,
% 5.97/5.91 (succ(succ(succ(Y6!48))) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15910])).
% 5.97/5.91 tff(15912,plain,
% 5.97/5.91 (succ(succ(succ(Y6!48))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[15911, 28])).
% 5.97/5.91 tff(15913,plain,
% 5.97/5.91 (succ(succ(succ(succ(Y6!48)))) = succ(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15912])).
% 5.97/5.91 tff(15914,plain,
% 5.97/5.91 (succ(succ(succ(succ(Y6!48)))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[15913, 42])).
% 5.97/5.91 tff(15915,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15914])).
% 5.97/5.91 tff(15916,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(Y6!48))))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[15915, 58])).
% 5.97/5.91 tff(15917,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15916])).
% 5.97/5.91 tff(15918,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[15917, 36])).
% 5.97/5.91 tff(15919,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15918])).
% 5.97/5.91 tff(15920,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[15919, 48])).
% 5.97/5.91 tff(15921,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15920])).
% 5.97/5.91 tff(15922,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[15921, 14])).
% 5.97/5.91 tff(15923,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15922])).
% 5.97/5.91 tff(15924,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[15923, 33])).
% 5.97/5.91 tff(15925,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15924])).
% 5.97/5.91 tff(15926,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[15925, 30])).
% 5.97/5.91 tff(15927,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15926])).
% 5.97/5.91 tff(15928,plain,
% 5.97/5.91 (NSY6!12 = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[1490, 15927, 39])).
% 5.97/5.91 tff(15929,plain,
% 5.97/5.91 (pred(NSY6!12) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15928])).
% 5.97/5.91 tff(15930,plain,
% 5.97/5.91 (pred(NSY6!12) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[15929, 18])).
% 5.97/5.91 tff(15931,plain,
% 5.97/5.91 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n6, n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15930, 15906])).
% 5.97/5.91 tff(15932,plain,
% 5.97/5.91 (sum(pred(NSY6!12), succ(NPY6!14)) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[15931, 52])).
% 5.97/5.91 tff(15933,plain,
% 5.97/5.91 (sum(pred(Y5!50), succ(X5!51)) = sum(n9, n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15776, 15858])).
% 5.97/5.91 tff(15934,plain,
% 5.97/5.91 (sum(pred(Y5!50), succ(X5!51)) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[15933, 41])).
% 5.97/5.91 tff(15935,plain,
% 5.97/5.91 (sum(pred(X5!51), succ(Y5!50)) = sum(n9, n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15832, 15800])).
% 5.97/5.91 tff(15936,plain,
% 5.97/5.91 (sum(pred(X5!51), succ(Y5!50)) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[15935, 41])).
% 5.97/5.91 tff(15937,plain,
% 5.97/5.91 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n9, n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15936, 15934])).
% 5.97/5.91 tff(15938,plain,
% 5.97/5.91 (X6!49 = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[669, 15937, 54])).
% 5.97/5.91 tff(15939,plain,
% 5.97/5.91 (pred(X6!49) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15938])).
% 5.97/5.91 tff(15940,plain,
% 5.97/5.91 (pred(X6!49) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[15939, 18])).
% 5.97/5.91 tff(15941,plain,
% 5.97/5.91 (pred(pred(X6!49)) = pred(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15940])).
% 5.97/5.91 tff(15942,plain,
% 5.97/5.91 (pred(pred(X6!49)) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[15941, 17])).
% 5.97/5.91 tff(15943,plain,
% 5.97/5.91 (pred(pred(pred(X6!49))) = pred(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15942])).
% 5.97/5.91 tff(15944,plain,
% 5.97/5.91 (pred(pred(pred(X6!49))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[15943, 16])).
% 5.97/5.91 tff(15945,plain,
% 5.97/5.91 (pred(pred(pred(pred(X6!49)))) = pred(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15944])).
% 5.97/5.91 tff(15946,plain,
% 5.97/5.91 (pred(pred(pred(pred(X6!49)))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[15945, 15])).
% 5.97/5.91 tff(15947,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(X6!49))))) = pred(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15946])).
% 5.97/5.91 tff(15948,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(X6!49))))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[15947, 25])).
% 5.97/5.91 tff(15949,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15948])).
% 5.97/5.91 tff(15950,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[15949, 24])).
% 5.97/5.91 tff(15951,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15950])).
% 5.97/5.91 tff(15952,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[15951, 23])).
% 5.97/5.91 tff(15953,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15952])).
% 5.97/5.91 tff(15954,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[15953, 22])).
% 5.97/5.91 tff(15955,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15954])).
% 5.97/5.91 tff(15956,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[15955, 21])).
% 5.97/5.91 tff(15957,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15956])).
% 5.97/5.91 tff(15958,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[15957, 20])).
% 5.97/5.91 tff(15959,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15958])).
% 5.97/5.91 tff(15960,plain,
% 5.97/5.91 (NPX6!15 = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[1523, 15959, 19])).
% 5.97/5.91 tff(15961,plain,
% 5.97/5.91 (succ(NPX6!15) = succ(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15960])).
% 5.97/5.91 tff(15962,plain,
% 5.97/5.91 (succ(NPX6!15) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[15961, 53])).
% 5.97/5.91 tff(15963,plain,
% 5.97/5.91 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n8, n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15962, 15932])).
% 5.97/5.91 tff(15964,plain,
% 5.97/5.91 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[15963, 64])).
% 5.97/5.91 tff(15965,plain,
% 5.97/5.91 (succ(X6!49) = succ(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15938])).
% 5.97/5.91 tff(15966,plain,
% 5.97/5.91 (succ(X6!49) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[15965, 53])).
% 5.97/5.91 tff(15967,plain,
% 5.97/5.91 (succ(succ(X6!49)) = succ(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15966])).
% 5.97/5.91 tff(15968,plain,
% 5.97/5.91 (succ(succ(X6!49)) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[15967, 45])).
% 5.97/5.91 tff(15969,plain,
% 5.97/5.91 (succ(succ(succ(X6!49))) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15968])).
% 5.97/5.91 tff(15970,plain,
% 5.97/5.91 (succ(succ(succ(X6!49))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[15969, 28])).
% 5.97/5.91 tff(15971,plain,
% 5.97/5.91 (succ(succ(succ(succ(X6!49)))) = succ(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15970])).
% 5.97/5.91 tff(15972,plain,
% 5.97/5.91 (succ(succ(succ(succ(X6!49)))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[15971, 42])).
% 5.97/5.91 tff(15973,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(X6!49))))) = succ(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15972])).
% 5.97/5.91 tff(15974,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(X6!49))))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[15973, 58])).
% 5.97/5.91 tff(15975,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15974])).
% 5.97/5.91 tff(15976,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[15975, 36])).
% 5.97/5.91 tff(15977,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15976])).
% 5.97/5.91 tff(15978,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[15977, 48])).
% 5.97/5.91 tff(15979,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15978])).
% 5.97/5.91 tff(15980,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[15979, 14])).
% 5.97/5.91 tff(15981,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15980])).
% 5.97/5.91 tff(15982,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[15981, 33])).
% 5.97/5.91 tff(15983,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15982])).
% 5.97/5.91 tff(15984,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[15983, 30])).
% 5.97/5.91 tff(15985,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15984])).
% 5.97/5.91 tff(15986,plain,
% 5.97/5.91 (NSX6!13 = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[1550, 15985, 39])).
% 5.97/5.91 tff(15987,plain,
% 5.97/5.91 (pred(NSX6!13) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15986])).
% 5.97/5.91 tff(15988,plain,
% 5.97/5.91 (pred(NSX6!13) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[15987, 18])).
% 5.97/5.91 tff(15989,plain,
% 5.97/5.91 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n6, n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15988, 15964])).
% 5.97/5.91 tff(15990,plain,
% 5.97/5.91 (sum(n6, n0) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.97/5.91 inference(symmetry,[status(thm)],[15989])).
% 5.97/5.91 tff(15991,plain,
% 5.97/5.91 (sum(pred(Y6!48), succ(X6!49)) = sum(n6, n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15884, 15966])).
% 5.97/5.91 tff(15992,plain,
% 5.97/5.91 (sum(pred(Y6!48), succ(X6!49)) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[15991, 52])).
% 5.97/5.91 tff(15993,plain,
% 5.97/5.91 (sum(pred(X6!49), succ(Y6!48)) = sum(n6, n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15940, 15908])).
% 5.97/5.91 tff(15994,plain,
% 5.97/5.91 (sum(pred(X6!49), succ(Y6!48)) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[15993, 52])).
% 5.97/5.91 tff(15995,plain,
% 5.97/5.91 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n3, n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[15994, 15992])).
% 5.97/5.91 tff(15996,plain,
% 5.97/5.91 (X7!47 = Y7!46),
% 5.97/5.91 inference(transitivity,[status(thm)],[785, 15995, 51, 11259, 15990, 794])).
% 5.97/5.91 tff(15997,plain,
% 5.97/5.91 ($false),
% 5.97/5.91 inference(unit_resolution,[status(thm)],[792, 15996])).
% 5.97/5.91 tff(15998,plain,((~(X0!61 = n7)) | (X7!47 = Y7!46) | (~(Y0!60 = n2))), inference(lemma,lemma(discharge,[]))).
% 5.97/5.91 tff(15999,plain,
% 5.97/5.91 (~(X0!61 = n7)),
% 5.97/5.91 inference(unit_resolution,[status(thm)],[15998, 14626, 792])).
% 5.97/5.91 tff(16000,plain,
% 5.97/5.91 (sum(n7, n2) = n9),
% 5.97/5.91 inference(and_elim,[status(thm)],[9])).
% 5.97/5.91 tff(16001,plain,
% 5.97/5.91 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n9, n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[5172, 14676])).
% 5.97/5.91 tff(16002,plain,
% 5.97/5.91 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16001, 6583])).
% 5.97/5.91 tff(16003,plain,
% 5.97/5.91 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n7, n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[5198, 16002])).
% 5.97/5.91 tff(16004,plain,
% 5.97/5.91 (Y1!58 = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[196, 16003, 16000])).
% 5.97/5.91 tff(16005,plain,
% 5.97/5.91 (pred(Y1!58) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16004])).
% 5.97/5.91 tff(16006,plain,
% 5.97/5.91 (pred(Y1!58) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16005, 20])).
% 5.97/5.91 tff(16007,plain,
% 5.97/5.91 (pred(pred(Y1!58)) = pred(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16006])).
% 5.97/5.91 tff(16008,plain,
% 5.97/5.91 (pred(pred(Y1!58)) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16007, 19])).
% 5.97/5.91 tff(16009,plain,
% 5.97/5.91 (pred(pred(pred(Y1!58))) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16008])).
% 5.97/5.91 tff(16010,plain,
% 5.97/5.91 (pred(pred(pred(Y1!58))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16009, 18])).
% 5.97/5.91 tff(16011,plain,
% 5.97/5.91 (pred(pred(pred(pred(Y1!58)))) = pred(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16010])).
% 5.97/5.91 tff(16012,plain,
% 5.97/5.91 (pred(pred(pred(pred(Y1!58)))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16011, 17])).
% 5.97/5.91 tff(16013,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16012])).
% 5.97/5.91 tff(16014,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(Y1!58))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16013, 16])).
% 5.97/5.91 tff(16015,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16014])).
% 5.97/5.91 tff(16016,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[16015, 15])).
% 5.97/5.91 tff(16017,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16016])).
% 5.97/5.91 tff(16018,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16017, 25])).
% 5.97/5.91 tff(16019,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16018])).
% 5.97/5.91 tff(16020,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16019, 24])).
% 5.97/5.91 tff(16021,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16020])).
% 5.97/5.91 tff(16022,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16021, 23])).
% 5.97/5.91 tff(16023,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16022])).
% 5.97/5.91 tff(16024,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16023, 22])).
% 5.97/5.91 tff(16025,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16024])).
% 5.97/5.91 tff(16026,plain,
% 5.97/5.91 (NPY1!34 = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[232, 16025, 21])).
% 5.97/5.91 tff(16027,plain,
% 5.97/5.91 (succ(NPY1!34) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16026])).
% 5.97/5.91 tff(16028,plain,
% 5.97/5.91 (succ(NPY1!34) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16027, 28])).
% 5.97/5.91 tff(16029,plain,
% 5.97/5.91 (succ(Y1!58) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16004])).
% 5.97/5.91 tff(16030,plain,
% 5.97/5.91 (succ(Y1!58) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16029, 28])).
% 5.97/5.91 tff(16031,plain,
% 5.97/5.91 (succ(succ(Y1!58)) = succ(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16030])).
% 5.97/5.91 tff(16032,plain,
% 5.97/5.91 (succ(succ(Y1!58)) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16031, 42])).
% 5.97/5.91 tff(16033,plain,
% 5.97/5.91 (succ(succ(succ(Y1!58))) = succ(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16032])).
% 5.97/5.91 tff(16034,plain,
% 5.97/5.91 (succ(succ(succ(Y1!58))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16033, 58])).
% 5.97/5.91 tff(16035,plain,
% 5.97/5.91 (succ(succ(succ(succ(Y1!58)))) = succ(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16034])).
% 5.97/5.91 tff(16036,plain,
% 5.97/5.91 (succ(succ(succ(succ(Y1!58)))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16035, 36])).
% 5.97/5.91 tff(16037,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16036])).
% 5.97/5.91 tff(16038,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(Y1!58))))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[16037, 48])).
% 5.97/5.91 tff(16039,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16038])).
% 5.97/5.91 tff(16040,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16039, 14])).
% 5.97/5.91 tff(16041,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16040])).
% 5.97/5.91 tff(16042,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16041, 33])).
% 5.97/5.91 tff(16043,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16042])).
% 5.97/5.91 tff(16044,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16043, 30])).
% 5.97/5.91 tff(16045,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16044])).
% 5.97/5.91 tff(16046,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16045, 39])).
% 5.97/5.91 tff(16047,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16046])).
% 5.97/5.91 tff(16048,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16047, 53])).
% 5.97/5.91 tff(16049,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16048])).
% 5.97/5.91 tff(16050,plain,
% 5.97/5.91 (NSY1!32 = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[255, 16049, 45])).
% 5.97/5.91 tff(16051,plain,
% 5.97/5.91 (pred(NSY1!32) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16050])).
% 5.97/5.91 tff(16052,plain,
% 5.97/5.91 (pred(NSY1!32) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16051, 20])).
% 5.97/5.91 tff(16053,plain,
% 5.97/5.91 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n8, n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16052, 16028])).
% 5.97/5.91 tff(16054,plain,
% 5.97/5.91 (sum(pred(NSY1!32), succ(NPY1!34)) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16053, 27])).
% 5.97/5.91 tff(16055,plain,
% 5.97/5.91 (sum(n1, n9) = n10),
% 5.97/5.91 inference(and_elim,[status(thm)],[9])).
% 5.97/5.91 tff(16056,plain,
% 5.97/5.91 (sum(pred(Y0!60), succ(X0!61)) = sum(n1, n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[14628, 5176])).
% 5.97/5.91 tff(16057,plain,
% 5.97/5.91 (sum(pred(Y0!60), succ(X0!61)) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16056, 16055])).
% 5.97/5.91 tff(16058,plain,
% 5.97/5.91 (sum(pred(X0!61), succ(Y0!60)) = sum(n7, n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[5150, 14652])).
% 5.97/5.91 tff(16059,plain,
% 5.97/5.91 (sum(pred(X0!61), succ(Y0!60)) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16058, 789])).
% 5.97/5.91 tff(16060,plain,
% 5.97/5.91 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n10, n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16059, 16057])).
% 5.97/5.91 tff(16061,plain,
% 5.97/5.91 (X1!59 = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[93, 16060, 29])).
% 5.97/5.91 tff(16062,plain,
% 5.97/5.91 (pred(X1!59) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16061])).
% 5.97/5.91 tff(16063,plain,
% 5.97/5.91 (pred(X1!59) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16062, 20])).
% 5.97/5.91 tff(16064,plain,
% 5.97/5.91 (pred(pred(X1!59)) = pred(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16063])).
% 5.97/5.91 tff(16065,plain,
% 5.97/5.91 (pred(pred(X1!59)) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16064, 19])).
% 5.97/5.91 tff(16066,plain,
% 5.97/5.91 (pred(pred(pred(X1!59))) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16065])).
% 5.97/5.91 tff(16067,plain,
% 5.97/5.91 (pred(pred(pred(X1!59))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16066, 18])).
% 5.97/5.91 tff(16068,plain,
% 5.97/5.91 (pred(pred(pred(pred(X1!59)))) = pred(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16067])).
% 5.97/5.91 tff(16069,plain,
% 5.97/5.91 (pred(pred(pred(pred(X1!59)))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16068, 17])).
% 5.97/5.91 tff(16070,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(X1!59))))) = pred(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16069])).
% 5.97/5.91 tff(16071,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(X1!59))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16070, 16])).
% 5.97/5.91 tff(16072,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16071])).
% 5.97/5.91 tff(16073,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[16072, 15])).
% 5.97/5.91 tff(16074,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16073])).
% 5.97/5.91 tff(16075,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16074, 25])).
% 5.97/5.91 tff(16076,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16075])).
% 5.97/5.91 tff(16077,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16076, 24])).
% 5.97/5.91 tff(16078,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16077])).
% 5.97/5.91 tff(16079,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16078, 23])).
% 5.97/5.91 tff(16080,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16079])).
% 5.97/5.91 tff(16081,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16080, 22])).
% 5.97/5.91 tff(16082,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16081])).
% 5.97/5.91 tff(16083,plain,
% 5.97/5.91 (NPX1!35 = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[280, 16082, 21])).
% 5.97/5.91 tff(16084,plain,
% 5.97/5.91 (succ(NPX1!35) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16083])).
% 5.97/5.91 tff(16085,plain,
% 5.97/5.91 (succ(NPX1!35) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16084, 28])).
% 5.97/5.91 tff(16086,plain,
% 5.97/5.91 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n10, n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16085, 16054])).
% 5.97/5.91 tff(16087,plain,
% 5.97/5.91 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16086, 69])).
% 5.97/5.91 tff(16088,plain,
% 5.97/5.91 (succ(X1!59) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16061])).
% 5.97/5.91 tff(16089,plain,
% 5.97/5.91 (succ(X1!59) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16088, 28])).
% 5.97/5.91 tff(16090,plain,
% 5.97/5.91 (succ(succ(X1!59)) = succ(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16089])).
% 5.97/5.91 tff(16091,plain,
% 5.97/5.91 (succ(succ(X1!59)) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16090, 42])).
% 5.97/5.91 tff(16092,plain,
% 5.97/5.91 (succ(succ(succ(X1!59))) = succ(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16091])).
% 5.97/5.91 tff(16093,plain,
% 5.97/5.91 (succ(succ(succ(X1!59))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16092, 58])).
% 5.97/5.91 tff(16094,plain,
% 5.97/5.91 (succ(succ(succ(succ(X1!59)))) = succ(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16093])).
% 5.97/5.91 tff(16095,plain,
% 5.97/5.91 (succ(succ(succ(succ(X1!59)))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16094, 36])).
% 5.97/5.91 tff(16096,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(X1!59))))) = succ(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16095])).
% 5.97/5.91 tff(16097,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(X1!59))))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[16096, 48])).
% 5.97/5.91 tff(16098,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16097])).
% 5.97/5.91 tff(16099,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16098, 14])).
% 5.97/5.91 tff(16100,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16099])).
% 5.97/5.91 tff(16101,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16100, 33])).
% 5.97/5.91 tff(16102,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16101])).
% 5.97/5.91 tff(16103,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16102, 30])).
% 5.97/5.91 tff(16104,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16103])).
% 5.97/5.91 tff(16105,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16104, 39])).
% 5.97/5.91 tff(16106,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16105])).
% 5.97/5.91 tff(16107,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16106, 53])).
% 5.97/5.91 tff(16108,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16107])).
% 5.97/5.91 tff(16109,plain,
% 5.97/5.91 (NSX1!33 = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[305, 16108, 45])).
% 5.97/5.91 tff(16110,plain,
% 5.97/5.91 (pred(NSX1!33) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16109])).
% 5.97/5.91 tff(16111,plain,
% 5.97/5.91 (pred(NSX1!33) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16110, 20])).
% 5.97/5.91 tff(16112,plain,
% 5.97/5.91 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n8, n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16111, 16087])).
% 5.97/5.91 tff(16113,plain,
% 5.97/5.91 (Y2!56 = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[310, 16112, 98])).
% 5.97/5.91 tff(16114,plain,
% 5.97/5.91 (pred(Y2!56) = pred(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16113])).
% 5.97/5.91 tff(16115,plain,
% 5.97/5.91 (pred(Y2!56) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16114, 25])).
% 5.97/5.91 tff(16116,plain,
% 5.97/5.91 (pred(pred(Y2!56)) = pred(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16115])).
% 5.97/5.91 tff(16117,plain,
% 5.97/5.91 (pred(pred(Y2!56)) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16116, 24])).
% 5.97/5.91 tff(16118,plain,
% 5.97/5.91 (pred(pred(pred(Y2!56))) = pred(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16117])).
% 5.97/5.91 tff(16119,plain,
% 5.97/5.91 (pred(pred(pred(Y2!56))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16118, 23])).
% 5.97/5.91 tff(16120,plain,
% 5.97/5.91 (pred(pred(pred(pred(Y2!56)))) = pred(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16119])).
% 5.97/5.91 tff(16121,plain,
% 5.97/5.91 (pred(pred(pred(pred(Y2!56)))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16120, 22])).
% 5.97/5.91 tff(16122,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16121])).
% 5.97/5.91 tff(16123,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(Y2!56))))) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[16122, 21])).
% 5.97/5.91 tff(16124,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16123])).
% 5.97/5.91 tff(16125,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16124, 20])).
% 5.97/5.91 tff(16126,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16125])).
% 5.97/5.91 tff(16127,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16126, 19])).
% 5.97/5.91 tff(16128,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16127])).
% 5.97/5.91 tff(16129,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16128, 18])).
% 5.97/5.91 tff(16130,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16129])).
% 5.97/5.91 tff(16131,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16130, 17])).
% 5.97/5.91 tff(16132,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16131])).
% 5.97/5.91 tff(16133,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16132, 16])).
% 5.97/5.91 tff(16134,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16133])).
% 5.97/5.91 tff(16135,plain,
% 5.97/5.91 (NPY2!30 = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[347, 16134, 15])).
% 5.97/5.91 tff(16136,plain,
% 5.97/5.91 (succ(NPY2!30) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16135])).
% 5.97/5.91 tff(16137,plain,
% 5.97/5.91 (succ(NPY2!30) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16136, 14])).
% 5.97/5.91 tff(16138,plain,
% 5.97/5.91 (succ(Y2!56) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16113])).
% 5.97/5.91 tff(16139,plain,
% 5.97/5.91 (succ(Y2!56) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16138, 14])).
% 5.97/5.91 tff(16140,plain,
% 5.97/5.91 (succ(succ(Y2!56)) = succ(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16139])).
% 5.97/5.91 tff(16141,plain,
% 5.97/5.91 (succ(succ(Y2!56)) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16140, 33])).
% 5.97/5.91 tff(16142,plain,
% 5.97/5.91 (succ(succ(succ(Y2!56))) = succ(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16141])).
% 5.97/5.91 tff(16143,plain,
% 5.97/5.91 (succ(succ(succ(Y2!56))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16142, 30])).
% 5.97/5.91 tff(16144,plain,
% 5.97/5.91 (succ(succ(succ(succ(Y2!56)))) = succ(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16143])).
% 5.97/5.91 tff(16145,plain,
% 5.97/5.91 (succ(succ(succ(succ(Y2!56)))) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16144, 39])).
% 5.97/5.91 tff(16146,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16145])).
% 5.97/5.91 tff(16147,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(Y2!56))))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16146, 53])).
% 5.97/5.91 tff(16148,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16147])).
% 5.97/5.91 tff(16149,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[16148, 45])).
% 5.97/5.91 tff(16150,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16149])).
% 5.97/5.91 tff(16151,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16150, 28])).
% 5.97/5.91 tff(16152,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16151])).
% 5.97/5.91 tff(16153,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16152, 42])).
% 5.97/5.91 tff(16154,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16153])).
% 5.97/5.91 tff(16155,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16154, 58])).
% 5.97/5.91 tff(16156,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16155])).
% 5.97/5.91 tff(16157,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16156, 36])).
% 5.97/5.91 tff(16158,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16157])).
% 5.97/5.91 tff(16159,plain,
% 5.97/5.91 (NSY2!28 = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[370, 16158, 48])).
% 5.97/5.91 tff(16160,plain,
% 5.97/5.91 (pred(NSY2!28) = pred(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16159])).
% 5.97/5.91 tff(16161,plain,
% 5.97/5.91 (pred(NSY2!28) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16160, 25])).
% 5.97/5.91 tff(16162,plain,
% 5.97/5.91 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n2, n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16161, 16137])).
% 5.97/5.91 tff(16163,plain,
% 5.97/5.91 (sum(pred(NSY2!28), succ(NPY2!30)) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16162, 13])).
% 5.97/5.91 tff(16164,plain,
% 5.97/5.91 (sum(pred(Y1!58), succ(X1!59)) = sum(n8, n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16006, 16089])).
% 5.97/5.91 tff(16165,plain,
% 5.97/5.91 (sum(pred(Y1!58), succ(X1!59)) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16164, 27])).
% 5.97/5.91 tff(16166,plain,
% 5.97/5.91 (sum(pred(X1!59), succ(Y1!58)) = sum(n8, n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16063, 16030])).
% 5.97/5.91 tff(16167,plain,
% 5.97/5.91 (sum(pred(X1!59), succ(Y1!58)) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16166, 27])).
% 5.97/5.91 tff(16168,plain,
% 5.97/5.91 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n7, n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16167, 16165])).
% 5.97/5.91 tff(16169,plain,
% 5.97/5.91 (X2!57 = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[209, 16168, 26])).
% 5.97/5.91 tff(16170,plain,
% 5.97/5.91 (pred(X2!57) = pred(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16169])).
% 5.97/5.91 tff(16171,plain,
% 5.97/5.91 (pred(X2!57) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16170, 25])).
% 5.97/5.91 tff(16172,plain,
% 5.97/5.91 (pred(pred(X2!57)) = pred(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16171])).
% 5.97/5.91 tff(16173,plain,
% 5.97/5.91 (pred(pred(X2!57)) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16172, 24])).
% 5.97/5.91 tff(16174,plain,
% 5.97/5.91 (pred(pred(pred(X2!57))) = pred(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16173])).
% 5.97/5.91 tff(16175,plain,
% 5.97/5.91 (pred(pred(pred(X2!57))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16174, 23])).
% 5.97/5.91 tff(16176,plain,
% 5.97/5.91 (pred(pred(pred(pred(X2!57)))) = pred(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16175])).
% 5.97/5.91 tff(16177,plain,
% 5.97/5.91 (pred(pred(pred(pred(X2!57)))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16176, 22])).
% 5.97/5.91 tff(16178,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(X2!57))))) = pred(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16177])).
% 5.97/5.91 tff(16179,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(X2!57))))) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[16178, 21])).
% 5.97/5.91 tff(16180,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16179])).
% 5.97/5.91 tff(16181,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16180, 20])).
% 5.97/5.91 tff(16182,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16181])).
% 5.97/5.91 tff(16183,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16182, 19])).
% 5.97/5.91 tff(16184,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16183])).
% 5.97/5.91 tff(16185,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16184, 18])).
% 5.97/5.91 tff(16186,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16185])).
% 5.97/5.91 tff(16187,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16186, 17])).
% 5.97/5.91 tff(16188,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16187])).
% 5.97/5.91 tff(16189,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16188, 16])).
% 5.97/5.91 tff(16190,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16189])).
% 5.97/5.91 tff(16191,plain,
% 5.97/5.91 (NPX2!31 = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[395, 16190, 15])).
% 5.97/5.91 tff(16192,plain,
% 5.97/5.91 (succ(NPX2!31) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16191])).
% 5.97/5.91 tff(16193,plain,
% 5.97/5.91 (succ(NPX2!31) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16192, 14])).
% 5.97/5.91 tff(16194,plain,
% 5.97/5.91 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n4, n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16193, 16163])).
% 5.97/5.91 tff(16195,plain,
% 5.97/5.91 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16194, 12])).
% 5.97/5.91 tff(16196,plain,
% 5.97/5.91 (succ(X2!57) = succ(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16169])).
% 5.97/5.91 tff(16197,plain,
% 5.97/5.91 (succ(X2!57) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16196, 14])).
% 5.97/5.91 tff(16198,plain,
% 5.97/5.91 (succ(succ(X2!57)) = succ(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16197])).
% 5.97/5.91 tff(16199,plain,
% 5.97/5.91 (succ(succ(X2!57)) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16198, 33])).
% 5.97/5.91 tff(16200,plain,
% 5.97/5.91 (succ(succ(succ(X2!57))) = succ(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16199])).
% 5.97/5.91 tff(16201,plain,
% 5.97/5.91 (succ(succ(succ(X2!57))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16200, 30])).
% 5.97/5.91 tff(16202,plain,
% 5.97/5.91 (succ(succ(succ(succ(X2!57)))) = succ(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16201])).
% 5.97/5.91 tff(16203,plain,
% 5.97/5.91 (succ(succ(succ(succ(X2!57)))) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16202, 39])).
% 5.97/5.91 tff(16204,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(X2!57))))) = succ(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16203])).
% 5.97/5.91 tff(16205,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(X2!57))))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16204, 53])).
% 5.97/5.91 tff(16206,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16205])).
% 5.97/5.91 tff(16207,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[16206, 45])).
% 5.97/5.91 tff(16208,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16207])).
% 5.97/5.91 tff(16209,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16208, 28])).
% 5.97/5.91 tff(16210,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16209])).
% 5.97/5.91 tff(16211,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16210, 42])).
% 5.97/5.91 tff(16212,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16211])).
% 5.97/5.91 tff(16213,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[16212, 58])).
% 5.97/5.91 tff(16214,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16213])).
% 5.97/5.91 tff(16215,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16214, 36])).
% 5.97/5.91 tff(16216,plain,
% 5.97/5.91 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n2)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16215])).
% 5.97/5.91 tff(16217,plain,
% 5.97/5.91 (NSX2!29 = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[420, 16216, 48])).
% 5.97/5.91 tff(16218,plain,
% 5.97/5.91 (pred(NSX2!29) = pred(n3)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16217])).
% 5.97/5.91 tff(16219,plain,
% 5.97/5.91 (pred(NSX2!29) = n2),
% 5.97/5.91 inference(transitivity,[status(thm)],[16218, 25])).
% 5.97/5.91 tff(16220,plain,
% 5.97/5.91 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n2, n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16219, 16195])).
% 5.97/5.91 tff(16221,plain,
% 5.97/5.91 (Y3!54 = n1),
% 5.97/5.91 inference(transitivity,[status(thm)],[425, 16220, 327])).
% 5.97/5.91 tff(16222,plain,
% 5.97/5.91 (pred(Y3!54) = pred(n1)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16221])).
% 5.97/5.91 tff(16223,plain,
% 5.97/5.91 (pred(Y3!54) = n0),
% 5.97/5.91 inference(transitivity,[status(thm)],[16222, 23])).
% 5.97/5.91 tff(16224,plain,
% 5.97/5.91 (pred(pred(Y3!54)) = pred(n0)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16223])).
% 5.97/5.91 tff(16225,plain,
% 5.97/5.91 (pred(pred(Y3!54)) = n10),
% 5.97/5.91 inference(transitivity,[status(thm)],[16224, 22])).
% 5.97/5.91 tff(16226,plain,
% 5.97/5.91 (pred(pred(pred(Y3!54))) = pred(n10)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16225])).
% 5.97/5.91 tff(16227,plain,
% 5.97/5.91 (pred(pred(pred(Y3!54))) = n9),
% 5.97/5.91 inference(transitivity,[status(thm)],[16226, 21])).
% 5.97/5.91 tff(16228,plain,
% 5.97/5.91 (pred(pred(pred(pred(Y3!54)))) = pred(n9)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16227])).
% 5.97/5.91 tff(16229,plain,
% 5.97/5.91 (pred(pred(pred(pred(Y3!54)))) = n8),
% 5.97/5.91 inference(transitivity,[status(thm)],[16228, 20])).
% 5.97/5.91 tff(16230,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n8)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16229])).
% 5.97/5.91 tff(16231,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(Y3!54))))) = n7),
% 5.97/5.91 inference(transitivity,[status(thm)],[16230, 19])).
% 5.97/5.91 tff(16232,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n7)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16231])).
% 5.97/5.91 tff(16233,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n6),
% 5.97/5.91 inference(transitivity,[status(thm)],[16232, 18])).
% 5.97/5.91 tff(16234,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n6)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16233])).
% 5.97/5.91 tff(16235,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n5),
% 5.97/5.91 inference(transitivity,[status(thm)],[16234, 17])).
% 5.97/5.91 tff(16236,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n5)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16235])).
% 5.97/5.91 tff(16237,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n4),
% 5.97/5.91 inference(transitivity,[status(thm)],[16236, 16])).
% 5.97/5.91 tff(16238,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n4)),
% 5.97/5.91 inference(monotonicity,[status(thm)],[16237])).
% 5.97/5.91 tff(16239,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n3),
% 5.97/5.91 inference(transitivity,[status(thm)],[16238, 15])).
% 5.97/5.91 tff(16240,plain,
% 5.97/5.91 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16239])).
% 5.97/5.92 tff(16241,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16240, 25])).
% 5.97/5.92 tff(16242,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16241])).
% 5.97/5.92 tff(16243,plain,
% 5.97/5.92 (NPY3!26 = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[462, 16242, 24])).
% 5.97/5.92 tff(16244,plain,
% 5.97/5.92 (succ(NPY3!26) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16243])).
% 5.97/5.92 tff(16245,plain,
% 5.97/5.92 (succ(NPY3!26) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16244, 36])).
% 5.97/5.92 tff(16246,plain,
% 5.97/5.92 (succ(Y3!54) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16221])).
% 5.97/5.92 tff(16247,plain,
% 5.97/5.92 (succ(Y3!54) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16246, 36])).
% 5.97/5.92 tff(16248,plain,
% 5.97/5.92 (succ(succ(Y3!54)) = succ(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16247])).
% 5.97/5.92 tff(16249,plain,
% 5.97/5.92 (succ(succ(Y3!54)) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16248, 48])).
% 5.97/5.92 tff(16250,plain,
% 5.97/5.92 (succ(succ(succ(Y3!54))) = succ(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16249])).
% 5.97/5.92 tff(16251,plain,
% 5.97/5.92 (succ(succ(succ(Y3!54))) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16250, 14])).
% 5.97/5.92 tff(16252,plain,
% 5.97/5.92 (succ(succ(succ(succ(Y3!54)))) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16251])).
% 5.97/5.92 tff(16253,plain,
% 5.97/5.92 (succ(succ(succ(succ(Y3!54)))) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16252, 33])).
% 5.97/5.92 tff(16254,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16253])).
% 5.97/5.92 tff(16255,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(Y3!54))))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16254, 30])).
% 5.97/5.92 tff(16256,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16255])).
% 5.97/5.92 tff(16257,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16256, 39])).
% 5.97/5.92 tff(16258,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16257])).
% 5.97/5.92 tff(16259,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16258, 53])).
% 5.97/5.92 tff(16260,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16259])).
% 5.97/5.92 tff(16261,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16260, 45])).
% 5.97/5.92 tff(16262,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16261])).
% 5.97/5.92 tff(16263,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16262, 28])).
% 5.97/5.92 tff(16264,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16263])).
% 5.97/5.92 tff(16265,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16264, 42])).
% 5.97/5.92 tff(16266,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16265])).
% 5.97/5.92 tff(16267,plain,
% 5.97/5.92 (NSY3!24 = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[485, 16266, 58])).
% 5.97/5.92 tff(16268,plain,
% 5.97/5.92 (pred(NSY3!24) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16267])).
% 5.97/5.92 tff(16269,plain,
% 5.97/5.92 (pred(NSY3!24) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16268, 23])).
% 5.97/5.92 tff(16270,plain,
% 5.97/5.92 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n0, n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16269, 16245])).
% 5.97/5.92 tff(16271,plain,
% 5.97/5.92 (sum(pred(NSY3!24), succ(NPY3!26)) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16270, 35])).
% 5.97/5.92 tff(16272,plain,
% 5.97/5.92 (sum(pred(Y2!56), succ(X2!57)) = sum(n2, n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16115, 16197])).
% 5.97/5.92 tff(16273,plain,
% 5.97/5.92 (sum(pred(Y2!56), succ(X2!57)) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16272, 13])).
% 5.97/5.92 tff(16274,plain,
% 5.97/5.92 (sum(pred(X2!57), succ(Y2!56)) = sum(n2, n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16171, 16139])).
% 5.97/5.92 tff(16275,plain,
% 5.97/5.92 (sum(pred(X2!57), succ(Y2!56)) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16274, 13])).
% 5.97/5.92 tff(16276,plain,
% 5.97/5.92 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n6, n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16275, 16273])).
% 5.97/5.92 tff(16277,plain,
% 5.97/5.92 (X3!55 = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[323, 16276, 37])).
% 5.97/5.92 tff(16278,plain,
% 5.97/5.92 (pred(X3!55) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16277])).
% 5.97/5.92 tff(16279,plain,
% 5.97/5.92 (pred(X3!55) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16278, 23])).
% 5.97/5.92 tff(16280,plain,
% 5.97/5.92 (pred(pred(X3!55)) = pred(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16279])).
% 5.97/5.92 tff(16281,plain,
% 5.97/5.92 (pred(pred(X3!55)) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16280, 22])).
% 5.97/5.92 tff(16282,plain,
% 5.97/5.92 (pred(pred(pred(X3!55))) = pred(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16281])).
% 5.97/5.92 tff(16283,plain,
% 5.97/5.92 (pred(pred(pred(X3!55))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16282, 21])).
% 5.97/5.92 tff(16284,plain,
% 5.97/5.92 (pred(pred(pred(pred(X3!55)))) = pred(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16283])).
% 5.97/5.92 tff(16285,plain,
% 5.97/5.92 (pred(pred(pred(pred(X3!55)))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16284, 20])).
% 5.97/5.92 tff(16286,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(X3!55))))) = pred(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16285])).
% 5.97/5.92 tff(16287,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(X3!55))))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16286, 19])).
% 5.97/5.92 tff(16288,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16287])).
% 5.97/5.92 tff(16289,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16288, 18])).
% 5.97/5.92 tff(16290,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16289])).
% 5.97/5.92 tff(16291,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16290, 17])).
% 5.97/5.92 tff(16292,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16291])).
% 5.97/5.92 tff(16293,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16292, 16])).
% 5.97/5.92 tff(16294,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16293])).
% 5.97/5.92 tff(16295,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16294, 15])).
% 5.97/5.92 tff(16296,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16295])).
% 5.97/5.92 tff(16297,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16296, 25])).
% 5.97/5.92 tff(16298,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16297])).
% 5.97/5.92 tff(16299,plain,
% 5.97/5.92 (NPX3!27 = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[510, 16298, 24])).
% 5.97/5.92 tff(16300,plain,
% 5.97/5.92 (succ(NPX3!27) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16299])).
% 5.97/5.92 tff(16301,plain,
% 5.97/5.92 (succ(NPX3!27) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16300, 36])).
% 5.97/5.92 tff(16302,plain,
% 5.97/5.92 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n2, n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16301, 16271])).
% 5.97/5.92 tff(16303,plain,
% 5.97/5.92 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16302, 34])).
% 5.97/5.92 tff(16304,plain,
% 5.97/5.92 (succ(X3!55) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16277])).
% 5.97/5.92 tff(16305,plain,
% 5.97/5.92 (succ(X3!55) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16304, 36])).
% 5.97/5.92 tff(16306,plain,
% 5.97/5.92 (succ(succ(X3!55)) = succ(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16305])).
% 5.97/5.92 tff(16307,plain,
% 5.97/5.92 (succ(succ(X3!55)) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16306, 48])).
% 5.97/5.92 tff(16308,plain,
% 5.97/5.92 (succ(succ(succ(X3!55))) = succ(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16307])).
% 5.97/5.92 tff(16309,plain,
% 5.97/5.92 (succ(succ(succ(X3!55))) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16308, 14])).
% 5.97/5.92 tff(16310,plain,
% 5.97/5.92 (succ(succ(succ(succ(X3!55)))) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16309])).
% 5.97/5.92 tff(16311,plain,
% 5.97/5.92 (succ(succ(succ(succ(X3!55)))) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16310, 33])).
% 5.97/5.92 tff(16312,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(X3!55))))) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16311])).
% 5.97/5.92 tff(16313,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(X3!55))))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16312, 30])).
% 5.97/5.92 tff(16314,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16313])).
% 5.97/5.92 tff(16315,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16314, 39])).
% 5.97/5.92 tff(16316,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16315])).
% 5.97/5.92 tff(16317,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16316, 53])).
% 5.97/5.92 tff(16318,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16317])).
% 5.97/5.92 tff(16319,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16318, 45])).
% 5.97/5.92 tff(16320,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16319])).
% 5.97/5.92 tff(16321,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16320, 28])).
% 5.97/5.92 tff(16322,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16321])).
% 5.97/5.92 tff(16323,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16322, 42])).
% 5.97/5.92 tff(16324,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16323])).
% 5.97/5.92 tff(16325,plain,
% 5.97/5.92 (NSX3!25 = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[535, 16324, 58])).
% 5.97/5.92 tff(16326,plain,
% 5.97/5.92 (pred(NSX3!25) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16325])).
% 5.97/5.92 tff(16327,plain,
% 5.97/5.92 (pred(NSX3!25) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16326, 23])).
% 5.97/5.92 tff(16328,plain,
% 5.97/5.92 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n0, n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16327, 16303])).
% 5.97/5.92 tff(16329,plain,
% 5.97/5.92 (Y4!52 = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[540, 16328, 442])).
% 5.97/5.92 tff(16330,plain,
% 5.97/5.92 (pred(Y4!52) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16329])).
% 5.97/5.92 tff(16331,plain,
% 5.97/5.92 (pred(Y4!52) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16330, 15])).
% 5.97/5.92 tff(16332,plain,
% 5.97/5.92 (pred(pred(Y4!52)) = pred(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16331])).
% 5.97/5.92 tff(16333,plain,
% 5.97/5.92 (pred(pred(Y4!52)) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16332, 25])).
% 5.97/5.92 tff(16334,plain,
% 5.97/5.92 (pred(pred(pred(Y4!52))) = pred(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16333])).
% 5.97/5.92 tff(16335,plain,
% 5.97/5.92 (pred(pred(pred(Y4!52))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16334, 24])).
% 5.97/5.92 tff(16336,plain,
% 5.97/5.92 (pred(pred(pred(pred(Y4!52)))) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16335])).
% 5.97/5.92 tff(16337,plain,
% 5.97/5.92 (pred(pred(pred(pred(Y4!52)))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16336, 23])).
% 5.97/5.92 tff(16338,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16337])).
% 5.97/5.92 tff(16339,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(Y4!52))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16338, 22])).
% 5.97/5.92 tff(16340,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16339])).
% 5.97/5.92 tff(16341,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16340, 21])).
% 5.97/5.92 tff(16342,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16341])).
% 5.97/5.92 tff(16343,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16342, 20])).
% 5.97/5.92 tff(16344,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16343])).
% 5.97/5.92 tff(16345,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16344, 19])).
% 5.97/5.92 tff(16346,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16345])).
% 5.97/5.92 tff(16347,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16346, 18])).
% 5.97/5.92 tff(16348,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16347])).
% 5.97/5.92 tff(16349,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16348, 17])).
% 5.97/5.92 tff(16350,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16349])).
% 5.97/5.92 tff(16351,plain,
% 5.97/5.92 (NPY4!22 = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[578, 16350, 16])).
% 5.97/5.92 tff(16352,plain,
% 5.97/5.92 (succ(NPY4!22) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16351])).
% 5.97/5.92 tff(16353,plain,
% 5.97/5.92 (succ(NPY4!22) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16352, 33])).
% 5.97/5.92 tff(16354,plain,
% 5.97/5.92 (succ(Y4!52) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16329])).
% 5.97/5.92 tff(16355,plain,
% 5.97/5.92 (succ(Y4!52) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16354, 33])).
% 5.97/5.92 tff(16356,plain,
% 5.97/5.92 (succ(succ(Y4!52)) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16355])).
% 5.97/5.92 tff(16357,plain,
% 5.97/5.92 (succ(succ(Y4!52)) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16356, 30])).
% 5.97/5.92 tff(16358,plain,
% 5.97/5.92 (succ(succ(succ(Y4!52))) = succ(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16357])).
% 5.97/5.92 tff(16359,plain,
% 5.97/5.92 (succ(succ(succ(Y4!52))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16358, 39])).
% 5.97/5.92 tff(16360,plain,
% 5.97/5.92 (succ(succ(succ(succ(Y4!52)))) = succ(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16359])).
% 5.97/5.92 tff(16361,plain,
% 5.97/5.92 (succ(succ(succ(succ(Y4!52)))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16360, 53])).
% 5.97/5.92 tff(16362,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16361])).
% 5.97/5.92 tff(16363,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(Y4!52))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16362, 45])).
% 5.97/5.92 tff(16364,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16363])).
% 5.97/5.92 tff(16365,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16364, 28])).
% 5.97/5.92 tff(16366,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16365])).
% 5.97/5.92 tff(16367,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16366, 42])).
% 5.97/5.92 tff(16368,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16367])).
% 5.97/5.92 tff(16369,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16368, 58])).
% 5.97/5.92 tff(16370,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16369])).
% 5.97/5.92 tff(16371,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16370, 36])).
% 5.97/5.92 tff(16372,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16371])).
% 5.97/5.92 tff(16373,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16372, 48])).
% 5.97/5.92 tff(16374,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16373])).
% 5.97/5.92 tff(16375,plain,
% 5.97/5.92 (NSY4!20 = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[601, 16374, 14])).
% 5.97/5.92 tff(16376,plain,
% 5.97/5.92 (pred(NSY4!20) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16375])).
% 5.97/5.92 tff(16377,plain,
% 5.97/5.92 (pred(NSY4!20) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16376, 15])).
% 5.97/5.92 tff(16378,plain,
% 5.97/5.92 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n3, n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16377, 16353])).
% 5.97/5.92 tff(16379,plain,
% 5.97/5.92 (sum(pred(NSY4!20), succ(NPY4!22)) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16378, 32])).
% 5.97/5.92 tff(16380,plain,
% 5.97/5.92 (sum(pred(Y3!54), succ(X3!55)) = sum(n0, n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16223, 16305])).
% 5.97/5.92 tff(16381,plain,
% 5.97/5.92 (sum(pred(Y3!54), succ(X3!55)) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16380, 35])).
% 5.97/5.92 tff(16382,plain,
% 5.97/5.92 (sum(pred(X3!55), succ(Y3!54)) = sum(n0, n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16279, 16247])).
% 5.97/5.92 tff(16383,plain,
% 5.97/5.92 (sum(pred(X3!55), succ(Y3!54)) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16382, 35])).
% 5.97/5.92 tff(16384,plain,
% 5.97/5.92 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n2, n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16383, 16381])).
% 5.97/5.92 tff(16385,plain,
% 5.97/5.92 (X4!53 = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[438, 16384, 34])).
% 5.97/5.92 tff(16386,plain,
% 5.97/5.92 (pred(X4!53) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16385])).
% 5.97/5.92 tff(16387,plain,
% 5.97/5.92 (pred(X4!53) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16386, 15])).
% 5.97/5.92 tff(16388,plain,
% 5.97/5.92 (pred(pred(X4!53)) = pred(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16387])).
% 5.97/5.92 tff(16389,plain,
% 5.97/5.92 (pred(pred(X4!53)) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16388, 25])).
% 5.97/5.92 tff(16390,plain,
% 5.97/5.92 (pred(pred(pred(X4!53))) = pred(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16389])).
% 5.97/5.92 tff(16391,plain,
% 5.97/5.92 (pred(pred(pred(X4!53))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16390, 24])).
% 5.97/5.92 tff(16392,plain,
% 5.97/5.92 (pred(pred(pred(pred(X4!53)))) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16391])).
% 5.97/5.92 tff(16393,plain,
% 5.97/5.92 (pred(pred(pred(pred(X4!53)))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16392, 23])).
% 5.97/5.92 tff(16394,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(X4!53))))) = pred(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16393])).
% 5.97/5.92 tff(16395,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(X4!53))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16394, 22])).
% 5.97/5.92 tff(16396,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16395])).
% 5.97/5.92 tff(16397,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16396, 21])).
% 5.97/5.92 tff(16398,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16397])).
% 5.97/5.92 tff(16399,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16398, 20])).
% 5.97/5.92 tff(16400,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16399])).
% 5.97/5.92 tff(16401,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16400, 19])).
% 5.97/5.92 tff(16402,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16401])).
% 5.97/5.92 tff(16403,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16402, 18])).
% 5.97/5.92 tff(16404,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16403])).
% 5.97/5.92 tff(16405,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16404, 17])).
% 5.97/5.92 tff(16406,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16405])).
% 5.97/5.92 tff(16407,plain,
% 5.97/5.92 (NPX4!23 = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[626, 16406, 16])).
% 5.97/5.92 tff(16408,plain,
% 5.97/5.92 (succ(NPX4!23) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16407])).
% 5.97/5.92 tff(16409,plain,
% 5.97/5.92 (succ(NPX4!23) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16408, 33])).
% 5.97/5.92 tff(16410,plain,
% 5.97/5.92 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n5, n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16409, 16379])).
% 5.97/5.92 tff(16411,plain,
% 5.97/5.92 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16410, 558])).
% 5.97/5.92 tff(16412,plain,
% 5.97/5.92 (succ(X4!53) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16385])).
% 5.97/5.92 tff(16413,plain,
% 5.97/5.92 (succ(X4!53) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16412, 33])).
% 5.97/5.92 tff(16414,plain,
% 5.97/5.92 (succ(succ(X4!53)) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16413])).
% 5.97/5.92 tff(16415,plain,
% 5.97/5.92 (succ(succ(X4!53)) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16414, 30])).
% 5.97/5.92 tff(16416,plain,
% 5.97/5.92 (succ(succ(succ(X4!53))) = succ(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16415])).
% 5.97/5.92 tff(16417,plain,
% 5.97/5.92 (succ(succ(succ(X4!53))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16416, 39])).
% 5.97/5.92 tff(16418,plain,
% 5.97/5.92 (succ(succ(succ(succ(X4!53)))) = succ(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16417])).
% 5.97/5.92 tff(16419,plain,
% 5.97/5.92 (succ(succ(succ(succ(X4!53)))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16418, 53])).
% 5.97/5.92 tff(16420,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(X4!53))))) = succ(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16419])).
% 5.97/5.92 tff(16421,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(X4!53))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16420, 45])).
% 5.97/5.92 tff(16422,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16421])).
% 5.97/5.92 tff(16423,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16422, 28])).
% 5.97/5.92 tff(16424,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16423])).
% 5.97/5.92 tff(16425,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16424, 42])).
% 5.97/5.92 tff(16426,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16425])).
% 5.97/5.92 tff(16427,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16426, 58])).
% 5.97/5.92 tff(16428,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16427])).
% 5.97/5.92 tff(16429,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16428, 36])).
% 5.97/5.92 tff(16430,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16429])).
% 5.97/5.92 tff(16431,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16430, 48])).
% 5.97/5.92 tff(16432,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16431])).
% 5.97/5.92 tff(16433,plain,
% 5.97/5.92 (NSX4!21 = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[651, 16432, 14])).
% 5.97/5.92 tff(16434,plain,
% 5.97/5.92 (pred(NSX4!21) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16433])).
% 5.97/5.92 tff(16435,plain,
% 5.97/5.92 (pred(NSX4!21) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16434, 15])).
% 5.97/5.92 tff(16436,plain,
% 5.97/5.92 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n3, n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16435, 16411])).
% 5.97/5.92 tff(16437,plain,
% 5.97/5.92 (Y5!50 = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[656, 16436, 557])).
% 5.97/5.92 tff(16438,plain,
% 5.97/5.92 (pred(Y5!50) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16437])).
% 5.97/5.92 tff(16439,plain,
% 5.97/5.92 (pred(Y5!50) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16438, 16])).
% 5.97/5.92 tff(16440,plain,
% 5.97/5.92 (pred(pred(Y5!50)) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16439])).
% 5.97/5.92 tff(16441,plain,
% 5.97/5.92 (pred(pred(Y5!50)) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16440, 15])).
% 5.97/5.92 tff(16442,plain,
% 5.97/5.92 (pred(pred(pred(Y5!50))) = pred(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16441])).
% 5.97/5.92 tff(16443,plain,
% 5.97/5.92 (pred(pred(pred(Y5!50))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16442, 25])).
% 5.97/5.92 tff(16444,plain,
% 5.97/5.92 (pred(pred(pred(pred(Y5!50)))) = pred(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16443])).
% 5.97/5.92 tff(16445,plain,
% 5.97/5.92 (pred(pred(pred(pred(Y5!50)))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16444, 24])).
% 5.97/5.92 tff(16446,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16445])).
% 5.97/5.92 tff(16447,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(Y5!50))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16446, 23])).
% 5.97/5.92 tff(16448,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16447])).
% 5.97/5.92 tff(16449,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16448, 22])).
% 5.97/5.92 tff(16450,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16449])).
% 5.97/5.92 tff(16451,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16450, 21])).
% 5.97/5.92 tff(16452,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16451])).
% 5.97/5.92 tff(16453,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16452, 20])).
% 5.97/5.92 tff(16454,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16453])).
% 5.97/5.92 tff(16455,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16454, 19])).
% 5.97/5.92 tff(16456,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16455])).
% 5.97/5.92 tff(16457,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16456, 18])).
% 5.97/5.92 tff(16458,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16457])).
% 5.97/5.92 tff(16459,plain,
% 5.97/5.92 (NPY5!18 = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[694, 16458, 17])).
% 5.97/5.92 tff(16460,plain,
% 5.97/5.92 (succ(NPY5!18) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16459])).
% 5.97/5.92 tff(16461,plain,
% 5.97/5.92 (succ(NPY5!18) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16460, 30])).
% 5.97/5.92 tff(16462,plain,
% 5.97/5.92 (succ(Y5!50) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16437])).
% 5.97/5.92 tff(16463,plain,
% 5.97/5.92 (succ(Y5!50) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16462, 30])).
% 5.97/5.92 tff(16464,plain,
% 5.97/5.92 (succ(succ(Y5!50)) = succ(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16463])).
% 5.97/5.92 tff(16465,plain,
% 5.97/5.92 (succ(succ(Y5!50)) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16464, 39])).
% 5.97/5.92 tff(16466,plain,
% 5.97/5.92 (succ(succ(succ(Y5!50))) = succ(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16465])).
% 5.97/5.92 tff(16467,plain,
% 5.97/5.92 (succ(succ(succ(Y5!50))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16466, 53])).
% 5.97/5.92 tff(16468,plain,
% 5.97/5.92 (succ(succ(succ(succ(Y5!50)))) = succ(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16467])).
% 5.97/5.92 tff(16469,plain,
% 5.97/5.92 (succ(succ(succ(succ(Y5!50)))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16468, 45])).
% 5.97/5.92 tff(16470,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16469])).
% 5.97/5.92 tff(16471,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(Y5!50))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16470, 28])).
% 5.97/5.92 tff(16472,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16471])).
% 5.97/5.92 tff(16473,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16472, 42])).
% 5.97/5.92 tff(16474,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16473])).
% 5.97/5.92 tff(16475,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16474, 58])).
% 5.97/5.92 tff(16476,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16475])).
% 5.97/5.92 tff(16477,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16476, 36])).
% 5.97/5.92 tff(16478,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16477])).
% 5.97/5.92 tff(16479,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16478, 48])).
% 5.97/5.92 tff(16480,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16479])).
% 5.97/5.92 tff(16481,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16480, 14])).
% 5.97/5.92 tff(16482,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16481])).
% 5.97/5.92 tff(16483,plain,
% 5.97/5.92 (NSY5!16 = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[717, 16482, 33])).
% 5.97/5.92 tff(16484,plain,
% 5.97/5.92 (pred(NSY5!16) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16483])).
% 5.97/5.92 tff(16485,plain,
% 5.97/5.92 (pred(NSY5!16) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16484, 16])).
% 5.97/5.92 tff(16486,plain,
% 5.97/5.92 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n4, n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16485, 16461])).
% 5.97/5.92 tff(16487,plain,
% 5.97/5.92 (sum(pred(NSY5!16), succ(NPY5!18)) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16486, 12])).
% 5.97/5.92 tff(16488,plain,
% 5.97/5.92 (sum(pred(Y4!52), succ(X4!53)) = sum(n3, n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16331, 16413])).
% 5.97/5.92 tff(16489,plain,
% 5.97/5.92 (sum(pred(Y4!52), succ(X4!53)) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16488, 32])).
% 5.97/5.92 tff(16490,plain,
% 5.97/5.92 (sum(pred(X4!53), succ(Y4!52)) = sum(n3, n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16387, 16355])).
% 5.97/5.92 tff(16491,plain,
% 5.97/5.92 (sum(pred(X4!53), succ(Y4!52)) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16490, 32])).
% 5.97/5.92 tff(16492,plain,
% 5.97/5.92 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n8, n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16491, 16489])).
% 5.97/5.92 tff(16493,plain,
% 5.97/5.92 (X5!51 = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[553, 16492, 31])).
% 5.97/5.92 tff(16494,plain,
% 5.97/5.92 (pred(X5!51) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16493])).
% 5.97/5.92 tff(16495,plain,
% 5.97/5.92 (pred(X5!51) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16494, 16])).
% 5.97/5.92 tff(16496,plain,
% 5.97/5.92 (pred(pred(X5!51)) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16495])).
% 5.97/5.92 tff(16497,plain,
% 5.97/5.92 (pred(pred(X5!51)) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16496, 15])).
% 5.97/5.92 tff(16498,plain,
% 5.97/5.92 (pred(pred(pred(X5!51))) = pred(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16497])).
% 5.97/5.92 tff(16499,plain,
% 5.97/5.92 (pred(pred(pred(X5!51))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16498, 25])).
% 5.97/5.92 tff(16500,plain,
% 5.97/5.92 (pred(pred(pred(pred(X5!51)))) = pred(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16499])).
% 5.97/5.92 tff(16501,plain,
% 5.97/5.92 (pred(pred(pred(pred(X5!51)))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16500, 24])).
% 5.97/5.92 tff(16502,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(X5!51))))) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16501])).
% 5.97/5.92 tff(16503,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(X5!51))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16502, 23])).
% 5.97/5.92 tff(16504,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16503])).
% 5.97/5.92 tff(16505,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16504, 22])).
% 5.97/5.92 tff(16506,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16505])).
% 5.97/5.92 tff(16507,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16506, 21])).
% 5.97/5.92 tff(16508,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16507])).
% 5.97/5.92 tff(16509,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16508, 20])).
% 5.97/5.92 tff(16510,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16509])).
% 5.97/5.92 tff(16511,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16510, 19])).
% 5.97/5.92 tff(16512,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16511])).
% 5.97/5.92 tff(16513,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16512, 18])).
% 5.97/5.92 tff(16514,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16513])).
% 5.97/5.92 tff(16515,plain,
% 5.97/5.92 (NPX5!19 = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[742, 16514, 17])).
% 5.97/5.92 tff(16516,plain,
% 5.97/5.92 (succ(NPX5!19) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16515])).
% 5.97/5.92 tff(16517,plain,
% 5.97/5.92 (succ(NPX5!19) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16516, 30])).
% 5.97/5.92 tff(16518,plain,
% 5.97/5.92 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n6, n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16517, 16487])).
% 5.97/5.92 tff(16519,plain,
% 5.97/5.92 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16518, 674])).
% 5.97/5.92 tff(16520,plain,
% 5.97/5.92 (succ(X5!51) = succ(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16493])).
% 5.97/5.92 tff(16521,plain,
% 5.97/5.92 (succ(X5!51) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16520, 30])).
% 5.97/5.92 tff(16522,plain,
% 5.97/5.92 (succ(succ(X5!51)) = succ(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16521])).
% 5.97/5.92 tff(16523,plain,
% 5.97/5.92 (succ(succ(X5!51)) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16522, 39])).
% 5.97/5.92 tff(16524,plain,
% 5.97/5.92 (succ(succ(succ(X5!51))) = succ(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16523])).
% 5.97/5.92 tff(16525,plain,
% 5.97/5.92 (succ(succ(succ(X5!51))) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16524, 53])).
% 5.97/5.92 tff(16526,plain,
% 5.97/5.92 (succ(succ(succ(succ(X5!51)))) = succ(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16525])).
% 5.97/5.92 tff(16527,plain,
% 5.97/5.92 (succ(succ(succ(succ(X5!51)))) = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[16526, 45])).
% 5.97/5.92 tff(16528,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(X5!51))))) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16527])).
% 5.97/5.92 tff(16529,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(X5!51))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16528, 28])).
% 5.97/5.92 tff(16530,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16529])).
% 5.97/5.92 tff(16531,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16530, 42])).
% 5.97/5.92 tff(16532,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16531])).
% 5.97/5.92 tff(16533,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16532, 58])).
% 5.97/5.92 tff(16534,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16533])).
% 5.97/5.92 tff(16535,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16534, 36])).
% 5.97/5.92 tff(16536,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16535])).
% 5.97/5.92 tff(16537,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16536, 48])).
% 5.97/5.92 tff(16538,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16537])).
% 5.97/5.92 tff(16539,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16538, 14])).
% 5.97/5.92 tff(16540,plain,
% 5.97/5.92 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16539])).
% 5.97/5.92 tff(16541,plain,
% 5.97/5.92 (NSX5!17 = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[767, 16540, 33])).
% 5.97/5.92 tff(16542,plain,
% 5.97/5.92 (pred(NSX5!17) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16541])).
% 5.97/5.92 tff(16543,plain,
% 5.97/5.92 (pred(NSX5!17) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16542, 16])).
% 5.97/5.92 tff(16544,plain,
% 5.97/5.92 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n4, n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16543, 16519])).
% 5.97/5.92 tff(16545,plain,
% 5.97/5.92 (Y6!48 = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[772, 16544, 673])).
% 5.97/5.92 tff(16546,plain,
% 5.97/5.92 (pred(Y6!48) = pred(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16545])).
% 5.97/5.92 tff(16547,plain,
% 5.97/5.92 (pred(Y6!48) = n8),
% 5.97/5.92 inference(transitivity,[status(thm)],[16546, 20])).
% 5.97/5.92 tff(16548,plain,
% 5.97/5.92 (pred(pred(Y6!48)) = pred(n8)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16547])).
% 5.97/5.92 tff(16549,plain,
% 5.97/5.92 (pred(pred(Y6!48)) = n7),
% 5.97/5.92 inference(transitivity,[status(thm)],[16548, 19])).
% 5.97/5.92 tff(16550,plain,
% 5.97/5.92 (pred(pred(pred(Y6!48))) = pred(n7)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16549])).
% 5.97/5.92 tff(16551,plain,
% 5.97/5.92 (pred(pred(pred(Y6!48))) = n6),
% 5.97/5.92 inference(transitivity,[status(thm)],[16550, 18])).
% 5.97/5.92 tff(16552,plain,
% 5.97/5.92 (pred(pred(pred(pred(Y6!48)))) = pred(n6)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16551])).
% 5.97/5.92 tff(16553,plain,
% 5.97/5.92 (pred(pred(pred(pred(Y6!48)))) = n5),
% 5.97/5.92 inference(transitivity,[status(thm)],[16552, 17])).
% 5.97/5.92 tff(16554,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n5)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16553])).
% 5.97/5.92 tff(16555,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(Y6!48))))) = n4),
% 5.97/5.92 inference(transitivity,[status(thm)],[16554, 16])).
% 5.97/5.92 tff(16556,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n4)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16555])).
% 5.97/5.92 tff(16557,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n3),
% 5.97/5.92 inference(transitivity,[status(thm)],[16556, 15])).
% 5.97/5.92 tff(16558,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n3)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16557])).
% 5.97/5.92 tff(16559,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n2),
% 5.97/5.92 inference(transitivity,[status(thm)],[16558, 25])).
% 5.97/5.92 tff(16560,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n2)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16559])).
% 5.97/5.92 tff(16561,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n1),
% 5.97/5.92 inference(transitivity,[status(thm)],[16560, 24])).
% 5.97/5.92 tff(16562,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n1)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16561])).
% 5.97/5.92 tff(16563,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n0),
% 5.97/5.92 inference(transitivity,[status(thm)],[16562, 23])).
% 5.97/5.92 tff(16564,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n0)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16563])).
% 5.97/5.92 tff(16565,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16564, 22])).
% 5.97/5.92 tff(16566,plain,
% 5.97/5.92 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n10)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16565])).
% 5.97/5.92 tff(16567,plain,
% 5.97/5.92 (NPY6!14 = n9),
% 5.97/5.92 inference(transitivity,[status(thm)],[1465, 16566, 21])).
% 5.97/5.92 tff(16568,plain,
% 5.97/5.92 (succ(NPY6!14) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16567])).
% 5.97/5.92 tff(16569,plain,
% 5.97/5.92 (succ(NPY6!14) = n10),
% 5.97/5.92 inference(transitivity,[status(thm)],[16568, 28])).
% 5.97/5.92 tff(16570,plain,
% 5.97/5.92 (succ(Y6!48) = succ(n9)),
% 5.97/5.92 inference(monotonicity,[status(thm)],[16545])).
% 5.97/5.93 tff(16571,plain,
% 5.97/5.93 (succ(Y6!48) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16570, 28])).
% 5.97/5.93 tff(16572,plain,
% 5.97/5.93 (succ(succ(Y6!48)) = succ(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16571])).
% 5.97/5.93 tff(16573,plain,
% 5.97/5.93 (succ(succ(Y6!48)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16572, 42])).
% 5.97/5.93 tff(16574,plain,
% 5.97/5.93 (succ(succ(succ(Y6!48))) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16573])).
% 5.97/5.93 tff(16575,plain,
% 5.97/5.93 (succ(succ(succ(Y6!48))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16574, 58])).
% 5.97/5.93 tff(16576,plain,
% 5.97/5.93 (succ(succ(succ(succ(Y6!48)))) = succ(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16575])).
% 5.97/5.93 tff(16577,plain,
% 5.97/5.93 (succ(succ(succ(succ(Y6!48)))) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16576, 36])).
% 5.97/5.93 tff(16578,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16577])).
% 5.97/5.93 tff(16579,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(Y6!48))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16578, 48])).
% 5.97/5.93 tff(16580,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16579])).
% 5.97/5.93 tff(16581,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16580, 14])).
% 5.97/5.93 tff(16582,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16581])).
% 5.97/5.93 tff(16583,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16582, 33])).
% 5.97/5.93 tff(16584,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16583])).
% 5.97/5.93 tff(16585,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16584, 30])).
% 5.97/5.93 tff(16586,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16585])).
% 5.97/5.93 tff(16587,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16586, 39])).
% 5.97/5.93 tff(16588,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16587])).
% 5.97/5.93 tff(16589,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16588, 53])).
% 5.97/5.93 tff(16590,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16589])).
% 5.97/5.93 tff(16591,plain,
% 5.97/5.93 (NSY6!12 = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[1490, 16590, 45])).
% 5.97/5.93 tff(16592,plain,
% 5.97/5.93 (pred(NSY6!12) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16591])).
% 5.97/5.93 tff(16593,plain,
% 5.97/5.93 (pred(NSY6!12) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16592, 20])).
% 5.97/5.93 tff(16594,plain,
% 5.97/5.93 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n8, n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16593, 16569])).
% 5.97/5.93 tff(16595,plain,
% 5.97/5.93 (sum(pred(NSY6!12), succ(NPY6!14)) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16594, 27])).
% 5.97/5.93 tff(16596,plain,
% 5.97/5.93 (sum(pred(Y5!50), succ(X5!51)) = sum(n4, n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16439, 16521])).
% 5.97/5.93 tff(16597,plain,
% 5.97/5.93 (sum(pred(Y5!50), succ(X5!51)) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16596, 12])).
% 5.97/5.93 tff(16598,plain,
% 5.97/5.93 (sum(pred(X5!51), succ(Y5!50)) = sum(n4, n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16495, 16463])).
% 5.97/5.93 tff(16599,plain,
% 5.97/5.93 (sum(pred(X5!51), succ(Y5!50)) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16598, 12])).
% 5.97/5.93 tff(16600,plain,
% 5.97/5.93 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n10, n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16599, 16597])).
% 5.97/5.93 tff(16601,plain,
% 5.97/5.93 (X6!49 = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[669, 16600, 29])).
% 5.97/5.93 tff(16602,plain,
% 5.97/5.93 (pred(X6!49) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16601])).
% 5.97/5.93 tff(16603,plain,
% 5.97/5.93 (pred(X6!49) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16602, 20])).
% 5.97/5.93 tff(16604,plain,
% 5.97/5.93 (pred(pred(X6!49)) = pred(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16603])).
% 5.97/5.93 tff(16605,plain,
% 5.97/5.93 (pred(pred(X6!49)) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16604, 19])).
% 5.97/5.93 tff(16606,plain,
% 5.97/5.93 (pred(pred(pred(X6!49))) = pred(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16605])).
% 5.97/5.93 tff(16607,plain,
% 5.97/5.93 (pred(pred(pred(X6!49))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16606, 18])).
% 5.97/5.93 tff(16608,plain,
% 5.97/5.93 (pred(pred(pred(pred(X6!49)))) = pred(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16607])).
% 5.97/5.93 tff(16609,plain,
% 5.97/5.93 (pred(pred(pred(pred(X6!49)))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16608, 17])).
% 5.97/5.93 tff(16610,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(X6!49))))) = pred(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16609])).
% 5.97/5.93 tff(16611,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(X6!49))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16610, 16])).
% 5.97/5.93 tff(16612,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16611])).
% 5.97/5.93 tff(16613,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16612, 15])).
% 5.97/5.93 tff(16614,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16613])).
% 5.97/5.93 tff(16615,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16614, 25])).
% 5.97/5.93 tff(16616,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16615])).
% 5.97/5.93 tff(16617,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16616, 24])).
% 5.97/5.93 tff(16618,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16617])).
% 5.97/5.93 tff(16619,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16618, 23])).
% 5.97/5.93 tff(16620,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16619])).
% 5.97/5.93 tff(16621,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16620, 22])).
% 5.97/5.93 tff(16622,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16621])).
% 5.97/5.93 tff(16623,plain,
% 5.97/5.93 (NPX6!15 = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[1523, 16622, 21])).
% 5.97/5.93 tff(16624,plain,
% 5.97/5.93 (succ(NPX6!15) = succ(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16623])).
% 5.97/5.93 tff(16625,plain,
% 5.97/5.93 (succ(NPX6!15) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16624, 28])).
% 5.97/5.93 tff(16626,plain,
% 5.97/5.93 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n10, n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16625, 16595])).
% 5.97/5.93 tff(16627,plain,
% 5.97/5.93 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16626, 69])).
% 5.97/5.93 tff(16628,plain,
% 5.97/5.93 (succ(X6!49) = succ(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16601])).
% 5.97/5.93 tff(16629,plain,
% 5.97/5.93 (succ(X6!49) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16628, 28])).
% 5.97/5.93 tff(16630,plain,
% 5.97/5.93 (succ(succ(X6!49)) = succ(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16629])).
% 5.97/5.93 tff(16631,plain,
% 5.97/5.93 (succ(succ(X6!49)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16630, 42])).
% 5.97/5.93 tff(16632,plain,
% 5.97/5.93 (succ(succ(succ(X6!49))) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16631])).
% 5.97/5.93 tff(16633,plain,
% 5.97/5.93 (succ(succ(succ(X6!49))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16632, 58])).
% 5.97/5.93 tff(16634,plain,
% 5.97/5.93 (succ(succ(succ(succ(X6!49)))) = succ(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16633])).
% 5.97/5.93 tff(16635,plain,
% 5.97/5.93 (succ(succ(succ(succ(X6!49)))) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16634, 36])).
% 5.97/5.93 tff(16636,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(X6!49))))) = succ(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16635])).
% 5.97/5.93 tff(16637,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(X6!49))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16636, 48])).
% 5.97/5.93 tff(16638,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16637])).
% 5.97/5.93 tff(16639,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16638, 14])).
% 5.97/5.93 tff(16640,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16639])).
% 5.97/5.93 tff(16641,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16640, 33])).
% 5.97/5.93 tff(16642,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16641])).
% 5.97/5.93 tff(16643,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16642, 30])).
% 5.97/5.93 tff(16644,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16643])).
% 5.97/5.93 tff(16645,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16644, 39])).
% 5.97/5.93 tff(16646,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16645])).
% 5.97/5.93 tff(16647,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16646, 53])).
% 5.97/5.93 tff(16648,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16647])).
% 5.97/5.93 tff(16649,plain,
% 5.97/5.93 (NSX6!13 = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[1550, 16648, 45])).
% 5.97/5.93 tff(16650,plain,
% 5.97/5.93 (pred(NSX6!13) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16649])).
% 5.97/5.93 tff(16651,plain,
% 5.97/5.93 (pred(NSX6!13) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16650, 20])).
% 5.97/5.93 tff(16652,plain,
% 5.97/5.93 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n8, n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16651, 16627])).
% 5.97/5.93 tff(16653,plain,
% 5.97/5.93 (sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.97/5.93 inference(symmetry,[status(thm)],[16652])).
% 5.97/5.93 tff(16654,plain,
% 5.97/5.93 (sum(pred(Y6!48), succ(X6!49)) = sum(n8, n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16547, 16629])).
% 5.97/5.93 tff(16655,plain,
% 5.97/5.93 (sum(pred(Y6!48), succ(X6!49)) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16654, 27])).
% 5.97/5.93 tff(16656,plain,
% 5.97/5.93 (sum(pred(X6!49), succ(Y6!48)) = sum(n8, n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16603, 16571])).
% 5.97/5.93 tff(16657,plain,
% 5.97/5.93 (sum(pred(X6!49), succ(Y6!48)) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16656, 27])).
% 5.97/5.93 tff(16658,plain,
% 5.97/5.93 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n7, n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16657, 16655])).
% 5.97/5.93 tff(16659,plain,
% 5.97/5.93 (X7!47 = Y7!46),
% 5.97/5.93 inference(transitivity,[status(thm)],[785, 16658, 26, 1556, 16653, 794])).
% 5.97/5.93 tff(16660,plain,
% 5.97/5.93 ($false),
% 5.97/5.93 inference(unit_resolution,[status(thm)],[792, 16659])).
% 5.97/5.93 tff(16661,plain,((~(X0!61 = n8)) | (X7!47 = Y7!46) | (~(Y0!60 = n2))), inference(lemma,lemma(discharge,[]))).
% 5.97/5.93 tff(16662,plain,
% 5.97/5.93 (~(X0!61 = n8)),
% 5.97/5.93 inference(unit_resolution,[status(thm)],[16661, 14626, 792])).
% 5.97/5.93 tff(16663,plain,
% 5.97/5.93 (sum(n10, n4) = n3),
% 5.97/5.93 inference(and_elim,[status(thm)],[9])).
% 5.97/5.93 tff(16664,plain,
% 5.97/5.93 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n10, n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[2362, 14676])).
% 5.97/5.93 tff(16665,plain,
% 5.97/5.93 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16664, 16663])).
% 5.97/5.93 tff(16666,plain,
% 5.97/5.93 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n8, n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[2388, 16665])).
% 5.97/5.93 tff(16667,plain,
% 5.97/5.93 (Y1!58 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[196, 16666, 64])).
% 5.97/5.93 tff(16668,plain,
% 5.97/5.93 (pred(Y1!58) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16667])).
% 5.97/5.93 tff(16669,plain,
% 5.97/5.93 (pred(Y1!58) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16668, 22])).
% 5.97/5.93 tff(16670,plain,
% 5.97/5.93 (pred(pred(Y1!58)) = pred(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16669])).
% 5.97/5.93 tff(16671,plain,
% 5.97/5.93 (pred(pred(Y1!58)) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16670, 21])).
% 5.97/5.93 tff(16672,plain,
% 5.97/5.93 (pred(pred(pred(Y1!58))) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16671])).
% 5.97/5.93 tff(16673,plain,
% 5.97/5.93 (pred(pred(pred(Y1!58))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16672, 20])).
% 5.97/5.93 tff(16674,plain,
% 5.97/5.93 (pred(pred(pred(pred(Y1!58)))) = pred(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16673])).
% 5.97/5.93 tff(16675,plain,
% 5.97/5.93 (pred(pred(pred(pred(Y1!58)))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16674, 19])).
% 5.97/5.93 tff(16676,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16675])).
% 5.97/5.93 tff(16677,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(Y1!58))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16676, 18])).
% 5.97/5.93 tff(16678,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16677])).
% 5.97/5.93 tff(16679,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16678, 17])).
% 5.97/5.93 tff(16680,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16679])).
% 5.97/5.93 tff(16681,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16680, 16])).
% 5.97/5.93 tff(16682,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16681])).
% 5.97/5.93 tff(16683,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16682, 15])).
% 5.97/5.93 tff(16684,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16683])).
% 5.97/5.93 tff(16685,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16684, 25])).
% 5.97/5.93 tff(16686,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16685])).
% 5.97/5.93 tff(16687,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16686, 24])).
% 5.97/5.93 tff(16688,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16687])).
% 5.97/5.93 tff(16689,plain,
% 5.97/5.93 (NPY1!34 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[232, 16688, 23])).
% 5.97/5.93 tff(16690,plain,
% 5.97/5.93 (succ(NPY1!34) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16689])).
% 5.97/5.93 tff(16691,plain,
% 5.97/5.93 (succ(NPY1!34) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16690, 58])).
% 5.97/5.93 tff(16692,plain,
% 5.97/5.93 (succ(Y1!58) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16667])).
% 5.97/5.93 tff(16693,plain,
% 5.97/5.93 (succ(Y1!58) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16692, 58])).
% 5.97/5.93 tff(16694,plain,
% 5.97/5.93 (succ(succ(Y1!58)) = succ(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16693])).
% 5.97/5.93 tff(16695,plain,
% 5.97/5.93 (succ(succ(Y1!58)) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16694, 36])).
% 5.97/5.93 tff(16696,plain,
% 5.97/5.93 (succ(succ(succ(Y1!58))) = succ(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16695])).
% 5.97/5.93 tff(16697,plain,
% 5.97/5.93 (succ(succ(succ(Y1!58))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16696, 48])).
% 5.97/5.93 tff(16698,plain,
% 5.97/5.93 (succ(succ(succ(succ(Y1!58)))) = succ(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16697])).
% 5.97/5.93 tff(16699,plain,
% 5.97/5.93 (succ(succ(succ(succ(Y1!58)))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16698, 14])).
% 5.97/5.93 tff(16700,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16699])).
% 5.97/5.93 tff(16701,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(Y1!58))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16700, 33])).
% 5.97/5.93 tff(16702,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16701])).
% 5.97/5.93 tff(16703,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16702, 30])).
% 5.97/5.93 tff(16704,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16703])).
% 5.97/5.93 tff(16705,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16704, 39])).
% 5.97/5.93 tff(16706,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16705])).
% 5.97/5.93 tff(16707,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16706, 53])).
% 5.97/5.93 tff(16708,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16707])).
% 5.97/5.93 tff(16709,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16708, 45])).
% 5.97/5.93 tff(16710,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16709])).
% 5.97/5.93 tff(16711,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16710, 28])).
% 5.97/5.93 tff(16712,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16711])).
% 5.97/5.93 tff(16713,plain,
% 5.97/5.93 (NSY1!32 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[255, 16712, 42])).
% 5.97/5.93 tff(16714,plain,
% 5.97/5.93 (pred(NSY1!32) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16713])).
% 5.97/5.93 tff(16715,plain,
% 5.97/5.93 (pred(NSY1!32) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16714, 22])).
% 5.97/5.93 tff(16716,plain,
% 5.97/5.93 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n10, n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16715, 16691])).
% 5.97/5.93 tff(16717,plain,
% 5.97/5.93 (sum(pred(NSY1!32), succ(NPY1!34)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16716, 57])).
% 5.97/5.93 tff(16718,plain,
% 5.97/5.93 (sum(n1, n10) = n0),
% 5.97/5.93 inference(and_elim,[status(thm)],[9])).
% 5.97/5.93 tff(16719,plain,
% 5.97/5.93 (sum(pred(Y0!60), succ(X0!61)) = sum(n1, n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[14628, 2366])).
% 5.97/5.93 tff(16720,plain,
% 5.97/5.93 (sum(pred(Y0!60), succ(X0!61)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16719, 16718])).
% 5.97/5.93 tff(16721,plain,
% 5.97/5.93 (sum(pred(X0!61), succ(Y0!60)) = sum(n8, n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[2340, 14652])).
% 5.97/5.93 tff(16722,plain,
% 5.97/5.93 (sum(pred(X0!61), succ(Y0!60)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16721, 64])).
% 5.97/5.93 tff(16723,plain,
% 5.97/5.93 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n0, n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16722, 16720])).
% 5.97/5.93 tff(16724,plain,
% 5.97/5.93 (X1!59 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[93, 16723, 59])).
% 5.97/5.93 tff(16725,plain,
% 5.97/5.93 (pred(X1!59) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16724])).
% 5.97/5.93 tff(16726,plain,
% 5.97/5.93 (pred(X1!59) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16725, 22])).
% 5.97/5.93 tff(16727,plain,
% 5.97/5.93 (pred(pred(X1!59)) = pred(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16726])).
% 5.97/5.93 tff(16728,plain,
% 5.97/5.93 (pred(pred(X1!59)) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16727, 21])).
% 5.97/5.93 tff(16729,plain,
% 5.97/5.93 (pred(pred(pred(X1!59))) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16728])).
% 5.97/5.93 tff(16730,plain,
% 5.97/5.93 (pred(pred(pred(X1!59))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16729, 20])).
% 5.97/5.93 tff(16731,plain,
% 5.97/5.93 (pred(pred(pred(pred(X1!59)))) = pred(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16730])).
% 5.97/5.93 tff(16732,plain,
% 5.97/5.93 (pred(pred(pred(pred(X1!59)))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16731, 19])).
% 5.97/5.93 tff(16733,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(X1!59))))) = pred(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16732])).
% 5.97/5.93 tff(16734,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(X1!59))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16733, 18])).
% 5.97/5.93 tff(16735,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16734])).
% 5.97/5.93 tff(16736,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16735, 17])).
% 5.97/5.93 tff(16737,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16736])).
% 5.97/5.93 tff(16738,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16737, 16])).
% 5.97/5.93 tff(16739,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16738])).
% 5.97/5.93 tff(16740,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16739, 15])).
% 5.97/5.93 tff(16741,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16740])).
% 5.97/5.93 tff(16742,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16741, 25])).
% 5.97/5.93 tff(16743,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16742])).
% 5.97/5.93 tff(16744,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16743, 24])).
% 5.97/5.93 tff(16745,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16744])).
% 5.97/5.93 tff(16746,plain,
% 5.97/5.93 (NPX1!35 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[280, 16745, 23])).
% 5.97/5.93 tff(16747,plain,
% 5.97/5.93 (succ(NPX1!35) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16746])).
% 5.97/5.93 tff(16748,plain,
% 5.97/5.93 (succ(NPX1!35) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16747, 58])).
% 5.97/5.93 tff(16749,plain,
% 5.97/5.93 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n1, n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16748, 16717])).
% 5.97/5.93 tff(16750,plain,
% 5.97/5.93 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16749, 56])).
% 5.97/5.93 tff(16751,plain,
% 5.97/5.93 (succ(X1!59) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16724])).
% 5.97/5.93 tff(16752,plain,
% 5.97/5.93 (succ(X1!59) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16751, 58])).
% 5.97/5.93 tff(16753,plain,
% 5.97/5.93 (succ(succ(X1!59)) = succ(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16752])).
% 5.97/5.93 tff(16754,plain,
% 5.97/5.93 (succ(succ(X1!59)) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16753, 36])).
% 5.97/5.93 tff(16755,plain,
% 5.97/5.93 (succ(succ(succ(X1!59))) = succ(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16754])).
% 5.97/5.93 tff(16756,plain,
% 5.97/5.93 (succ(succ(succ(X1!59))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16755, 48])).
% 5.97/5.93 tff(16757,plain,
% 5.97/5.93 (succ(succ(succ(succ(X1!59)))) = succ(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16756])).
% 5.97/5.93 tff(16758,plain,
% 5.97/5.93 (succ(succ(succ(succ(X1!59)))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16757, 14])).
% 5.97/5.93 tff(16759,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(X1!59))))) = succ(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16758])).
% 5.97/5.93 tff(16760,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(X1!59))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16759, 33])).
% 5.97/5.93 tff(16761,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16760])).
% 5.97/5.93 tff(16762,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16761, 30])).
% 5.97/5.93 tff(16763,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16762])).
% 5.97/5.93 tff(16764,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16763, 39])).
% 5.97/5.93 tff(16765,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16764])).
% 5.97/5.93 tff(16766,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16765, 53])).
% 5.97/5.93 tff(16767,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16766])).
% 5.97/5.93 tff(16768,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16767, 45])).
% 5.97/5.93 tff(16769,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16768])).
% 5.97/5.93 tff(16770,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16769, 28])).
% 5.97/5.93 tff(16771,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16770])).
% 5.97/5.93 tff(16772,plain,
% 5.97/5.93 (NSX1!33 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[305, 16771, 42])).
% 5.97/5.93 tff(16773,plain,
% 5.97/5.93 (pred(NSX1!33) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16772])).
% 5.97/5.93 tff(16774,plain,
% 5.97/5.93 (pred(NSX1!33) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16773, 22])).
% 5.97/5.93 tff(16775,plain,
% 5.97/5.93 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n10, n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16774, 16750])).
% 5.97/5.93 tff(16776,plain,
% 5.97/5.93 (Y2!56 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[310, 16775, 57])).
% 5.97/5.93 tff(16777,plain,
% 5.97/5.93 (pred(Y2!56) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16776])).
% 5.97/5.93 tff(16778,plain,
% 5.97/5.93 (pred(Y2!56) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16777, 22])).
% 5.97/5.93 tff(16779,plain,
% 5.97/5.93 (pred(pred(Y2!56)) = pred(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16778])).
% 5.97/5.93 tff(16780,plain,
% 5.97/5.93 (pred(pred(Y2!56)) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16779, 21])).
% 5.97/5.93 tff(16781,plain,
% 5.97/5.93 (pred(pred(pred(Y2!56))) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16780])).
% 5.97/5.93 tff(16782,plain,
% 5.97/5.93 (pred(pred(pred(Y2!56))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16781, 20])).
% 5.97/5.93 tff(16783,plain,
% 5.97/5.93 (pred(pred(pred(pred(Y2!56)))) = pred(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16782])).
% 5.97/5.93 tff(16784,plain,
% 5.97/5.93 (pred(pred(pred(pred(Y2!56)))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16783, 19])).
% 5.97/5.93 tff(16785,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16784])).
% 5.97/5.93 tff(16786,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(Y2!56))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16785, 18])).
% 5.97/5.93 tff(16787,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16786])).
% 5.97/5.93 tff(16788,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16787, 17])).
% 5.97/5.93 tff(16789,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16788])).
% 5.97/5.93 tff(16790,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16789, 16])).
% 5.97/5.93 tff(16791,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16790])).
% 5.97/5.93 tff(16792,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16791, 15])).
% 5.97/5.93 tff(16793,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16792])).
% 5.97/5.93 tff(16794,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16793, 25])).
% 5.97/5.93 tff(16795,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16794])).
% 5.97/5.93 tff(16796,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16795, 24])).
% 5.97/5.93 tff(16797,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16796])).
% 5.97/5.93 tff(16798,plain,
% 5.97/5.93 (NPY2!30 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[347, 16797, 23])).
% 5.97/5.93 tff(16799,plain,
% 5.97/5.93 (succ(NPY2!30) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16798])).
% 5.97/5.93 tff(16800,plain,
% 5.97/5.93 (succ(NPY2!30) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16799, 58])).
% 5.97/5.93 tff(16801,plain,
% 5.97/5.93 (succ(Y2!56) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16776])).
% 5.97/5.93 tff(16802,plain,
% 5.97/5.93 (succ(Y2!56) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16801, 58])).
% 5.97/5.93 tff(16803,plain,
% 5.97/5.93 (succ(succ(Y2!56)) = succ(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16802])).
% 5.97/5.93 tff(16804,plain,
% 5.97/5.93 (succ(succ(Y2!56)) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16803, 36])).
% 5.97/5.93 tff(16805,plain,
% 5.97/5.93 (succ(succ(succ(Y2!56))) = succ(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16804])).
% 5.97/5.93 tff(16806,plain,
% 5.97/5.93 (succ(succ(succ(Y2!56))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16805, 48])).
% 5.97/5.93 tff(16807,plain,
% 5.97/5.93 (succ(succ(succ(succ(Y2!56)))) = succ(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16806])).
% 5.97/5.93 tff(16808,plain,
% 5.97/5.93 (succ(succ(succ(succ(Y2!56)))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16807, 14])).
% 5.97/5.93 tff(16809,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16808])).
% 5.97/5.93 tff(16810,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(Y2!56))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16809, 33])).
% 5.97/5.93 tff(16811,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16810])).
% 5.97/5.93 tff(16812,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16811, 30])).
% 5.97/5.93 tff(16813,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16812])).
% 5.97/5.93 tff(16814,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16813, 39])).
% 5.97/5.93 tff(16815,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16814])).
% 5.97/5.93 tff(16816,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16815, 53])).
% 5.97/5.93 tff(16817,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16816])).
% 5.97/5.93 tff(16818,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16817, 45])).
% 5.97/5.93 tff(16819,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16818])).
% 5.97/5.93 tff(16820,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16819, 28])).
% 5.97/5.93 tff(16821,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16820])).
% 5.97/5.93 tff(16822,plain,
% 5.97/5.93 (NSY2!28 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[370, 16821, 42])).
% 5.97/5.93 tff(16823,plain,
% 5.97/5.93 (pred(NSY2!28) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16822])).
% 5.97/5.93 tff(16824,plain,
% 5.97/5.93 (pred(NSY2!28) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16823, 22])).
% 5.97/5.93 tff(16825,plain,
% 5.97/5.93 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n10, n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16824, 16800])).
% 5.97/5.93 tff(16826,plain,
% 5.97/5.93 (sum(pred(NSY2!28), succ(NPY2!30)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16825, 57])).
% 5.97/5.93 tff(16827,plain,
% 5.97/5.93 (sum(pred(Y1!58), succ(X1!59)) = sum(n10, n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16669, 16752])).
% 5.97/5.93 tff(16828,plain,
% 5.97/5.93 (sum(pred(Y1!58), succ(X1!59)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16827, 57])).
% 5.97/5.93 tff(16829,plain,
% 5.97/5.93 (sum(pred(X1!59), succ(Y1!58)) = sum(n10, n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16726, 16693])).
% 5.97/5.93 tff(16830,plain,
% 5.97/5.93 (sum(pred(X1!59), succ(Y1!58)) = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[16829, 57])).
% 5.97/5.93 tff(16831,plain,
% 5.97/5.93 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n0, n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16830, 16828])).
% 5.97/5.93 tff(16832,plain,
% 5.97/5.93 (X2!57 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[209, 16831, 59])).
% 5.97/5.93 tff(16833,plain,
% 5.97/5.93 (pred(X2!57) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16832])).
% 5.97/5.93 tff(16834,plain,
% 5.97/5.93 (pred(X2!57) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16833, 22])).
% 5.97/5.93 tff(16835,plain,
% 5.97/5.93 (pred(pred(X2!57)) = pred(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16834])).
% 5.97/5.93 tff(16836,plain,
% 5.97/5.93 (pred(pred(X2!57)) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16835, 21])).
% 5.97/5.93 tff(16837,plain,
% 5.97/5.93 (pred(pred(pred(X2!57))) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16836])).
% 5.97/5.93 tff(16838,plain,
% 5.97/5.93 (pred(pred(pred(X2!57))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16837, 20])).
% 5.97/5.93 tff(16839,plain,
% 5.97/5.93 (pred(pred(pred(pred(X2!57)))) = pred(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16838])).
% 5.97/5.93 tff(16840,plain,
% 5.97/5.93 (pred(pred(pred(pred(X2!57)))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16839, 19])).
% 5.97/5.93 tff(16841,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(X2!57))))) = pred(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16840])).
% 5.97/5.93 tff(16842,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(X2!57))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16841, 18])).
% 5.97/5.93 tff(16843,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16842])).
% 5.97/5.93 tff(16844,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16843, 17])).
% 5.97/5.93 tff(16845,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16844])).
% 5.97/5.93 tff(16846,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16845, 16])).
% 5.97/5.93 tff(16847,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16846])).
% 5.97/5.93 tff(16848,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16847, 15])).
% 5.97/5.93 tff(16849,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16848])).
% 5.97/5.93 tff(16850,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16849, 25])).
% 5.97/5.93 tff(16851,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16850])).
% 5.97/5.93 tff(16852,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16851, 24])).
% 5.97/5.93 tff(16853,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16852])).
% 5.97/5.93 tff(16854,plain,
% 5.97/5.93 (NPX2!31 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[395, 16853, 23])).
% 5.97/5.93 tff(16855,plain,
% 5.97/5.93 (succ(NPX2!31) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16854])).
% 5.97/5.93 tff(16856,plain,
% 5.97/5.93 (succ(NPX2!31) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16855, 58])).
% 5.97/5.93 tff(16857,plain,
% 5.97/5.93 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n1, n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16856, 16826])).
% 5.97/5.93 tff(16858,plain,
% 5.97/5.93 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16857, 56])).
% 5.97/5.93 tff(16859,plain,
% 5.97/5.93 (succ(X2!57) = succ(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16832])).
% 5.97/5.93 tff(16860,plain,
% 5.97/5.93 (succ(X2!57) = n1),
% 5.97/5.93 inference(transitivity,[status(thm)],[16859, 58])).
% 5.97/5.93 tff(16861,plain,
% 5.97/5.93 (succ(succ(X2!57)) = succ(n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16860])).
% 5.97/5.93 tff(16862,plain,
% 5.97/5.93 (succ(succ(X2!57)) = n2),
% 5.97/5.93 inference(transitivity,[status(thm)],[16861, 36])).
% 5.97/5.93 tff(16863,plain,
% 5.97/5.93 (succ(succ(succ(X2!57))) = succ(n2)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16862])).
% 5.97/5.93 tff(16864,plain,
% 5.97/5.93 (succ(succ(succ(X2!57))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16863, 48])).
% 5.97/5.93 tff(16865,plain,
% 5.97/5.93 (succ(succ(succ(succ(X2!57)))) = succ(n3)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16864])).
% 5.97/5.93 tff(16866,plain,
% 5.97/5.93 (succ(succ(succ(succ(X2!57)))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16865, 14])).
% 5.97/5.93 tff(16867,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(X2!57))))) = succ(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16866])).
% 5.97/5.93 tff(16868,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(X2!57))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16867, 33])).
% 5.97/5.93 tff(16869,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16868])).
% 5.97/5.93 tff(16870,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16869, 30])).
% 5.97/5.93 tff(16871,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16870])).
% 5.97/5.93 tff(16872,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16871, 39])).
% 5.97/5.93 tff(16873,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16872])).
% 5.97/5.93 tff(16874,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16873, 53])).
% 5.97/5.93 tff(16875,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16874])).
% 5.97/5.93 tff(16876,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16875, 45])).
% 5.97/5.93 tff(16877,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16876])).
% 5.97/5.93 tff(16878,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16877, 28])).
% 5.97/5.93 tff(16879,plain,
% 5.97/5.93 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16878])).
% 5.97/5.93 tff(16880,plain,
% 5.97/5.93 (NSX2!29 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[420, 16879, 42])).
% 5.97/5.93 tff(16881,plain,
% 5.97/5.93 (pred(NSX2!29) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16880])).
% 5.97/5.93 tff(16882,plain,
% 5.97/5.93 (pred(NSX2!29) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16881, 22])).
% 5.97/5.93 tff(16883,plain,
% 5.97/5.93 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n10, n1)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16882, 16858])).
% 5.97/5.93 tff(16884,plain,
% 5.97/5.93 (Y3!54 = n0),
% 5.97/5.93 inference(transitivity,[status(thm)],[425, 16883, 57])).
% 5.97/5.93 tff(16885,plain,
% 5.97/5.93 (pred(Y3!54) = pred(n0)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16884])).
% 5.97/5.93 tff(16886,plain,
% 5.97/5.93 (pred(Y3!54) = n10),
% 5.97/5.93 inference(transitivity,[status(thm)],[16885, 22])).
% 5.97/5.93 tff(16887,plain,
% 5.97/5.93 (pred(pred(Y3!54)) = pred(n10)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16886])).
% 5.97/5.93 tff(16888,plain,
% 5.97/5.93 (pred(pred(Y3!54)) = n9),
% 5.97/5.93 inference(transitivity,[status(thm)],[16887, 21])).
% 5.97/5.93 tff(16889,plain,
% 5.97/5.93 (pred(pred(pred(Y3!54))) = pred(n9)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16888])).
% 5.97/5.93 tff(16890,plain,
% 5.97/5.93 (pred(pred(pred(Y3!54))) = n8),
% 5.97/5.93 inference(transitivity,[status(thm)],[16889, 20])).
% 5.97/5.93 tff(16891,plain,
% 5.97/5.93 (pred(pred(pred(pred(Y3!54)))) = pred(n8)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16890])).
% 5.97/5.93 tff(16892,plain,
% 5.97/5.93 (pred(pred(pred(pred(Y3!54)))) = n7),
% 5.97/5.93 inference(transitivity,[status(thm)],[16891, 19])).
% 5.97/5.93 tff(16893,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n7)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16892])).
% 5.97/5.93 tff(16894,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(Y3!54))))) = n6),
% 5.97/5.93 inference(transitivity,[status(thm)],[16893, 18])).
% 5.97/5.93 tff(16895,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n6)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16894])).
% 5.97/5.93 tff(16896,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n5),
% 5.97/5.93 inference(transitivity,[status(thm)],[16895, 17])).
% 5.97/5.93 tff(16897,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n5)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16896])).
% 5.97/5.93 tff(16898,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n4),
% 5.97/5.93 inference(transitivity,[status(thm)],[16897, 16])).
% 5.97/5.93 tff(16899,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n4)),
% 5.97/5.93 inference(monotonicity,[status(thm)],[16898])).
% 5.97/5.93 tff(16900,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n3),
% 5.97/5.93 inference(transitivity,[status(thm)],[16899, 15])).
% 5.97/5.93 tff(16901,plain,
% 5.97/5.93 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16900])).
% 5.97/5.94 tff(16902,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[16901, 25])).
% 5.97/5.94 tff(16903,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16902])).
% 5.97/5.94 tff(16904,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[16903, 24])).
% 5.97/5.94 tff(16905,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16904])).
% 5.97/5.94 tff(16906,plain,
% 5.97/5.94 (NPY3!26 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[462, 16905, 23])).
% 5.97/5.94 tff(16907,plain,
% 5.97/5.94 (succ(NPY3!26) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16906])).
% 5.97/5.94 tff(16908,plain,
% 5.97/5.94 (succ(NPY3!26) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[16907, 58])).
% 5.97/5.94 tff(16909,plain,
% 5.97/5.94 (succ(Y3!54) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16884])).
% 5.97/5.94 tff(16910,plain,
% 5.97/5.94 (succ(Y3!54) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[16909, 58])).
% 5.97/5.94 tff(16911,plain,
% 5.97/5.94 (succ(succ(Y3!54)) = succ(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16910])).
% 5.97/5.94 tff(16912,plain,
% 5.97/5.94 (succ(succ(Y3!54)) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[16911, 36])).
% 5.97/5.94 tff(16913,plain,
% 5.97/5.94 (succ(succ(succ(Y3!54))) = succ(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16912])).
% 5.97/5.94 tff(16914,plain,
% 5.97/5.94 (succ(succ(succ(Y3!54))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[16913, 48])).
% 5.97/5.94 tff(16915,plain,
% 5.97/5.94 (succ(succ(succ(succ(Y3!54)))) = succ(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16914])).
% 5.97/5.94 tff(16916,plain,
% 5.97/5.94 (succ(succ(succ(succ(Y3!54)))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[16915, 14])).
% 5.97/5.94 tff(16917,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16916])).
% 5.97/5.94 tff(16918,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(Y3!54))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[16917, 33])).
% 5.97/5.94 tff(16919,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16918])).
% 5.97/5.94 tff(16920,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[16919, 30])).
% 5.97/5.94 tff(16921,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16920])).
% 5.97/5.94 tff(16922,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[16921, 39])).
% 5.97/5.94 tff(16923,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16922])).
% 5.97/5.94 tff(16924,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[16923, 53])).
% 5.97/5.94 tff(16925,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16924])).
% 5.97/5.94 tff(16926,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[16925, 45])).
% 5.97/5.94 tff(16927,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16926])).
% 5.97/5.94 tff(16928,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[16927, 28])).
% 5.97/5.94 tff(16929,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16928])).
% 5.97/5.94 tff(16930,plain,
% 5.97/5.94 (NSY3!24 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[485, 16929, 42])).
% 5.97/5.94 tff(16931,plain,
% 5.97/5.94 (pred(NSY3!24) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16930])).
% 5.97/5.94 tff(16932,plain,
% 5.97/5.94 (pred(NSY3!24) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[16931, 22])).
% 5.97/5.94 tff(16933,plain,
% 5.97/5.94 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16932, 16908])).
% 5.97/5.94 tff(16934,plain,
% 5.97/5.94 (sum(pred(NSY3!24), succ(NPY3!26)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[16933, 57])).
% 5.97/5.94 tff(16935,plain,
% 5.97/5.94 (sum(pred(Y2!56), succ(X2!57)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16778, 16860])).
% 5.97/5.94 tff(16936,plain,
% 5.97/5.94 (sum(pred(Y2!56), succ(X2!57)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[16935, 57])).
% 5.97/5.94 tff(16937,plain,
% 5.97/5.94 (sum(pred(X2!57), succ(Y2!56)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16834, 16802])).
% 5.97/5.94 tff(16938,plain,
% 5.97/5.94 (sum(pred(X2!57), succ(Y2!56)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[16937, 57])).
% 5.97/5.94 tff(16939,plain,
% 5.97/5.94 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n0, n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16938, 16936])).
% 5.97/5.94 tff(16940,plain,
% 5.97/5.94 (X3!55 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[323, 16939, 59])).
% 5.97/5.94 tff(16941,plain,
% 5.97/5.94 (pred(X3!55) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16940])).
% 5.97/5.94 tff(16942,plain,
% 5.97/5.94 (pred(X3!55) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[16941, 22])).
% 5.97/5.94 tff(16943,plain,
% 5.97/5.94 (pred(pred(X3!55)) = pred(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16942])).
% 5.97/5.94 tff(16944,plain,
% 5.97/5.94 (pred(pred(X3!55)) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[16943, 21])).
% 5.97/5.94 tff(16945,plain,
% 5.97/5.94 (pred(pred(pred(X3!55))) = pred(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16944])).
% 5.97/5.94 tff(16946,plain,
% 5.97/5.94 (pred(pred(pred(X3!55))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[16945, 20])).
% 5.97/5.94 tff(16947,plain,
% 5.97/5.94 (pred(pred(pred(pred(X3!55)))) = pred(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16946])).
% 5.97/5.94 tff(16948,plain,
% 5.97/5.94 (pred(pred(pred(pred(X3!55)))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[16947, 19])).
% 5.97/5.94 tff(16949,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(X3!55))))) = pred(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16948])).
% 5.97/5.94 tff(16950,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(X3!55))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[16949, 18])).
% 5.97/5.94 tff(16951,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16950])).
% 5.97/5.94 tff(16952,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[16951, 17])).
% 5.97/5.94 tff(16953,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16952])).
% 5.97/5.94 tff(16954,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[16953, 16])).
% 5.97/5.94 tff(16955,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16954])).
% 5.97/5.94 tff(16956,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[16955, 15])).
% 5.97/5.94 tff(16957,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16956])).
% 5.97/5.94 tff(16958,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[16957, 25])).
% 5.97/5.94 tff(16959,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16958])).
% 5.97/5.94 tff(16960,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[16959, 24])).
% 5.97/5.94 tff(16961,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16960])).
% 5.97/5.94 tff(16962,plain,
% 5.97/5.94 (NPX3!27 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[510, 16961, 23])).
% 5.97/5.94 tff(16963,plain,
% 5.97/5.94 (succ(NPX3!27) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16962])).
% 5.97/5.94 tff(16964,plain,
% 5.97/5.94 (succ(NPX3!27) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[16963, 58])).
% 5.97/5.94 tff(16965,plain,
% 5.97/5.94 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n1, n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16964, 16934])).
% 5.97/5.94 tff(16966,plain,
% 5.97/5.94 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[16965, 56])).
% 5.97/5.94 tff(16967,plain,
% 5.97/5.94 (succ(X3!55) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16940])).
% 5.97/5.94 tff(16968,plain,
% 5.97/5.94 (succ(X3!55) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[16967, 58])).
% 5.97/5.94 tff(16969,plain,
% 5.97/5.94 (succ(succ(X3!55)) = succ(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16968])).
% 5.97/5.94 tff(16970,plain,
% 5.97/5.94 (succ(succ(X3!55)) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[16969, 36])).
% 5.97/5.94 tff(16971,plain,
% 5.97/5.94 (succ(succ(succ(X3!55))) = succ(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16970])).
% 5.97/5.94 tff(16972,plain,
% 5.97/5.94 (succ(succ(succ(X3!55))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[16971, 48])).
% 5.97/5.94 tff(16973,plain,
% 5.97/5.94 (succ(succ(succ(succ(X3!55)))) = succ(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16972])).
% 5.97/5.94 tff(16974,plain,
% 5.97/5.94 (succ(succ(succ(succ(X3!55)))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[16973, 14])).
% 5.97/5.94 tff(16975,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(X3!55))))) = succ(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16974])).
% 5.97/5.94 tff(16976,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(X3!55))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[16975, 33])).
% 5.97/5.94 tff(16977,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16976])).
% 5.97/5.94 tff(16978,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[16977, 30])).
% 5.97/5.94 tff(16979,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16978])).
% 5.97/5.94 tff(16980,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[16979, 39])).
% 5.97/5.94 tff(16981,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16980])).
% 5.97/5.94 tff(16982,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[16981, 53])).
% 5.97/5.94 tff(16983,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16982])).
% 5.97/5.94 tff(16984,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[16983, 45])).
% 5.97/5.94 tff(16985,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16984])).
% 5.97/5.94 tff(16986,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[16985, 28])).
% 5.97/5.94 tff(16987,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16986])).
% 5.97/5.94 tff(16988,plain,
% 5.97/5.94 (NSX3!25 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[535, 16987, 42])).
% 5.97/5.94 tff(16989,plain,
% 5.97/5.94 (pred(NSX3!25) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16988])).
% 5.97/5.94 tff(16990,plain,
% 5.97/5.94 (pred(NSX3!25) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[16989, 22])).
% 5.97/5.94 tff(16991,plain,
% 5.97/5.94 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16990, 16966])).
% 5.97/5.94 tff(16992,plain,
% 5.97/5.94 (Y4!52 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[540, 16991, 57])).
% 5.97/5.94 tff(16993,plain,
% 5.97/5.94 (pred(Y4!52) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16992])).
% 5.97/5.94 tff(16994,plain,
% 5.97/5.94 (pred(Y4!52) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[16993, 22])).
% 5.97/5.94 tff(16995,plain,
% 5.97/5.94 (pred(pred(Y4!52)) = pred(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16994])).
% 5.97/5.94 tff(16996,plain,
% 5.97/5.94 (pred(pred(Y4!52)) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[16995, 21])).
% 5.97/5.94 tff(16997,plain,
% 5.97/5.94 (pred(pred(pred(Y4!52))) = pred(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16996])).
% 5.97/5.94 tff(16998,plain,
% 5.97/5.94 (pred(pred(pred(Y4!52))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[16997, 20])).
% 5.97/5.94 tff(16999,plain,
% 5.97/5.94 (pred(pred(pred(pred(Y4!52)))) = pred(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16998])).
% 5.97/5.94 tff(17000,plain,
% 5.97/5.94 (pred(pred(pred(pred(Y4!52)))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[16999, 19])).
% 5.97/5.94 tff(17001,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17000])).
% 5.97/5.94 tff(17002,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(Y4!52))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17001, 18])).
% 5.97/5.94 tff(17003,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17002])).
% 5.97/5.94 tff(17004,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17003, 17])).
% 5.97/5.94 tff(17005,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17004])).
% 5.97/5.94 tff(17006,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17005, 16])).
% 5.97/5.94 tff(17007,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17006])).
% 5.97/5.94 tff(17008,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17007, 15])).
% 5.97/5.94 tff(17009,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17008])).
% 5.97/5.94 tff(17010,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17009, 25])).
% 5.97/5.94 tff(17011,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17010])).
% 5.97/5.94 tff(17012,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17011, 24])).
% 5.97/5.94 tff(17013,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17012])).
% 5.97/5.94 tff(17014,plain,
% 5.97/5.94 (NPY4!22 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[578, 17013, 23])).
% 5.97/5.94 tff(17015,plain,
% 5.97/5.94 (succ(NPY4!22) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17014])).
% 5.97/5.94 tff(17016,plain,
% 5.97/5.94 (succ(NPY4!22) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17015, 58])).
% 5.97/5.94 tff(17017,plain,
% 5.97/5.94 (succ(Y4!52) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16992])).
% 5.97/5.94 tff(17018,plain,
% 5.97/5.94 (succ(Y4!52) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17017, 58])).
% 5.97/5.94 tff(17019,plain,
% 5.97/5.94 (succ(succ(Y4!52)) = succ(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17018])).
% 5.97/5.94 tff(17020,plain,
% 5.97/5.94 (succ(succ(Y4!52)) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17019, 36])).
% 5.97/5.94 tff(17021,plain,
% 5.97/5.94 (succ(succ(succ(Y4!52))) = succ(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17020])).
% 5.97/5.94 tff(17022,plain,
% 5.97/5.94 (succ(succ(succ(Y4!52))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17021, 48])).
% 5.97/5.94 tff(17023,plain,
% 5.97/5.94 (succ(succ(succ(succ(Y4!52)))) = succ(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17022])).
% 5.97/5.94 tff(17024,plain,
% 5.97/5.94 (succ(succ(succ(succ(Y4!52)))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17023, 14])).
% 5.97/5.94 tff(17025,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17024])).
% 5.97/5.94 tff(17026,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(Y4!52))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17025, 33])).
% 5.97/5.94 tff(17027,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17026])).
% 5.97/5.94 tff(17028,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17027, 30])).
% 5.97/5.94 tff(17029,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17028])).
% 5.97/5.94 tff(17030,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17029, 39])).
% 5.97/5.94 tff(17031,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17030])).
% 5.97/5.94 tff(17032,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17031, 53])).
% 5.97/5.94 tff(17033,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17032])).
% 5.97/5.94 tff(17034,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17033, 45])).
% 5.97/5.94 tff(17035,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17034])).
% 5.97/5.94 tff(17036,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17035, 28])).
% 5.97/5.94 tff(17037,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17036])).
% 5.97/5.94 tff(17038,plain,
% 5.97/5.94 (NSY4!20 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[601, 17037, 42])).
% 5.97/5.94 tff(17039,plain,
% 5.97/5.94 (pred(NSY4!20) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17038])).
% 5.97/5.94 tff(17040,plain,
% 5.97/5.94 (pred(NSY4!20) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17039, 22])).
% 5.97/5.94 tff(17041,plain,
% 5.97/5.94 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17040, 17016])).
% 5.97/5.94 tff(17042,plain,
% 5.97/5.94 (sum(pred(NSY4!20), succ(NPY4!22)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[17041, 57])).
% 5.97/5.94 tff(17043,plain,
% 5.97/5.94 (sum(pred(Y3!54), succ(X3!55)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16886, 16968])).
% 5.97/5.94 tff(17044,plain,
% 5.97/5.94 (sum(pred(Y3!54), succ(X3!55)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[17043, 57])).
% 5.97/5.94 tff(17045,plain,
% 5.97/5.94 (sum(pred(X3!55), succ(Y3!54)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16942, 16910])).
% 5.97/5.94 tff(17046,plain,
% 5.97/5.94 (sum(pred(X3!55), succ(Y3!54)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[17045, 57])).
% 5.97/5.94 tff(17047,plain,
% 5.97/5.94 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n0, n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17046, 17044])).
% 5.97/5.94 tff(17048,plain,
% 5.97/5.94 (X4!53 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[438, 17047, 59])).
% 5.97/5.94 tff(17049,plain,
% 5.97/5.94 (pred(X4!53) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17048])).
% 5.97/5.94 tff(17050,plain,
% 5.97/5.94 (pred(X4!53) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17049, 22])).
% 5.97/5.94 tff(17051,plain,
% 5.97/5.94 (pred(pred(X4!53)) = pred(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17050])).
% 5.97/5.94 tff(17052,plain,
% 5.97/5.94 (pred(pred(X4!53)) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17051, 21])).
% 5.97/5.94 tff(17053,plain,
% 5.97/5.94 (pred(pred(pred(X4!53))) = pred(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17052])).
% 5.97/5.94 tff(17054,plain,
% 5.97/5.94 (pred(pred(pred(X4!53))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17053, 20])).
% 5.97/5.94 tff(17055,plain,
% 5.97/5.94 (pred(pred(pred(pred(X4!53)))) = pred(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17054])).
% 5.97/5.94 tff(17056,plain,
% 5.97/5.94 (pred(pred(pred(pred(X4!53)))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17055, 19])).
% 5.97/5.94 tff(17057,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(X4!53))))) = pred(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17056])).
% 5.97/5.94 tff(17058,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(X4!53))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17057, 18])).
% 5.97/5.94 tff(17059,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17058])).
% 5.97/5.94 tff(17060,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17059, 17])).
% 5.97/5.94 tff(17061,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17060])).
% 5.97/5.94 tff(17062,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17061, 16])).
% 5.97/5.94 tff(17063,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17062])).
% 5.97/5.94 tff(17064,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17063, 15])).
% 5.97/5.94 tff(17065,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17064])).
% 5.97/5.94 tff(17066,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17065, 25])).
% 5.97/5.94 tff(17067,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17066])).
% 5.97/5.94 tff(17068,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17067, 24])).
% 5.97/5.94 tff(17069,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17068])).
% 5.97/5.94 tff(17070,plain,
% 5.97/5.94 (NPX4!23 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[626, 17069, 23])).
% 5.97/5.94 tff(17071,plain,
% 5.97/5.94 (succ(NPX4!23) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17070])).
% 5.97/5.94 tff(17072,plain,
% 5.97/5.94 (succ(NPX4!23) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17071, 58])).
% 5.97/5.94 tff(17073,plain,
% 5.97/5.94 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n1, n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17072, 17042])).
% 5.97/5.94 tff(17074,plain,
% 5.97/5.94 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17073, 56])).
% 5.97/5.94 tff(17075,plain,
% 5.97/5.94 (succ(X4!53) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17048])).
% 5.97/5.94 tff(17076,plain,
% 5.97/5.94 (succ(X4!53) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17075, 58])).
% 5.97/5.94 tff(17077,plain,
% 5.97/5.94 (succ(succ(X4!53)) = succ(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17076])).
% 5.97/5.94 tff(17078,plain,
% 5.97/5.94 (succ(succ(X4!53)) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17077, 36])).
% 5.97/5.94 tff(17079,plain,
% 5.97/5.94 (succ(succ(succ(X4!53))) = succ(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17078])).
% 5.97/5.94 tff(17080,plain,
% 5.97/5.94 (succ(succ(succ(X4!53))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17079, 48])).
% 5.97/5.94 tff(17081,plain,
% 5.97/5.94 (succ(succ(succ(succ(X4!53)))) = succ(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17080])).
% 5.97/5.94 tff(17082,plain,
% 5.97/5.94 (succ(succ(succ(succ(X4!53)))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17081, 14])).
% 5.97/5.94 tff(17083,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(X4!53))))) = succ(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17082])).
% 5.97/5.94 tff(17084,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(X4!53))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17083, 33])).
% 5.97/5.94 tff(17085,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17084])).
% 5.97/5.94 tff(17086,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17085, 30])).
% 5.97/5.94 tff(17087,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17086])).
% 5.97/5.94 tff(17088,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17087, 39])).
% 5.97/5.94 tff(17089,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17088])).
% 5.97/5.94 tff(17090,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17089, 53])).
% 5.97/5.94 tff(17091,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17090])).
% 5.97/5.94 tff(17092,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17091, 45])).
% 5.97/5.94 tff(17093,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17092])).
% 5.97/5.94 tff(17094,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17093, 28])).
% 5.97/5.94 tff(17095,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17094])).
% 5.97/5.94 tff(17096,plain,
% 5.97/5.94 (NSX4!21 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[651, 17095, 42])).
% 5.97/5.94 tff(17097,plain,
% 5.97/5.94 (pred(NSX4!21) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17096])).
% 5.97/5.94 tff(17098,plain,
% 5.97/5.94 (pred(NSX4!21) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17097, 22])).
% 5.97/5.94 tff(17099,plain,
% 5.97/5.94 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17098, 17074])).
% 5.97/5.94 tff(17100,plain,
% 5.97/5.94 (Y5!50 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[656, 17099, 57])).
% 5.97/5.94 tff(17101,plain,
% 5.97/5.94 (pred(Y5!50) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17100])).
% 5.97/5.94 tff(17102,plain,
% 5.97/5.94 (pred(Y5!50) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17101, 22])).
% 5.97/5.94 tff(17103,plain,
% 5.97/5.94 (pred(pred(Y5!50)) = pred(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17102])).
% 5.97/5.94 tff(17104,plain,
% 5.97/5.94 (pred(pred(Y5!50)) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17103, 21])).
% 5.97/5.94 tff(17105,plain,
% 5.97/5.94 (pred(pred(pred(Y5!50))) = pred(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17104])).
% 5.97/5.94 tff(17106,plain,
% 5.97/5.94 (pred(pred(pred(Y5!50))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17105, 20])).
% 5.97/5.94 tff(17107,plain,
% 5.97/5.94 (pred(pred(pred(pred(Y5!50)))) = pred(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17106])).
% 5.97/5.94 tff(17108,plain,
% 5.97/5.94 (pred(pred(pred(pred(Y5!50)))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17107, 19])).
% 5.97/5.94 tff(17109,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17108])).
% 5.97/5.94 tff(17110,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(Y5!50))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17109, 18])).
% 5.97/5.94 tff(17111,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17110])).
% 5.97/5.94 tff(17112,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17111, 17])).
% 5.97/5.94 tff(17113,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17112])).
% 5.97/5.94 tff(17114,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17113, 16])).
% 5.97/5.94 tff(17115,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17114])).
% 5.97/5.94 tff(17116,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17115, 15])).
% 5.97/5.94 tff(17117,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17116])).
% 5.97/5.94 tff(17118,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17117, 25])).
% 5.97/5.94 tff(17119,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17118])).
% 5.97/5.94 tff(17120,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17119, 24])).
% 5.97/5.94 tff(17121,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17120])).
% 5.97/5.94 tff(17122,plain,
% 5.97/5.94 (NPY5!18 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[694, 17121, 23])).
% 5.97/5.94 tff(17123,plain,
% 5.97/5.94 (succ(NPY5!18) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17122])).
% 5.97/5.94 tff(17124,plain,
% 5.97/5.94 (succ(NPY5!18) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17123, 58])).
% 5.97/5.94 tff(17125,plain,
% 5.97/5.94 (succ(Y5!50) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17100])).
% 5.97/5.94 tff(17126,plain,
% 5.97/5.94 (succ(Y5!50) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17125, 58])).
% 5.97/5.94 tff(17127,plain,
% 5.97/5.94 (succ(succ(Y5!50)) = succ(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17126])).
% 5.97/5.94 tff(17128,plain,
% 5.97/5.94 (succ(succ(Y5!50)) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17127, 36])).
% 5.97/5.94 tff(17129,plain,
% 5.97/5.94 (succ(succ(succ(Y5!50))) = succ(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17128])).
% 5.97/5.94 tff(17130,plain,
% 5.97/5.94 (succ(succ(succ(Y5!50))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17129, 48])).
% 5.97/5.94 tff(17131,plain,
% 5.97/5.94 (succ(succ(succ(succ(Y5!50)))) = succ(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17130])).
% 5.97/5.94 tff(17132,plain,
% 5.97/5.94 (succ(succ(succ(succ(Y5!50)))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17131, 14])).
% 5.97/5.94 tff(17133,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17132])).
% 5.97/5.94 tff(17134,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(Y5!50))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17133, 33])).
% 5.97/5.94 tff(17135,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17134])).
% 5.97/5.94 tff(17136,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17135, 30])).
% 5.97/5.94 tff(17137,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17136])).
% 5.97/5.94 tff(17138,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17137, 39])).
% 5.97/5.94 tff(17139,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17138])).
% 5.97/5.94 tff(17140,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17139, 53])).
% 5.97/5.94 tff(17141,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17140])).
% 5.97/5.94 tff(17142,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17141, 45])).
% 5.97/5.94 tff(17143,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17142])).
% 5.97/5.94 tff(17144,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17143, 28])).
% 5.97/5.94 tff(17145,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17144])).
% 5.97/5.94 tff(17146,plain,
% 5.97/5.94 (NSY5!16 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[717, 17145, 42])).
% 5.97/5.94 tff(17147,plain,
% 5.97/5.94 (pred(NSY5!16) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17146])).
% 5.97/5.94 tff(17148,plain,
% 5.97/5.94 (pred(NSY5!16) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17147, 22])).
% 5.97/5.94 tff(17149,plain,
% 5.97/5.94 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17148, 17124])).
% 5.97/5.94 tff(17150,plain,
% 5.97/5.94 (sum(pred(NSY5!16), succ(NPY5!18)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[17149, 57])).
% 5.97/5.94 tff(17151,plain,
% 5.97/5.94 (sum(pred(Y4!52), succ(X4!53)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[16994, 17076])).
% 5.97/5.94 tff(17152,plain,
% 5.97/5.94 (sum(pred(Y4!52), succ(X4!53)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[17151, 57])).
% 5.97/5.94 tff(17153,plain,
% 5.97/5.94 (sum(pred(X4!53), succ(Y4!52)) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17050, 17018])).
% 5.97/5.94 tff(17154,plain,
% 5.97/5.94 (sum(pred(X4!53), succ(Y4!52)) = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[17153, 57])).
% 5.97/5.94 tff(17155,plain,
% 5.97/5.94 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n0, n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17154, 17152])).
% 5.97/5.94 tff(17156,plain,
% 5.97/5.94 (X5!51 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[553, 17155, 59])).
% 5.97/5.94 tff(17157,plain,
% 5.97/5.94 (pred(X5!51) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17156])).
% 5.97/5.94 tff(17158,plain,
% 5.97/5.94 (pred(X5!51) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17157, 22])).
% 5.97/5.94 tff(17159,plain,
% 5.97/5.94 (pred(pred(X5!51)) = pred(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17158])).
% 5.97/5.94 tff(17160,plain,
% 5.97/5.94 (pred(pred(X5!51)) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17159, 21])).
% 5.97/5.94 tff(17161,plain,
% 5.97/5.94 (pred(pred(pred(X5!51))) = pred(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17160])).
% 5.97/5.94 tff(17162,plain,
% 5.97/5.94 (pred(pred(pred(X5!51))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17161, 20])).
% 5.97/5.94 tff(17163,plain,
% 5.97/5.94 (pred(pred(pred(pred(X5!51)))) = pred(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17162])).
% 5.97/5.94 tff(17164,plain,
% 5.97/5.94 (pred(pred(pred(pred(X5!51)))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17163, 19])).
% 5.97/5.94 tff(17165,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(X5!51))))) = pred(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17164])).
% 5.97/5.94 tff(17166,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(X5!51))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17165, 18])).
% 5.97/5.94 tff(17167,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17166])).
% 5.97/5.94 tff(17168,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17167, 17])).
% 5.97/5.94 tff(17169,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17168])).
% 5.97/5.94 tff(17170,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17169, 16])).
% 5.97/5.94 tff(17171,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17170])).
% 5.97/5.94 tff(17172,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17171, 15])).
% 5.97/5.94 tff(17173,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17172])).
% 5.97/5.94 tff(17174,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17173, 25])).
% 5.97/5.94 tff(17175,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17174])).
% 5.97/5.94 tff(17176,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17175, 24])).
% 5.97/5.94 tff(17177,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17176])).
% 5.97/5.94 tff(17178,plain,
% 5.97/5.94 (NPX5!19 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[742, 17177, 23])).
% 5.97/5.94 tff(17179,plain,
% 5.97/5.94 (succ(NPX5!19) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17178])).
% 5.97/5.94 tff(17180,plain,
% 5.97/5.94 (succ(NPX5!19) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17179, 58])).
% 5.97/5.94 tff(17181,plain,
% 5.97/5.94 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n1, n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17180, 17150])).
% 5.97/5.94 tff(17182,plain,
% 5.97/5.94 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17181, 56])).
% 5.97/5.94 tff(17183,plain,
% 5.97/5.94 (succ(X5!51) = succ(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17156])).
% 5.97/5.94 tff(17184,plain,
% 5.97/5.94 (succ(X5!51) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17183, 58])).
% 5.97/5.94 tff(17185,plain,
% 5.97/5.94 (succ(succ(X5!51)) = succ(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17184])).
% 5.97/5.94 tff(17186,plain,
% 5.97/5.94 (succ(succ(X5!51)) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17185, 36])).
% 5.97/5.94 tff(17187,plain,
% 5.97/5.94 (succ(succ(succ(X5!51))) = succ(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17186])).
% 5.97/5.94 tff(17188,plain,
% 5.97/5.94 (succ(succ(succ(X5!51))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17187, 48])).
% 5.97/5.94 tff(17189,plain,
% 5.97/5.94 (succ(succ(succ(succ(X5!51)))) = succ(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17188])).
% 5.97/5.94 tff(17190,plain,
% 5.97/5.94 (succ(succ(succ(succ(X5!51)))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17189, 14])).
% 5.97/5.94 tff(17191,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(X5!51))))) = succ(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17190])).
% 5.97/5.94 tff(17192,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(X5!51))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17191, 33])).
% 5.97/5.94 tff(17193,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17192])).
% 5.97/5.94 tff(17194,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17193, 30])).
% 5.97/5.94 tff(17195,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17194])).
% 5.97/5.94 tff(17196,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17195, 39])).
% 5.97/5.94 tff(17197,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17196])).
% 5.97/5.94 tff(17198,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17197, 53])).
% 5.97/5.94 tff(17199,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17198])).
% 5.97/5.94 tff(17200,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17199, 45])).
% 5.97/5.94 tff(17201,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17200])).
% 5.97/5.94 tff(17202,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17201, 28])).
% 5.97/5.94 tff(17203,plain,
% 5.97/5.94 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17202])).
% 5.97/5.94 tff(17204,plain,
% 5.97/5.94 (NSX5!17 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[767, 17203, 42])).
% 5.97/5.94 tff(17205,plain,
% 5.97/5.94 (pred(NSX5!17) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17204])).
% 5.97/5.94 tff(17206,plain,
% 5.97/5.94 (pred(NSX5!17) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17205, 22])).
% 5.97/5.94 tff(17207,plain,
% 5.97/5.94 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n10, n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17206, 17182])).
% 5.97/5.94 tff(17208,plain,
% 5.97/5.94 (Y6!48 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[772, 17207, 57])).
% 5.97/5.94 tff(17209,plain,
% 5.97/5.94 (pred(Y6!48) = pred(n0)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17208])).
% 5.97/5.94 tff(17210,plain,
% 5.97/5.94 (pred(Y6!48) = n10),
% 5.97/5.94 inference(transitivity,[status(thm)],[17209, 22])).
% 5.97/5.94 tff(17211,plain,
% 5.97/5.94 (pred(pred(Y6!48)) = pred(n10)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17210])).
% 5.97/5.94 tff(17212,plain,
% 5.97/5.94 (pred(pred(Y6!48)) = n9),
% 5.97/5.94 inference(transitivity,[status(thm)],[17211, 21])).
% 5.97/5.94 tff(17213,plain,
% 5.97/5.94 (pred(pred(pred(Y6!48))) = pred(n9)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17212])).
% 5.97/5.94 tff(17214,plain,
% 5.97/5.94 (pred(pred(pred(Y6!48))) = n8),
% 5.97/5.94 inference(transitivity,[status(thm)],[17213, 20])).
% 5.97/5.94 tff(17215,plain,
% 5.97/5.94 (pred(pred(pred(pred(Y6!48)))) = pred(n8)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17214])).
% 5.97/5.94 tff(17216,plain,
% 5.97/5.94 (pred(pred(pred(pred(Y6!48)))) = n7),
% 5.97/5.94 inference(transitivity,[status(thm)],[17215, 19])).
% 5.97/5.94 tff(17217,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n7)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17216])).
% 5.97/5.94 tff(17218,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(Y6!48))))) = n6),
% 5.97/5.94 inference(transitivity,[status(thm)],[17217, 18])).
% 5.97/5.94 tff(17219,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n6)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17218])).
% 5.97/5.94 tff(17220,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n5),
% 5.97/5.94 inference(transitivity,[status(thm)],[17219, 17])).
% 5.97/5.94 tff(17221,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n5)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17220])).
% 5.97/5.94 tff(17222,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n4),
% 5.97/5.94 inference(transitivity,[status(thm)],[17221, 16])).
% 5.97/5.94 tff(17223,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n4)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17222])).
% 5.97/5.94 tff(17224,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n3),
% 5.97/5.94 inference(transitivity,[status(thm)],[17223, 15])).
% 5.97/5.94 tff(17225,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n3)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17224])).
% 5.97/5.94 tff(17226,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n2),
% 5.97/5.94 inference(transitivity,[status(thm)],[17225, 25])).
% 5.97/5.94 tff(17227,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n2)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17226])).
% 5.97/5.94 tff(17228,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n1),
% 5.97/5.94 inference(transitivity,[status(thm)],[17227, 24])).
% 5.97/5.94 tff(17229,plain,
% 5.97/5.94 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n1)),
% 5.97/5.94 inference(monotonicity,[status(thm)],[17228])).
% 5.97/5.94 tff(17230,plain,
% 5.97/5.94 (NPY6!14 = n0),
% 5.97/5.94 inference(transitivity,[status(thm)],[1465, 17229, 23])).
% 5.97/5.95 tff(17231,plain,
% 5.97/5.95 (succ(NPY6!14) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17230])).
% 5.97/5.95 tff(17232,plain,
% 5.97/5.95 (succ(NPY6!14) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17231, 58])).
% 5.97/5.95 tff(17233,plain,
% 5.97/5.95 (succ(Y6!48) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17208])).
% 5.97/5.95 tff(17234,plain,
% 5.97/5.95 (succ(Y6!48) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17233, 58])).
% 5.97/5.95 tff(17235,plain,
% 5.97/5.95 (succ(succ(Y6!48)) = succ(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17234])).
% 5.97/5.95 tff(17236,plain,
% 5.97/5.95 (succ(succ(Y6!48)) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17235, 36])).
% 5.97/5.95 tff(17237,plain,
% 5.97/5.95 (succ(succ(succ(Y6!48))) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17236])).
% 5.97/5.95 tff(17238,plain,
% 5.97/5.95 (succ(succ(succ(Y6!48))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17237, 48])).
% 5.97/5.95 tff(17239,plain,
% 5.97/5.95 (succ(succ(succ(succ(Y6!48)))) = succ(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17238])).
% 5.97/5.95 tff(17240,plain,
% 5.97/5.95 (succ(succ(succ(succ(Y6!48)))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17239, 14])).
% 5.97/5.95 tff(17241,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17240])).
% 5.97/5.95 tff(17242,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(Y6!48))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17241, 33])).
% 5.97/5.95 tff(17243,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17242])).
% 5.97/5.95 tff(17244,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17243, 30])).
% 5.97/5.95 tff(17245,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17244])).
% 5.97/5.95 tff(17246,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17245, 39])).
% 5.97/5.95 tff(17247,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17246])).
% 5.97/5.95 tff(17248,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17247, 53])).
% 5.97/5.95 tff(17249,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17248])).
% 5.97/5.95 tff(17250,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17249, 45])).
% 5.97/5.95 tff(17251,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17250])).
% 5.97/5.95 tff(17252,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17251, 28])).
% 5.97/5.95 tff(17253,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17252])).
% 5.97/5.95 tff(17254,plain,
% 5.97/5.95 (NSY6!12 = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[1490, 17253, 42])).
% 5.97/5.95 tff(17255,plain,
% 5.97/5.95 (pred(NSY6!12) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17254])).
% 5.97/5.95 tff(17256,plain,
% 5.97/5.95 (pred(NSY6!12) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17255, 22])).
% 5.97/5.95 tff(17257,plain,
% 5.97/5.95 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n10, n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17256, 17232])).
% 5.97/5.95 tff(17258,plain,
% 5.97/5.95 (sum(pred(NSY6!12), succ(NPY6!14)) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17257, 57])).
% 5.97/5.95 tff(17259,plain,
% 5.97/5.95 (sum(pred(Y5!50), succ(X5!51)) = sum(n10, n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17102, 17184])).
% 5.97/5.95 tff(17260,plain,
% 5.97/5.95 (sum(pred(Y5!50), succ(X5!51)) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17259, 57])).
% 5.97/5.95 tff(17261,plain,
% 5.97/5.95 (sum(pred(X5!51), succ(Y5!50)) = sum(n10, n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17158, 17126])).
% 5.97/5.95 tff(17262,plain,
% 5.97/5.95 (sum(pred(X5!51), succ(Y5!50)) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17261, 57])).
% 5.97/5.95 tff(17263,plain,
% 5.97/5.95 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n0, n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17262, 17260])).
% 5.97/5.95 tff(17264,plain,
% 5.97/5.95 (X6!49 = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[669, 17263, 59])).
% 5.97/5.95 tff(17265,plain,
% 5.97/5.95 (pred(X6!49) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17264])).
% 5.97/5.95 tff(17266,plain,
% 5.97/5.95 (pred(X6!49) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17265, 22])).
% 5.97/5.95 tff(17267,plain,
% 5.97/5.95 (pred(pred(X6!49)) = pred(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17266])).
% 5.97/5.95 tff(17268,plain,
% 5.97/5.95 (pred(pred(X6!49)) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17267, 21])).
% 5.97/5.95 tff(17269,plain,
% 5.97/5.95 (pred(pred(pred(X6!49))) = pred(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17268])).
% 5.97/5.95 tff(17270,plain,
% 5.97/5.95 (pred(pred(pred(X6!49))) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17269, 20])).
% 5.97/5.95 tff(17271,plain,
% 5.97/5.95 (pred(pred(pred(pred(X6!49)))) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17270])).
% 5.97/5.95 tff(17272,plain,
% 5.97/5.95 (pred(pred(pred(pred(X6!49)))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17271, 19])).
% 5.97/5.95 tff(17273,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(X6!49))))) = pred(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17272])).
% 5.97/5.95 tff(17274,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(X6!49))))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17273, 18])).
% 5.97/5.95 tff(17275,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17274])).
% 5.97/5.95 tff(17276,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17275, 17])).
% 5.97/5.95 tff(17277,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17276])).
% 5.97/5.95 tff(17278,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17277, 16])).
% 5.97/5.95 tff(17279,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17278])).
% 5.97/5.95 tff(17280,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17279, 15])).
% 5.97/5.95 tff(17281,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17280])).
% 5.97/5.95 tff(17282,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17281, 25])).
% 5.97/5.95 tff(17283,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17282])).
% 5.97/5.95 tff(17284,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17283, 24])).
% 5.97/5.95 tff(17285,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17284])).
% 5.97/5.95 tff(17286,plain,
% 5.97/5.95 (NPX6!15 = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[1523, 17285, 23])).
% 5.97/5.95 tff(17287,plain,
% 5.97/5.95 (succ(NPX6!15) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17286])).
% 5.97/5.95 tff(17288,plain,
% 5.97/5.95 (succ(NPX6!15) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17287, 58])).
% 5.97/5.95 tff(17289,plain,
% 5.97/5.95 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n1, n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17288, 17258])).
% 5.97/5.95 tff(17290,plain,
% 5.97/5.95 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17289, 56])).
% 5.97/5.95 tff(17291,plain,
% 5.97/5.95 (succ(X6!49) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17264])).
% 5.97/5.95 tff(17292,plain,
% 5.97/5.95 (succ(X6!49) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17291, 58])).
% 5.97/5.95 tff(17293,plain,
% 5.97/5.95 (succ(succ(X6!49)) = succ(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17292])).
% 5.97/5.95 tff(17294,plain,
% 5.97/5.95 (succ(succ(X6!49)) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17293, 36])).
% 5.97/5.95 tff(17295,plain,
% 5.97/5.95 (succ(succ(succ(X6!49))) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17294])).
% 5.97/5.95 tff(17296,plain,
% 5.97/5.95 (succ(succ(succ(X6!49))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17295, 48])).
% 5.97/5.95 tff(17297,plain,
% 5.97/5.95 (succ(succ(succ(succ(X6!49)))) = succ(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17296])).
% 5.97/5.95 tff(17298,plain,
% 5.97/5.95 (succ(succ(succ(succ(X6!49)))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17297, 14])).
% 5.97/5.95 tff(17299,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(X6!49))))) = succ(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17298])).
% 5.97/5.95 tff(17300,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(X6!49))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17299, 33])).
% 5.97/5.95 tff(17301,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17300])).
% 5.97/5.95 tff(17302,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17301, 30])).
% 5.97/5.95 tff(17303,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17302])).
% 5.97/5.95 tff(17304,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17303, 39])).
% 5.97/5.95 tff(17305,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17304])).
% 5.97/5.95 tff(17306,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17305, 53])).
% 5.97/5.95 tff(17307,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17306])).
% 5.97/5.95 tff(17308,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17307, 45])).
% 5.97/5.95 tff(17309,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17308])).
% 5.97/5.95 tff(17310,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17309, 28])).
% 5.97/5.95 tff(17311,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17310])).
% 5.97/5.95 tff(17312,plain,
% 5.97/5.95 (NSX6!13 = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[1550, 17311, 42])).
% 5.97/5.95 tff(17313,plain,
% 5.97/5.95 (pred(NSX6!13) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17312])).
% 5.97/5.95 tff(17314,plain,
% 5.97/5.95 (pred(NSX6!13) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17313, 22])).
% 5.97/5.95 tff(17315,plain,
% 5.97/5.95 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n10, n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17314, 17290])).
% 5.97/5.95 tff(17316,plain,
% 5.97/5.95 (sum(n10, n1) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.97/5.95 inference(symmetry,[status(thm)],[17315])).
% 5.97/5.95 tff(17317,plain,
% 5.97/5.95 (sum(pred(Y6!48), succ(X6!49)) = sum(n10, n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17210, 17292])).
% 5.97/5.95 tff(17318,plain,
% 5.97/5.95 (sum(pred(Y6!48), succ(X6!49)) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17317, 57])).
% 5.97/5.95 tff(17319,plain,
% 5.97/5.95 (sum(pred(X6!49), succ(Y6!48)) = sum(n10, n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17266, 17234])).
% 5.97/5.95 tff(17320,plain,
% 5.97/5.95 (sum(pred(X6!49), succ(Y6!48)) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17319, 57])).
% 5.97/5.95 tff(17321,plain,
% 5.97/5.95 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n0, n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17320, 17318])).
% 5.97/5.95 tff(17322,plain,
% 5.97/5.95 (X7!47 = Y7!46),
% 5.97/5.95 inference(transitivity,[status(thm)],[785, 17321, 59, 5850, 17316, 794])).
% 5.97/5.95 tff(17323,plain,
% 5.97/5.95 ($false),
% 5.97/5.95 inference(unit_resolution,[status(thm)],[792, 17322])).
% 5.97/5.95 tff(17324,plain,((~(X0!61 = n9)) | (X7!47 = Y7!46) | (~(Y0!60 = n2))), inference(lemma,lemma(discharge,[]))).
% 5.97/5.95 tff(17325,plain,
% 5.97/5.95 (~(X0!61 = n9)),
% 5.97/5.95 inference(unit_resolution,[status(thm)],[17324, 14626, 792])).
% 5.97/5.95 tff(17326,plain,
% 5.97/5.95 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n0, n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[3792, 14676])).
% 5.97/5.95 tff(17327,plain,
% 5.97/5.95 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17326, 442])).
% 5.97/5.95 tff(17328,plain,
% 5.97/5.95 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n9, n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[3818, 17327])).
% 5.97/5.95 tff(17329,plain,
% 5.97/5.95 (Y1!58 = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[196, 17328, 6583])).
% 5.97/5.95 tff(17330,plain,
% 5.97/5.95 (pred(Y1!58) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17329])).
% 5.97/5.95 tff(17331,plain,
% 5.97/5.95 (pred(Y1!58) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17330, 24])).
% 5.97/5.95 tff(17332,plain,
% 5.97/5.95 (pred(pred(Y1!58)) = pred(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17331])).
% 5.97/5.95 tff(17333,plain,
% 5.97/5.95 (pred(pred(Y1!58)) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17332, 23])).
% 5.97/5.95 tff(17334,plain,
% 5.97/5.95 (pred(pred(pred(Y1!58))) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17333])).
% 5.97/5.95 tff(17335,plain,
% 5.97/5.95 (pred(pred(pred(Y1!58))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17334, 22])).
% 5.97/5.95 tff(17336,plain,
% 5.97/5.95 (pred(pred(pred(pred(Y1!58)))) = pred(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17335])).
% 5.97/5.95 tff(17337,plain,
% 5.97/5.95 (pred(pred(pred(pred(Y1!58)))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17336, 21])).
% 5.97/5.95 tff(17338,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17337])).
% 5.97/5.95 tff(17339,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(Y1!58))))) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17338, 20])).
% 5.97/5.95 tff(17340,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17339])).
% 5.97/5.95 tff(17341,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17340, 19])).
% 5.97/5.95 tff(17342,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17341])).
% 5.97/5.95 tff(17343,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17342, 18])).
% 5.97/5.95 tff(17344,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17343])).
% 5.97/5.95 tff(17345,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17344, 17])).
% 5.97/5.95 tff(17346,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17345])).
% 5.97/5.95 tff(17347,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17346, 16])).
% 5.97/5.95 tff(17348,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17347])).
% 5.97/5.95 tff(17349,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17348, 15])).
% 5.97/5.95 tff(17350,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17349])).
% 5.97/5.95 tff(17351,plain,
% 5.97/5.95 (NPY1!34 = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[232, 17350, 25])).
% 5.97/5.95 tff(17352,plain,
% 5.97/5.95 (succ(NPY1!34) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17351])).
% 5.97/5.95 tff(17353,plain,
% 5.97/5.95 (succ(NPY1!34) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17352, 48])).
% 5.97/5.95 tff(17354,plain,
% 5.97/5.95 (succ(Y1!58) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17329])).
% 5.97/5.95 tff(17355,plain,
% 5.97/5.95 (succ(Y1!58) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17354, 48])).
% 5.97/5.95 tff(17356,plain,
% 5.97/5.95 (succ(succ(Y1!58)) = succ(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17355])).
% 5.97/5.95 tff(17357,plain,
% 5.97/5.95 (succ(succ(Y1!58)) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17356, 14])).
% 5.97/5.95 tff(17358,plain,
% 5.97/5.95 (succ(succ(succ(Y1!58))) = succ(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17357])).
% 5.97/5.95 tff(17359,plain,
% 5.97/5.95 (succ(succ(succ(Y1!58))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17358, 33])).
% 5.97/5.95 tff(17360,plain,
% 5.97/5.95 (succ(succ(succ(succ(Y1!58)))) = succ(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17359])).
% 5.97/5.95 tff(17361,plain,
% 5.97/5.95 (succ(succ(succ(succ(Y1!58)))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17360, 30])).
% 5.97/5.95 tff(17362,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17361])).
% 5.97/5.95 tff(17363,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(Y1!58))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17362, 39])).
% 5.97/5.95 tff(17364,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17363])).
% 5.97/5.95 tff(17365,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17364, 53])).
% 5.97/5.95 tff(17366,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17365])).
% 5.97/5.95 tff(17367,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17366, 45])).
% 5.97/5.95 tff(17368,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17367])).
% 5.97/5.95 tff(17369,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17368, 28])).
% 5.97/5.95 tff(17370,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17369])).
% 5.97/5.95 tff(17371,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17370, 42])).
% 5.97/5.95 tff(17372,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17371])).
% 5.97/5.95 tff(17373,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17372, 58])).
% 5.97/5.95 tff(17374,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17373])).
% 5.97/5.95 tff(17375,plain,
% 5.97/5.95 (NSY1!32 = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[255, 17374, 36])).
% 5.97/5.95 tff(17376,plain,
% 5.97/5.95 (pred(NSY1!32) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17375])).
% 5.97/5.95 tff(17377,plain,
% 5.97/5.95 (pred(NSY1!32) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17376, 24])).
% 5.97/5.95 tff(17378,plain,
% 5.97/5.95 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n1, n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17377, 17353])).
% 5.97/5.95 tff(17379,plain,
% 5.97/5.95 (sum(pred(NSY1!32), succ(NPY1!34)) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17378, 47])).
% 5.97/5.95 tff(17380,plain,
% 5.97/5.95 (sum(pred(Y0!60), succ(X0!61)) = sum(n1, n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[14628, 3796])).
% 5.97/5.95 tff(17381,plain,
% 5.97/5.95 (sum(pred(Y0!60), succ(X0!61)) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17380, 56])).
% 5.97/5.95 tff(17382,plain,
% 5.97/5.95 (sum(pred(X0!61), succ(Y0!60)) = sum(n9, n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[3770, 14652])).
% 5.97/5.95 tff(17383,plain,
% 5.97/5.95 (sum(pred(X0!61), succ(Y0!60)) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17382, 3713])).
% 5.97/5.95 tff(17384,plain,
% 5.97/5.95 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n1, n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17383, 17381])).
% 5.97/5.95 tff(17385,plain,
% 5.97/5.95 (X1!59 = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[93, 17384, 49])).
% 5.97/5.95 tff(17386,plain,
% 5.97/5.95 (pred(X1!59) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17385])).
% 5.97/5.95 tff(17387,plain,
% 5.97/5.95 (pred(X1!59) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17386, 24])).
% 5.97/5.95 tff(17388,plain,
% 5.97/5.95 (pred(pred(X1!59)) = pred(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17387])).
% 5.97/5.95 tff(17389,plain,
% 5.97/5.95 (pred(pred(X1!59)) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17388, 23])).
% 5.97/5.95 tff(17390,plain,
% 5.97/5.95 (pred(pred(pred(X1!59))) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17389])).
% 5.97/5.95 tff(17391,plain,
% 5.97/5.95 (pred(pred(pred(X1!59))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17390, 22])).
% 5.97/5.95 tff(17392,plain,
% 5.97/5.95 (pred(pred(pred(pred(X1!59)))) = pred(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17391])).
% 5.97/5.95 tff(17393,plain,
% 5.97/5.95 (pred(pred(pred(pred(X1!59)))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17392, 21])).
% 5.97/5.95 tff(17394,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(X1!59))))) = pred(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17393])).
% 5.97/5.95 tff(17395,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(X1!59))))) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17394, 20])).
% 5.97/5.95 tff(17396,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17395])).
% 5.97/5.95 tff(17397,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17396, 19])).
% 5.97/5.95 tff(17398,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17397])).
% 5.97/5.95 tff(17399,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17398, 18])).
% 5.97/5.95 tff(17400,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17399])).
% 5.97/5.95 tff(17401,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17400, 17])).
% 5.97/5.95 tff(17402,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17401])).
% 5.97/5.95 tff(17403,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17402, 16])).
% 5.97/5.95 tff(17404,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17403])).
% 5.97/5.95 tff(17405,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17404, 15])).
% 5.97/5.95 tff(17406,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17405])).
% 5.97/5.95 tff(17407,plain,
% 5.97/5.95 (NPX1!35 = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[280, 17406, 25])).
% 5.97/5.95 tff(17408,plain,
% 5.97/5.95 (succ(NPX1!35) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17407])).
% 5.97/5.95 tff(17409,plain,
% 5.97/5.95 (succ(NPX1!35) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17408, 48])).
% 5.97/5.95 tff(17410,plain,
% 5.97/5.95 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n3, n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17409, 17379])).
% 5.97/5.95 tff(17411,plain,
% 5.97/5.95 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17410, 786])).
% 5.97/5.95 tff(17412,plain,
% 5.97/5.95 (succ(X1!59) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17385])).
% 5.97/5.95 tff(17413,plain,
% 5.97/5.95 (succ(X1!59) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17412, 48])).
% 5.97/5.95 tff(17414,plain,
% 5.97/5.95 (succ(succ(X1!59)) = succ(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17413])).
% 5.97/5.95 tff(17415,plain,
% 5.97/5.95 (succ(succ(X1!59)) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17414, 14])).
% 5.97/5.95 tff(17416,plain,
% 5.97/5.95 (succ(succ(succ(X1!59))) = succ(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17415])).
% 5.97/5.95 tff(17417,plain,
% 5.97/5.95 (succ(succ(succ(X1!59))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17416, 33])).
% 5.97/5.95 tff(17418,plain,
% 5.97/5.95 (succ(succ(succ(succ(X1!59)))) = succ(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17417])).
% 5.97/5.95 tff(17419,plain,
% 5.97/5.95 (succ(succ(succ(succ(X1!59)))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17418, 30])).
% 5.97/5.95 tff(17420,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(X1!59))))) = succ(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17419])).
% 5.97/5.95 tff(17421,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(X1!59))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17420, 39])).
% 5.97/5.95 tff(17422,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17421])).
% 5.97/5.95 tff(17423,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17422, 53])).
% 5.97/5.95 tff(17424,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17423])).
% 5.97/5.95 tff(17425,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17424, 45])).
% 5.97/5.95 tff(17426,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17425])).
% 5.97/5.95 tff(17427,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17426, 28])).
% 5.97/5.95 tff(17428,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17427])).
% 5.97/5.95 tff(17429,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17428, 42])).
% 5.97/5.95 tff(17430,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17429])).
% 5.97/5.95 tff(17431,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17430, 58])).
% 5.97/5.95 tff(17432,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17431])).
% 5.97/5.95 tff(17433,plain,
% 5.97/5.95 (NSX1!33 = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[305, 17432, 36])).
% 5.97/5.95 tff(17434,plain,
% 5.97/5.95 (pred(NSX1!33) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17433])).
% 5.97/5.95 tff(17435,plain,
% 5.97/5.95 (pred(NSX1!33) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17434, 24])).
% 5.97/5.95 tff(17436,plain,
% 5.97/5.95 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n1, n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17435, 17411])).
% 5.97/5.95 tff(17437,plain,
% 5.97/5.95 (Y2!56 = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[310, 17436, 791])).
% 5.97/5.95 tff(17438,plain,
% 5.97/5.95 (pred(Y2!56) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17437])).
% 5.97/5.95 tff(17439,plain,
% 5.97/5.95 (pred(Y2!56) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17438, 19])).
% 5.97/5.95 tff(17440,plain,
% 5.97/5.95 (pred(pred(Y2!56)) = pred(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17439])).
% 5.97/5.95 tff(17441,plain,
% 5.97/5.95 (pred(pred(Y2!56)) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17440, 18])).
% 5.97/5.95 tff(17442,plain,
% 5.97/5.95 (pred(pred(pred(Y2!56))) = pred(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17441])).
% 5.97/5.95 tff(17443,plain,
% 5.97/5.95 (pred(pred(pred(Y2!56))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17442, 17])).
% 5.97/5.95 tff(17444,plain,
% 5.97/5.95 (pred(pred(pred(pred(Y2!56)))) = pred(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17443])).
% 5.97/5.95 tff(17445,plain,
% 5.97/5.95 (pred(pred(pred(pred(Y2!56)))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17444, 16])).
% 5.97/5.95 tff(17446,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17445])).
% 5.97/5.95 tff(17447,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(Y2!56))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17446, 15])).
% 5.97/5.95 tff(17448,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17447])).
% 5.97/5.95 tff(17449,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17448, 25])).
% 5.97/5.95 tff(17450,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17449])).
% 5.97/5.95 tff(17451,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17450, 24])).
% 5.97/5.95 tff(17452,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17451])).
% 5.97/5.95 tff(17453,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17452, 23])).
% 5.97/5.95 tff(17454,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17453])).
% 5.97/5.95 tff(17455,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17454, 22])).
% 5.97/5.95 tff(17456,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17455])).
% 5.97/5.95 tff(17457,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17456, 21])).
% 5.97/5.95 tff(17458,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17457])).
% 5.97/5.95 tff(17459,plain,
% 5.97/5.95 (NPY2!30 = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[347, 17458, 20])).
% 5.97/5.95 tff(17460,plain,
% 5.97/5.95 (succ(NPY2!30) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17459])).
% 5.97/5.95 tff(17461,plain,
% 5.97/5.95 (succ(NPY2!30) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17460, 45])).
% 5.97/5.95 tff(17462,plain,
% 5.97/5.95 (succ(Y2!56) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17437])).
% 5.97/5.95 tff(17463,plain,
% 5.97/5.95 (succ(Y2!56) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17462, 45])).
% 5.97/5.95 tff(17464,plain,
% 5.97/5.95 (succ(succ(Y2!56)) = succ(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17463])).
% 5.97/5.95 tff(17465,plain,
% 5.97/5.95 (succ(succ(Y2!56)) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17464, 28])).
% 5.97/5.95 tff(17466,plain,
% 5.97/5.95 (succ(succ(succ(Y2!56))) = succ(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17465])).
% 5.97/5.95 tff(17467,plain,
% 5.97/5.95 (succ(succ(succ(Y2!56))) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17466, 42])).
% 5.97/5.95 tff(17468,plain,
% 5.97/5.95 (succ(succ(succ(succ(Y2!56)))) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17467])).
% 5.97/5.95 tff(17469,plain,
% 5.97/5.95 (succ(succ(succ(succ(Y2!56)))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17468, 58])).
% 5.97/5.95 tff(17470,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17469])).
% 5.97/5.95 tff(17471,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(Y2!56))))) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17470, 36])).
% 5.97/5.95 tff(17472,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17471])).
% 5.97/5.95 tff(17473,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17472, 48])).
% 5.97/5.95 tff(17474,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17473])).
% 5.97/5.95 tff(17475,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17474, 14])).
% 5.97/5.95 tff(17476,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17475])).
% 5.97/5.95 tff(17477,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17476, 33])).
% 5.97/5.95 tff(17478,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17477])).
% 5.97/5.95 tff(17479,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17478, 30])).
% 5.97/5.95 tff(17480,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17479])).
% 5.97/5.95 tff(17481,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17480, 39])).
% 5.97/5.95 tff(17482,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17481])).
% 5.97/5.95 tff(17483,plain,
% 5.97/5.95 (NSY2!28 = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[370, 17482, 53])).
% 5.97/5.95 tff(17484,plain,
% 5.97/5.95 (pred(NSY2!28) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17483])).
% 5.97/5.95 tff(17485,plain,
% 5.97/5.95 (pred(NSY2!28) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17484, 19])).
% 5.97/5.95 tff(17486,plain,
% 5.97/5.95 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n7, n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17485, 17461])).
% 5.97/5.95 tff(17487,plain,
% 5.97/5.95 (sum(pred(NSY2!28), succ(NPY2!30)) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17486, 44])).
% 5.97/5.95 tff(17488,plain,
% 5.97/5.95 (sum(pred(Y1!58), succ(X1!59)) = sum(n1, n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17331, 17413])).
% 5.97/5.95 tff(17489,plain,
% 5.97/5.95 (sum(pred(Y1!58), succ(X1!59)) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17488, 47])).
% 5.97/5.95 tff(17490,plain,
% 5.97/5.95 (sum(pred(X1!59), succ(Y1!58)) = sum(n1, n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17387, 17355])).
% 5.97/5.95 tff(17491,plain,
% 5.97/5.95 (sum(pred(X1!59), succ(Y1!58)) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17490, 47])).
% 5.97/5.95 tff(17492,plain,
% 5.97/5.95 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n4, n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17491, 17489])).
% 5.97/5.95 tff(17493,plain,
% 5.97/5.95 (X2!57 = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[209, 17492, 46])).
% 5.97/5.95 tff(17494,plain,
% 5.97/5.95 (pred(X2!57) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17493])).
% 5.97/5.95 tff(17495,plain,
% 5.97/5.95 (pred(X2!57) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17494, 19])).
% 5.97/5.95 tff(17496,plain,
% 5.97/5.95 (pred(pred(X2!57)) = pred(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17495])).
% 5.97/5.95 tff(17497,plain,
% 5.97/5.95 (pred(pred(X2!57)) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17496, 18])).
% 5.97/5.95 tff(17498,plain,
% 5.97/5.95 (pred(pred(pred(X2!57))) = pred(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17497])).
% 5.97/5.95 tff(17499,plain,
% 5.97/5.95 (pred(pred(pred(X2!57))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17498, 17])).
% 5.97/5.95 tff(17500,plain,
% 5.97/5.95 (pred(pred(pred(pred(X2!57)))) = pred(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17499])).
% 5.97/5.95 tff(17501,plain,
% 5.97/5.95 (pred(pred(pred(pred(X2!57)))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17500, 16])).
% 5.97/5.95 tff(17502,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(X2!57))))) = pred(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17501])).
% 5.97/5.95 tff(17503,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(X2!57))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17502, 15])).
% 5.97/5.95 tff(17504,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17503])).
% 5.97/5.95 tff(17505,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17504, 25])).
% 5.97/5.95 tff(17506,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17505])).
% 5.97/5.95 tff(17507,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17506, 24])).
% 5.97/5.95 tff(17508,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17507])).
% 5.97/5.95 tff(17509,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17508, 23])).
% 5.97/5.95 tff(17510,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17509])).
% 5.97/5.95 tff(17511,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17510, 22])).
% 5.97/5.95 tff(17512,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17511])).
% 5.97/5.95 tff(17513,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17512, 21])).
% 5.97/5.95 tff(17514,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17513])).
% 5.97/5.95 tff(17515,plain,
% 5.97/5.95 (NPX2!31 = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[395, 17514, 20])).
% 5.97/5.95 tff(17516,plain,
% 5.97/5.95 (succ(NPX2!31) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17515])).
% 5.97/5.95 tff(17517,plain,
% 5.97/5.95 (succ(NPX2!31) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17516, 45])).
% 5.97/5.95 tff(17518,plain,
% 5.97/5.95 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n9, n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17517, 17487])).
% 5.97/5.95 tff(17519,plain,
% 5.97/5.95 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17518, 790])).
% 5.97/5.95 tff(17520,plain,
% 5.97/5.95 (succ(X2!57) = succ(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17493])).
% 5.97/5.95 tff(17521,plain,
% 5.97/5.95 (succ(X2!57) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17520, 45])).
% 5.97/5.95 tff(17522,plain,
% 5.97/5.95 (succ(succ(X2!57)) = succ(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17521])).
% 5.97/5.95 tff(17523,plain,
% 5.97/5.95 (succ(succ(X2!57)) = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[17522, 28])).
% 5.97/5.95 tff(17524,plain,
% 5.97/5.95 (succ(succ(succ(X2!57))) = succ(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17523])).
% 5.97/5.95 tff(17525,plain,
% 5.97/5.95 (succ(succ(succ(X2!57))) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17524, 42])).
% 5.97/5.95 tff(17526,plain,
% 5.97/5.95 (succ(succ(succ(succ(X2!57)))) = succ(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17525])).
% 5.97/5.95 tff(17527,plain,
% 5.97/5.95 (succ(succ(succ(succ(X2!57)))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17526, 58])).
% 5.97/5.95 tff(17528,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(X2!57))))) = succ(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17527])).
% 5.97/5.95 tff(17529,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(X2!57))))) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17528, 36])).
% 5.97/5.95 tff(17530,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17529])).
% 5.97/5.95 tff(17531,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17530, 48])).
% 5.97/5.95 tff(17532,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17531])).
% 5.97/5.95 tff(17533,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17532, 14])).
% 5.97/5.95 tff(17534,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17533])).
% 5.97/5.95 tff(17535,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17534, 33])).
% 5.97/5.95 tff(17536,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17535])).
% 5.97/5.95 tff(17537,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17536, 30])).
% 5.97/5.95 tff(17538,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17537])).
% 5.97/5.95 tff(17539,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17538, 39])).
% 5.97/5.95 tff(17540,plain,
% 5.97/5.95 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17539])).
% 5.97/5.95 tff(17541,plain,
% 5.97/5.95 (NSX2!29 = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[420, 17540, 53])).
% 5.97/5.95 tff(17542,plain,
% 5.97/5.95 (pred(NSX2!29) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17541])).
% 5.97/5.95 tff(17543,plain,
% 5.97/5.95 (pred(NSX2!29) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17542, 19])).
% 5.97/5.95 tff(17544,plain,
% 5.97/5.95 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n7, n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17543, 17519])).
% 5.97/5.95 tff(17545,plain,
% 5.97/5.95 (Y3!54 = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[425, 17544, 789])).
% 5.97/5.95 tff(17546,plain,
% 5.97/5.95 (pred(Y3!54) = pred(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17545])).
% 5.97/5.95 tff(17547,plain,
% 5.97/5.95 (pred(Y3!54) = n9),
% 5.97/5.95 inference(transitivity,[status(thm)],[17546, 21])).
% 5.97/5.95 tff(17548,plain,
% 5.97/5.95 (pred(pred(Y3!54)) = pred(n9)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17547])).
% 5.97/5.95 tff(17549,plain,
% 5.97/5.95 (pred(pred(Y3!54)) = n8),
% 5.97/5.95 inference(transitivity,[status(thm)],[17548, 20])).
% 5.97/5.95 tff(17550,plain,
% 5.97/5.95 (pred(pred(pred(Y3!54))) = pred(n8)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17549])).
% 5.97/5.95 tff(17551,plain,
% 5.97/5.95 (pred(pred(pred(Y3!54))) = n7),
% 5.97/5.95 inference(transitivity,[status(thm)],[17550, 19])).
% 5.97/5.95 tff(17552,plain,
% 5.97/5.95 (pred(pred(pred(pred(Y3!54)))) = pred(n7)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17551])).
% 5.97/5.95 tff(17553,plain,
% 5.97/5.95 (pred(pred(pred(pred(Y3!54)))) = n6),
% 5.97/5.95 inference(transitivity,[status(thm)],[17552, 18])).
% 5.97/5.95 tff(17554,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n6)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17553])).
% 5.97/5.95 tff(17555,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(Y3!54))))) = n5),
% 5.97/5.95 inference(transitivity,[status(thm)],[17554, 17])).
% 5.97/5.95 tff(17556,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n5)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17555])).
% 5.97/5.95 tff(17557,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n4),
% 5.97/5.95 inference(transitivity,[status(thm)],[17556, 16])).
% 5.97/5.95 tff(17558,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n4)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17557])).
% 5.97/5.95 tff(17559,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n3),
% 5.97/5.95 inference(transitivity,[status(thm)],[17558, 15])).
% 5.97/5.95 tff(17560,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n3)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17559])).
% 5.97/5.95 tff(17561,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n2),
% 5.97/5.95 inference(transitivity,[status(thm)],[17560, 25])).
% 5.97/5.95 tff(17562,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n2)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17561])).
% 5.97/5.95 tff(17563,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n1),
% 5.97/5.95 inference(transitivity,[status(thm)],[17562, 24])).
% 5.97/5.95 tff(17564,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n1)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17563])).
% 5.97/5.95 tff(17565,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n0),
% 5.97/5.95 inference(transitivity,[status(thm)],[17564, 23])).
% 5.97/5.95 tff(17566,plain,
% 5.97/5.95 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n0)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17565])).
% 5.97/5.95 tff(17567,plain,
% 5.97/5.95 (NPY3!26 = n10),
% 5.97/5.95 inference(transitivity,[status(thm)],[462, 17566, 22])).
% 5.97/5.95 tff(17568,plain,
% 5.97/5.95 (succ(NPY3!26) = succ(n10)),
% 5.97/5.95 inference(monotonicity,[status(thm)],[17567])).
% 5.97/5.96 tff(17569,plain,
% 5.97/5.96 (succ(NPY3!26) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17568, 42])).
% 5.97/5.96 tff(17570,plain,
% 5.97/5.96 (succ(Y3!54) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17545])).
% 5.97/5.96 tff(17571,plain,
% 5.97/5.96 (succ(Y3!54) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17570, 42])).
% 5.97/5.96 tff(17572,plain,
% 5.97/5.96 (succ(succ(Y3!54)) = succ(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17571])).
% 5.97/5.96 tff(17573,plain,
% 5.97/5.96 (succ(succ(Y3!54)) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17572, 58])).
% 5.97/5.96 tff(17574,plain,
% 5.97/5.96 (succ(succ(succ(Y3!54))) = succ(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17573])).
% 5.97/5.96 tff(17575,plain,
% 5.97/5.96 (succ(succ(succ(Y3!54))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17574, 36])).
% 5.97/5.96 tff(17576,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y3!54)))) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17575])).
% 5.97/5.96 tff(17577,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y3!54)))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17576, 48])).
% 5.97/5.96 tff(17578,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17577])).
% 5.97/5.96 tff(17579,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y3!54))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17578, 14])).
% 5.97/5.96 tff(17580,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17579])).
% 5.97/5.96 tff(17581,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17580, 33])).
% 5.97/5.96 tff(17582,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17581])).
% 5.97/5.96 tff(17583,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17582, 30])).
% 5.97/5.96 tff(17584,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17583])).
% 5.97/5.96 tff(17585,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17584, 39])).
% 5.97/5.96 tff(17586,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17585])).
% 5.97/5.96 tff(17587,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17586, 53])).
% 5.97/5.96 tff(17588,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17587])).
% 5.97/5.96 tff(17589,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17588, 45])).
% 5.97/5.96 tff(17590,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17589])).
% 5.97/5.96 tff(17591,plain,
% 5.97/5.96 (NSY3!24 = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[485, 17590, 28])).
% 5.97/5.96 tff(17592,plain,
% 5.97/5.96 (pred(NSY3!24) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17591])).
% 5.97/5.96 tff(17593,plain,
% 5.97/5.96 (pred(NSY3!24) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17592, 21])).
% 5.97/5.96 tff(17594,plain,
% 5.97/5.96 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n9, n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17593, 17569])).
% 5.97/5.96 tff(17595,plain,
% 5.97/5.96 (sum(pred(NSY3!24), succ(NPY3!26)) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17594, 41])).
% 5.97/5.96 tff(17596,plain,
% 5.97/5.96 (sum(pred(Y2!56), succ(X2!57)) = sum(n7, n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17439, 17521])).
% 5.97/5.96 tff(17597,plain,
% 5.97/5.96 (sum(pred(Y2!56), succ(X2!57)) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17596, 44])).
% 5.97/5.96 tff(17598,plain,
% 5.97/5.96 (sum(pred(X2!57), succ(Y2!56)) = sum(n7, n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17495, 17463])).
% 5.97/5.96 tff(17599,plain,
% 5.97/5.96 (sum(pred(X2!57), succ(Y2!56)) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17598, 44])).
% 5.97/5.96 tff(17600,plain,
% 5.97/5.96 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n5, n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17599, 17597])).
% 5.97/5.96 tff(17601,plain,
% 5.97/5.96 (X3!55 = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[323, 17600, 43])).
% 5.97/5.96 tff(17602,plain,
% 5.97/5.96 (pred(X3!55) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17601])).
% 5.97/5.96 tff(17603,plain,
% 5.97/5.96 (pred(X3!55) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17602, 21])).
% 5.97/5.96 tff(17604,plain,
% 5.97/5.96 (pred(pred(X3!55)) = pred(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17603])).
% 5.97/5.96 tff(17605,plain,
% 5.97/5.96 (pred(pred(X3!55)) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17604, 20])).
% 5.97/5.96 tff(17606,plain,
% 5.97/5.96 (pred(pred(pred(X3!55))) = pred(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17605])).
% 5.97/5.96 tff(17607,plain,
% 5.97/5.96 (pred(pred(pred(X3!55))) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17606, 19])).
% 5.97/5.96 tff(17608,plain,
% 5.97/5.96 (pred(pred(pred(pred(X3!55)))) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17607])).
% 5.97/5.96 tff(17609,plain,
% 5.97/5.96 (pred(pred(pred(pred(X3!55)))) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17608, 18])).
% 5.97/5.96 tff(17610,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(X3!55))))) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17609])).
% 5.97/5.96 tff(17611,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(X3!55))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17610, 17])).
% 5.97/5.96 tff(17612,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17611])).
% 5.97/5.96 tff(17613,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17612, 16])).
% 5.97/5.96 tff(17614,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17613])).
% 5.97/5.96 tff(17615,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17614, 15])).
% 5.97/5.96 tff(17616,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17615])).
% 5.97/5.96 tff(17617,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17616, 25])).
% 5.97/5.96 tff(17618,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17617])).
% 5.97/5.96 tff(17619,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17618, 24])).
% 5.97/5.96 tff(17620,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17619])).
% 5.97/5.96 tff(17621,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17620, 23])).
% 5.97/5.96 tff(17622,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17621])).
% 5.97/5.96 tff(17623,plain,
% 5.97/5.96 (NPX3!27 = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[510, 17622, 22])).
% 5.97/5.96 tff(17624,plain,
% 5.97/5.96 (succ(NPX3!27) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17623])).
% 5.97/5.96 tff(17625,plain,
% 5.97/5.96 (succ(NPX3!27) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17624, 42])).
% 5.97/5.96 tff(17626,plain,
% 5.97/5.96 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n0, n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17625, 17595])).
% 5.97/5.96 tff(17627,plain,
% 5.97/5.96 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17626, 40])).
% 5.97/5.96 tff(17628,plain,
% 5.97/5.96 (succ(X3!55) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17601])).
% 5.97/5.96 tff(17629,plain,
% 5.97/5.96 (succ(X3!55) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17628, 42])).
% 5.97/5.96 tff(17630,plain,
% 5.97/5.96 (succ(succ(X3!55)) = succ(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17629])).
% 5.97/5.96 tff(17631,plain,
% 5.97/5.96 (succ(succ(X3!55)) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17630, 58])).
% 5.97/5.96 tff(17632,plain,
% 5.97/5.96 (succ(succ(succ(X3!55))) = succ(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17631])).
% 5.97/5.96 tff(17633,plain,
% 5.97/5.96 (succ(succ(succ(X3!55))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17632, 36])).
% 5.97/5.96 tff(17634,plain,
% 5.97/5.96 (succ(succ(succ(succ(X3!55)))) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17633])).
% 5.97/5.96 tff(17635,plain,
% 5.97/5.96 (succ(succ(succ(succ(X3!55)))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17634, 48])).
% 5.97/5.96 tff(17636,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(X3!55))))) = succ(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17635])).
% 5.97/5.96 tff(17637,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(X3!55))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17636, 14])).
% 5.97/5.96 tff(17638,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17637])).
% 5.97/5.96 tff(17639,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17638, 33])).
% 5.97/5.96 tff(17640,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17639])).
% 5.97/5.96 tff(17641,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17640, 30])).
% 5.97/5.96 tff(17642,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17641])).
% 5.97/5.96 tff(17643,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17642, 39])).
% 5.97/5.96 tff(17644,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17643])).
% 5.97/5.96 tff(17645,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17644, 53])).
% 5.97/5.96 tff(17646,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17645])).
% 5.97/5.96 tff(17647,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17646, 45])).
% 5.97/5.96 tff(17648,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17647])).
% 5.97/5.96 tff(17649,plain,
% 5.97/5.96 (NSX3!25 = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[535, 17648, 28])).
% 5.97/5.96 tff(17650,plain,
% 5.97/5.96 (pred(NSX3!25) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17649])).
% 5.97/5.96 tff(17651,plain,
% 5.97/5.96 (pred(NSX3!25) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17650, 21])).
% 5.97/5.96 tff(17652,plain,
% 5.97/5.96 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n9, n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17651, 17627])).
% 5.97/5.96 tff(17653,plain,
% 5.97/5.96 (Y4!52 = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[540, 17652, 54])).
% 5.97/5.96 tff(17654,plain,
% 5.97/5.96 (pred(Y4!52) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17653])).
% 5.97/5.96 tff(17655,plain,
% 5.97/5.96 (pred(Y4!52) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17654, 18])).
% 5.97/5.96 tff(17656,plain,
% 5.97/5.96 (pred(pred(Y4!52)) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17655])).
% 5.97/5.96 tff(17657,plain,
% 5.97/5.96 (pred(pred(Y4!52)) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17656, 17])).
% 5.97/5.96 tff(17658,plain,
% 5.97/5.96 (pred(pred(pred(Y4!52))) = pred(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17657])).
% 5.97/5.96 tff(17659,plain,
% 5.97/5.96 (pred(pred(pred(Y4!52))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17658, 16])).
% 5.97/5.96 tff(17660,plain,
% 5.97/5.96 (pred(pred(pred(pred(Y4!52)))) = pred(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17659])).
% 5.97/5.96 tff(17661,plain,
% 5.97/5.96 (pred(pred(pred(pred(Y4!52)))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17660, 15])).
% 5.97/5.96 tff(17662,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17661])).
% 5.97/5.96 tff(17663,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(Y4!52))))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17662, 25])).
% 5.97/5.96 tff(17664,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17663])).
% 5.97/5.96 tff(17665,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17664, 24])).
% 5.97/5.96 tff(17666,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17665])).
% 5.97/5.96 tff(17667,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17666, 23])).
% 5.97/5.96 tff(17668,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17667])).
% 5.97/5.96 tff(17669,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17668, 22])).
% 5.97/5.96 tff(17670,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17669])).
% 5.97/5.96 tff(17671,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17670, 21])).
% 5.97/5.96 tff(17672,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17671])).
% 5.97/5.96 tff(17673,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17672, 20])).
% 5.97/5.96 tff(17674,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17673])).
% 5.97/5.96 tff(17675,plain,
% 5.97/5.96 (NPY4!22 = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[578, 17674, 19])).
% 5.97/5.96 tff(17676,plain,
% 5.97/5.96 (succ(NPY4!22) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17675])).
% 5.97/5.96 tff(17677,plain,
% 5.97/5.96 (succ(NPY4!22) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17676, 53])).
% 5.97/5.96 tff(17678,plain,
% 5.97/5.96 (succ(Y4!52) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17653])).
% 5.97/5.96 tff(17679,plain,
% 5.97/5.96 (succ(Y4!52) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17678, 53])).
% 5.97/5.96 tff(17680,plain,
% 5.97/5.96 (succ(succ(Y4!52)) = succ(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17679])).
% 5.97/5.96 tff(17681,plain,
% 5.97/5.96 (succ(succ(Y4!52)) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17680, 45])).
% 5.97/5.96 tff(17682,plain,
% 5.97/5.96 (succ(succ(succ(Y4!52))) = succ(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17681])).
% 5.97/5.96 tff(17683,plain,
% 5.97/5.96 (succ(succ(succ(Y4!52))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17682, 28])).
% 5.97/5.96 tff(17684,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y4!52)))) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17683])).
% 5.97/5.96 tff(17685,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y4!52)))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17684, 42])).
% 5.97/5.96 tff(17686,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17685])).
% 5.97/5.96 tff(17687,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y4!52))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17686, 58])).
% 5.97/5.96 tff(17688,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17687])).
% 5.97/5.96 tff(17689,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17688, 36])).
% 5.97/5.96 tff(17690,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17689])).
% 5.97/5.96 tff(17691,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17690, 48])).
% 5.97/5.96 tff(17692,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17691])).
% 5.97/5.96 tff(17693,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17692, 14])).
% 5.97/5.96 tff(17694,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17693])).
% 5.97/5.96 tff(17695,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17694, 33])).
% 5.97/5.96 tff(17696,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17695])).
% 5.97/5.96 tff(17697,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17696, 30])).
% 5.97/5.96 tff(17698,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17697])).
% 5.97/5.96 tff(17699,plain,
% 5.97/5.96 (NSY4!20 = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[601, 17698, 39])).
% 5.97/5.96 tff(17700,plain,
% 5.97/5.96 (pred(NSY4!20) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17699])).
% 5.97/5.96 tff(17701,plain,
% 5.97/5.96 (pred(NSY4!20) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17700, 18])).
% 5.97/5.96 tff(17702,plain,
% 5.97/5.96 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n6, n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17701, 17677])).
% 5.97/5.96 tff(17703,plain,
% 5.97/5.96 (sum(pred(NSY4!20), succ(NPY4!22)) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17702, 52])).
% 5.97/5.96 tff(17704,plain,
% 5.97/5.96 (sum(pred(Y3!54), succ(X3!55)) = sum(n9, n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17547, 17629])).
% 5.97/5.96 tff(17705,plain,
% 5.97/5.96 (sum(pred(Y3!54), succ(X3!55)) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17704, 41])).
% 5.97/5.96 tff(17706,plain,
% 5.97/5.96 (sum(pred(X3!55), succ(Y3!54)) = sum(n9, n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17603, 17571])).
% 5.97/5.96 tff(17707,plain,
% 5.97/5.96 (sum(pred(X3!55), succ(Y3!54)) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17706, 41])).
% 5.97/5.96 tff(17708,plain,
% 5.97/5.96 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n9, n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17707, 17705])).
% 5.97/5.96 tff(17709,plain,
% 5.97/5.96 (X4!53 = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[438, 17708, 54])).
% 5.97/5.96 tff(17710,plain,
% 5.97/5.96 (pred(X4!53) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17709])).
% 5.97/5.96 tff(17711,plain,
% 5.97/5.96 (pred(X4!53) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17710, 18])).
% 5.97/5.96 tff(17712,plain,
% 5.97/5.96 (pred(pred(X4!53)) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17711])).
% 5.97/5.96 tff(17713,plain,
% 5.97/5.96 (pred(pred(X4!53)) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17712, 17])).
% 5.97/5.96 tff(17714,plain,
% 5.97/5.96 (pred(pred(pred(X4!53))) = pred(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17713])).
% 5.97/5.96 tff(17715,plain,
% 5.97/5.96 (pred(pred(pred(X4!53))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17714, 16])).
% 5.97/5.96 tff(17716,plain,
% 5.97/5.96 (pred(pred(pred(pred(X4!53)))) = pred(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17715])).
% 5.97/5.96 tff(17717,plain,
% 5.97/5.96 (pred(pred(pred(pred(X4!53)))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17716, 15])).
% 5.97/5.96 tff(17718,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(X4!53))))) = pred(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17717])).
% 5.97/5.96 tff(17719,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(X4!53))))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17718, 25])).
% 5.97/5.96 tff(17720,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17719])).
% 5.97/5.96 tff(17721,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17720, 24])).
% 5.97/5.96 tff(17722,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17721])).
% 5.97/5.96 tff(17723,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17722, 23])).
% 5.97/5.96 tff(17724,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17723])).
% 5.97/5.96 tff(17725,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17724, 22])).
% 5.97/5.96 tff(17726,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17725])).
% 5.97/5.96 tff(17727,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17726, 21])).
% 5.97/5.96 tff(17728,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17727])).
% 5.97/5.96 tff(17729,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17728, 20])).
% 5.97/5.96 tff(17730,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17729])).
% 5.97/5.96 tff(17731,plain,
% 5.97/5.96 (NPX4!23 = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[626, 17730, 19])).
% 5.97/5.96 tff(17732,plain,
% 5.97/5.96 (succ(NPX4!23) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17731])).
% 5.97/5.96 tff(17733,plain,
% 5.97/5.96 (succ(NPX4!23) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17732, 53])).
% 5.97/5.96 tff(17734,plain,
% 5.97/5.96 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n8, n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17733, 17703])).
% 5.97/5.96 tff(17735,plain,
% 5.97/5.96 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17734, 64])).
% 5.97/5.96 tff(17736,plain,
% 5.97/5.96 (succ(X4!53) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17709])).
% 5.97/5.96 tff(17737,plain,
% 5.97/5.96 (succ(X4!53) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17736, 53])).
% 5.97/5.96 tff(17738,plain,
% 5.97/5.96 (succ(succ(X4!53)) = succ(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17737])).
% 5.97/5.96 tff(17739,plain,
% 5.97/5.96 (succ(succ(X4!53)) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17738, 45])).
% 5.97/5.96 tff(17740,plain,
% 5.97/5.96 (succ(succ(succ(X4!53))) = succ(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17739])).
% 5.97/5.96 tff(17741,plain,
% 5.97/5.96 (succ(succ(succ(X4!53))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17740, 28])).
% 5.97/5.96 tff(17742,plain,
% 5.97/5.96 (succ(succ(succ(succ(X4!53)))) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17741])).
% 5.97/5.96 tff(17743,plain,
% 5.97/5.96 (succ(succ(succ(succ(X4!53)))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17742, 42])).
% 5.97/5.96 tff(17744,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(X4!53))))) = succ(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17743])).
% 5.97/5.96 tff(17745,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(X4!53))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17744, 58])).
% 5.97/5.96 tff(17746,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17745])).
% 5.97/5.96 tff(17747,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17746, 36])).
% 5.97/5.96 tff(17748,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17747])).
% 5.97/5.96 tff(17749,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17748, 48])).
% 5.97/5.96 tff(17750,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17749])).
% 5.97/5.96 tff(17751,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17750, 14])).
% 5.97/5.96 tff(17752,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17751])).
% 5.97/5.96 tff(17753,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17752, 33])).
% 5.97/5.96 tff(17754,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17753])).
% 5.97/5.96 tff(17755,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17754, 30])).
% 5.97/5.96 tff(17756,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17755])).
% 5.97/5.96 tff(17757,plain,
% 5.97/5.96 (NSX4!21 = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[651, 17756, 39])).
% 5.97/5.96 tff(17758,plain,
% 5.97/5.96 (pred(NSX4!21) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17757])).
% 5.97/5.96 tff(17759,plain,
% 5.97/5.96 (pred(NSX4!21) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17758, 18])).
% 5.97/5.96 tff(17760,plain,
% 5.97/5.96 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n6, n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17759, 17735])).
% 5.97/5.96 tff(17761,plain,
% 5.97/5.96 (Y5!50 = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[656, 17760, 788])).
% 5.97/5.96 tff(17762,plain,
% 5.97/5.96 (pred(Y5!50) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17761])).
% 5.97/5.96 tff(17763,plain,
% 5.97/5.96 (pred(Y5!50) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17762, 17])).
% 5.97/5.96 tff(17764,plain,
% 5.97/5.96 (pred(pred(Y5!50)) = pred(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17763])).
% 5.97/5.96 tff(17765,plain,
% 5.97/5.96 (pred(pred(Y5!50)) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17764, 16])).
% 5.97/5.96 tff(17766,plain,
% 5.97/5.96 (pred(pred(pred(Y5!50))) = pred(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17765])).
% 5.97/5.96 tff(17767,plain,
% 5.97/5.96 (pred(pred(pred(Y5!50))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17766, 15])).
% 5.97/5.96 tff(17768,plain,
% 5.97/5.96 (pred(pred(pred(pred(Y5!50)))) = pred(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17767])).
% 5.97/5.96 tff(17769,plain,
% 5.97/5.96 (pred(pred(pred(pred(Y5!50)))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17768, 25])).
% 5.97/5.96 tff(17770,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17769])).
% 5.97/5.96 tff(17771,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(Y5!50))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17770, 24])).
% 5.97/5.96 tff(17772,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17771])).
% 5.97/5.96 tff(17773,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17772, 23])).
% 5.97/5.96 tff(17774,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17773])).
% 5.97/5.96 tff(17775,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17774, 22])).
% 5.97/5.96 tff(17776,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17775])).
% 5.97/5.96 tff(17777,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17776, 21])).
% 5.97/5.96 tff(17778,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17777])).
% 5.97/5.96 tff(17779,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17778, 20])).
% 5.97/5.96 tff(17780,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17779])).
% 5.97/5.96 tff(17781,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17780, 19])).
% 5.97/5.96 tff(17782,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17781])).
% 5.97/5.96 tff(17783,plain,
% 5.97/5.96 (NPY5!18 = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[694, 17782, 18])).
% 5.97/5.96 tff(17784,plain,
% 5.97/5.96 (succ(NPY5!18) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17783])).
% 5.97/5.96 tff(17785,plain,
% 5.97/5.96 (succ(NPY5!18) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17784, 39])).
% 5.97/5.96 tff(17786,plain,
% 5.97/5.96 (succ(Y5!50) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17761])).
% 5.97/5.96 tff(17787,plain,
% 5.97/5.96 (succ(Y5!50) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17786, 39])).
% 5.97/5.96 tff(17788,plain,
% 5.97/5.96 (succ(succ(Y5!50)) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17787])).
% 5.97/5.96 tff(17789,plain,
% 5.97/5.96 (succ(succ(Y5!50)) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17788, 53])).
% 5.97/5.96 tff(17790,plain,
% 5.97/5.96 (succ(succ(succ(Y5!50))) = succ(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17789])).
% 5.97/5.96 tff(17791,plain,
% 5.97/5.96 (succ(succ(succ(Y5!50))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17790, 45])).
% 5.97/5.96 tff(17792,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y5!50)))) = succ(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17791])).
% 5.97/5.96 tff(17793,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y5!50)))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17792, 28])).
% 5.97/5.96 tff(17794,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17793])).
% 5.97/5.96 tff(17795,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y5!50))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17794, 42])).
% 5.97/5.96 tff(17796,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17795])).
% 5.97/5.96 tff(17797,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17796, 58])).
% 5.97/5.96 tff(17798,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17797])).
% 5.97/5.96 tff(17799,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17798, 36])).
% 5.97/5.96 tff(17800,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17799])).
% 5.97/5.96 tff(17801,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17800, 48])).
% 5.97/5.96 tff(17802,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17801])).
% 5.97/5.96 tff(17803,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17802, 14])).
% 5.97/5.96 tff(17804,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17803])).
% 5.97/5.96 tff(17805,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17804, 33])).
% 5.97/5.96 tff(17806,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17805])).
% 5.97/5.96 tff(17807,plain,
% 5.97/5.96 (NSY5!16 = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[717, 17806, 30])).
% 5.97/5.96 tff(17808,plain,
% 5.97/5.96 (pred(NSY5!16) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17807])).
% 5.97/5.96 tff(17809,plain,
% 5.97/5.96 (pred(NSY5!16) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17808, 17])).
% 5.97/5.96 tff(17810,plain,
% 5.97/5.96 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n5, n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17809, 17785])).
% 5.97/5.96 tff(17811,plain,
% 5.97/5.96 (sum(pred(NSY5!16), succ(NPY5!18)) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17810, 50])).
% 5.97/5.96 tff(17812,plain,
% 5.97/5.96 (sum(pred(Y4!52), succ(X4!53)) = sum(n6, n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17655, 17737])).
% 5.97/5.96 tff(17813,plain,
% 5.97/5.96 (sum(pred(Y4!52), succ(X4!53)) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17812, 52])).
% 5.97/5.96 tff(17814,plain,
% 5.97/5.96 (sum(pred(X4!53), succ(Y4!52)) = sum(n6, n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17711, 17679])).
% 5.97/5.96 tff(17815,plain,
% 5.97/5.96 (sum(pred(X4!53), succ(Y4!52)) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17814, 52])).
% 5.97/5.96 tff(17816,plain,
% 5.97/5.96 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n3, n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17815, 17813])).
% 5.97/5.96 tff(17817,plain,
% 5.97/5.96 (X5!51 = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[553, 17816, 51])).
% 5.97/5.96 tff(17818,plain,
% 5.97/5.96 (pred(X5!51) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17817])).
% 5.97/5.96 tff(17819,plain,
% 5.97/5.96 (pred(X5!51) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17818, 17])).
% 5.97/5.96 tff(17820,plain,
% 5.97/5.96 (pred(pred(X5!51)) = pred(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17819])).
% 5.97/5.96 tff(17821,plain,
% 5.97/5.96 (pred(pred(X5!51)) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17820, 16])).
% 5.97/5.96 tff(17822,plain,
% 5.97/5.96 (pred(pred(pred(X5!51))) = pred(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17821])).
% 5.97/5.96 tff(17823,plain,
% 5.97/5.96 (pred(pred(pred(X5!51))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17822, 15])).
% 5.97/5.96 tff(17824,plain,
% 5.97/5.96 (pred(pred(pred(pred(X5!51)))) = pred(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17823])).
% 5.97/5.96 tff(17825,plain,
% 5.97/5.96 (pred(pred(pred(pred(X5!51)))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17824, 25])).
% 5.97/5.96 tff(17826,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(X5!51))))) = pred(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17825])).
% 5.97/5.96 tff(17827,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(X5!51))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17826, 24])).
% 5.97/5.96 tff(17828,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17827])).
% 5.97/5.96 tff(17829,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17828, 23])).
% 5.97/5.96 tff(17830,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17829])).
% 5.97/5.96 tff(17831,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17830, 22])).
% 5.97/5.96 tff(17832,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17831])).
% 5.97/5.96 tff(17833,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17832, 21])).
% 5.97/5.96 tff(17834,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17833])).
% 5.97/5.96 tff(17835,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17834, 20])).
% 5.97/5.96 tff(17836,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17835])).
% 5.97/5.96 tff(17837,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17836, 19])).
% 5.97/5.96 tff(17838,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17837])).
% 5.97/5.96 tff(17839,plain,
% 5.97/5.96 (NPX5!19 = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[742, 17838, 18])).
% 5.97/5.96 tff(17840,plain,
% 5.97/5.96 (succ(NPX5!19) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17839])).
% 5.97/5.96 tff(17841,plain,
% 5.97/5.96 (succ(NPX5!19) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17840, 39])).
% 5.97/5.96 tff(17842,plain,
% 5.97/5.96 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n7, n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17841, 17811])).
% 5.97/5.96 tff(17843,plain,
% 5.97/5.96 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17842, 787])).
% 5.97/5.96 tff(17844,plain,
% 5.97/5.96 (succ(X5!51) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17817])).
% 5.97/5.96 tff(17845,plain,
% 5.97/5.96 (succ(X5!51) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17844, 39])).
% 5.97/5.96 tff(17846,plain,
% 5.97/5.96 (succ(succ(X5!51)) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17845])).
% 5.97/5.96 tff(17847,plain,
% 5.97/5.96 (succ(succ(X5!51)) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17846, 53])).
% 5.97/5.96 tff(17848,plain,
% 5.97/5.96 (succ(succ(succ(X5!51))) = succ(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17847])).
% 5.97/5.96 tff(17849,plain,
% 5.97/5.96 (succ(succ(succ(X5!51))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17848, 45])).
% 5.97/5.96 tff(17850,plain,
% 5.97/5.96 (succ(succ(succ(succ(X5!51)))) = succ(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17849])).
% 5.97/5.96 tff(17851,plain,
% 5.97/5.96 (succ(succ(succ(succ(X5!51)))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17850, 28])).
% 5.97/5.96 tff(17852,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(X5!51))))) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17851])).
% 5.97/5.96 tff(17853,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(X5!51))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17852, 42])).
% 5.97/5.96 tff(17854,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17853])).
% 5.97/5.96 tff(17855,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17854, 58])).
% 5.97/5.96 tff(17856,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17855])).
% 5.97/5.96 tff(17857,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[17856, 36])).
% 5.97/5.96 tff(17858,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17857])).
% 5.97/5.96 tff(17859,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17858, 48])).
% 5.97/5.96 tff(17860,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17859])).
% 5.97/5.96 tff(17861,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17860, 14])).
% 5.97/5.96 tff(17862,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17861])).
% 5.97/5.96 tff(17863,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17862, 33])).
% 5.97/5.96 tff(17864,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17863])).
% 5.97/5.96 tff(17865,plain,
% 5.97/5.96 (NSX5!17 = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[767, 17864, 30])).
% 5.97/5.96 tff(17866,plain,
% 5.97/5.96 (pred(NSX5!17) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17865])).
% 5.97/5.96 tff(17867,plain,
% 5.97/5.96 (pred(NSX5!17) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17866, 17])).
% 5.97/5.96 tff(17868,plain,
% 5.97/5.96 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n5, n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17867, 17843])).
% 5.97/5.96 tff(17869,plain,
% 5.97/5.96 (Y6!48 = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[772, 17868, 558])).
% 5.97/5.96 tff(17870,plain,
% 5.97/5.96 (pred(Y6!48) = pred(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17869])).
% 5.97/5.96 tff(17871,plain,
% 5.97/5.96 (pred(Y6!48) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17870, 24])).
% 5.97/5.96 tff(17872,plain,
% 5.97/5.96 (pred(pred(Y6!48)) = pred(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17871])).
% 5.97/5.96 tff(17873,plain,
% 5.97/5.96 (pred(pred(Y6!48)) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17872, 23])).
% 5.97/5.96 tff(17874,plain,
% 5.97/5.96 (pred(pred(pred(Y6!48))) = pred(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17873])).
% 5.97/5.96 tff(17875,plain,
% 5.97/5.96 (pred(pred(pred(Y6!48))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17874, 22])).
% 5.97/5.96 tff(17876,plain,
% 5.97/5.96 (pred(pred(pred(pred(Y6!48)))) = pred(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17875])).
% 5.97/5.96 tff(17877,plain,
% 5.97/5.96 (pred(pred(pred(pred(Y6!48)))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17876, 21])).
% 5.97/5.96 tff(17878,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17877])).
% 5.97/5.96 tff(17879,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(Y6!48))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17878, 20])).
% 5.97/5.96 tff(17880,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17879])).
% 5.97/5.96 tff(17881,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17880, 19])).
% 5.97/5.96 tff(17882,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17881])).
% 5.97/5.96 tff(17883,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17882, 18])).
% 5.97/5.96 tff(17884,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17883])).
% 5.97/5.96 tff(17885,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17884, 17])).
% 5.97/5.96 tff(17886,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17885])).
% 5.97/5.96 tff(17887,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17886, 16])).
% 5.97/5.96 tff(17888,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17887])).
% 5.97/5.96 tff(17889,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17888, 15])).
% 5.97/5.96 tff(17890,plain,
% 5.97/5.96 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17889])).
% 5.97/5.96 tff(17891,plain,
% 5.97/5.96 (NPY6!14 = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[1465, 17890, 25])).
% 5.97/5.96 tff(17892,plain,
% 5.97/5.96 (succ(NPY6!14) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17891])).
% 5.97/5.96 tff(17893,plain,
% 5.97/5.96 (succ(NPY6!14) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17892, 48])).
% 5.97/5.96 tff(17894,plain,
% 5.97/5.96 (succ(Y6!48) = succ(n2)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17869])).
% 5.97/5.96 tff(17895,plain,
% 5.97/5.96 (succ(Y6!48) = n3),
% 5.97/5.96 inference(transitivity,[status(thm)],[17894, 48])).
% 5.97/5.96 tff(17896,plain,
% 5.97/5.96 (succ(succ(Y6!48)) = succ(n3)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17895])).
% 5.97/5.96 tff(17897,plain,
% 5.97/5.96 (succ(succ(Y6!48)) = n4),
% 5.97/5.96 inference(transitivity,[status(thm)],[17896, 14])).
% 5.97/5.96 tff(17898,plain,
% 5.97/5.96 (succ(succ(succ(Y6!48))) = succ(n4)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17897])).
% 5.97/5.96 tff(17899,plain,
% 5.97/5.96 (succ(succ(succ(Y6!48))) = n5),
% 5.97/5.96 inference(transitivity,[status(thm)],[17898, 33])).
% 5.97/5.96 tff(17900,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y6!48)))) = succ(n5)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17899])).
% 5.97/5.96 tff(17901,plain,
% 5.97/5.96 (succ(succ(succ(succ(Y6!48)))) = n6),
% 5.97/5.96 inference(transitivity,[status(thm)],[17900, 30])).
% 5.97/5.96 tff(17902,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n6)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17901])).
% 5.97/5.96 tff(17903,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(Y6!48))))) = n7),
% 5.97/5.96 inference(transitivity,[status(thm)],[17902, 39])).
% 5.97/5.96 tff(17904,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n7)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17903])).
% 5.97/5.96 tff(17905,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n8),
% 5.97/5.96 inference(transitivity,[status(thm)],[17904, 53])).
% 5.97/5.96 tff(17906,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n8)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17905])).
% 5.97/5.96 tff(17907,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n9),
% 5.97/5.96 inference(transitivity,[status(thm)],[17906, 45])).
% 5.97/5.96 tff(17908,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n9)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17907])).
% 5.97/5.96 tff(17909,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n10),
% 5.97/5.96 inference(transitivity,[status(thm)],[17908, 28])).
% 5.97/5.96 tff(17910,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n10)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17909])).
% 5.97/5.96 tff(17911,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n0),
% 5.97/5.96 inference(transitivity,[status(thm)],[17910, 42])).
% 5.97/5.96 tff(17912,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n0)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17911])).
% 5.97/5.96 tff(17913,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n1),
% 5.97/5.96 inference(transitivity,[status(thm)],[17912, 58])).
% 5.97/5.96 tff(17914,plain,
% 5.97/5.96 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n1)),
% 5.97/5.96 inference(monotonicity,[status(thm)],[17913])).
% 5.97/5.96 tff(17915,plain,
% 5.97/5.96 (NSY6!12 = n2),
% 5.97/5.96 inference(transitivity,[status(thm)],[1490, 17914, 36])).
% 5.97/5.97 tff(17916,plain,
% 5.97/5.97 (pred(NSY6!12) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17915])).
% 5.97/5.97 tff(17917,plain,
% 5.97/5.97 (pred(NSY6!12) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[17916, 24])).
% 5.97/5.97 tff(17918,plain,
% 5.97/5.97 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n1, n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17917, 17893])).
% 5.97/5.97 tff(17919,plain,
% 5.97/5.97 (sum(pred(NSY6!12), succ(NPY6!14)) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[17918, 47])).
% 5.97/5.97 tff(17920,plain,
% 5.97/5.97 (sum(pred(Y5!50), succ(X5!51)) = sum(n5, n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17763, 17845])).
% 5.97/5.97 tff(17921,plain,
% 5.97/5.97 (sum(pred(Y5!50), succ(X5!51)) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[17920, 50])).
% 5.97/5.97 tff(17922,plain,
% 5.97/5.97 (sum(pred(X5!51), succ(Y5!50)) = sum(n5, n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17819, 17787])).
% 5.97/5.97 tff(17923,plain,
% 5.97/5.97 (sum(pred(X5!51), succ(Y5!50)) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[17922, 50])).
% 5.97/5.97 tff(17924,plain,
% 5.97/5.97 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n1, n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17923, 17921])).
% 5.97/5.97 tff(17925,plain,
% 5.97/5.97 (X6!49 = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[669, 17924, 49])).
% 5.97/5.97 tff(17926,plain,
% 5.97/5.97 (pred(X6!49) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17925])).
% 5.97/5.97 tff(17927,plain,
% 5.97/5.97 (pred(X6!49) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[17926, 24])).
% 5.97/5.97 tff(17928,plain,
% 5.97/5.97 (pred(pred(X6!49)) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17927])).
% 5.97/5.97 tff(17929,plain,
% 5.97/5.97 (pred(pred(X6!49)) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[17928, 23])).
% 5.97/5.97 tff(17930,plain,
% 5.97/5.97 (pred(pred(pred(X6!49))) = pred(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17929])).
% 5.97/5.97 tff(17931,plain,
% 5.97/5.97 (pred(pred(pred(X6!49))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[17930, 22])).
% 5.97/5.97 tff(17932,plain,
% 5.97/5.97 (pred(pred(pred(pred(X6!49)))) = pred(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17931])).
% 5.97/5.97 tff(17933,plain,
% 5.97/5.97 (pred(pred(pred(pred(X6!49)))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[17932, 21])).
% 5.97/5.97 tff(17934,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X6!49))))) = pred(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17933])).
% 5.97/5.97 tff(17935,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X6!49))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[17934, 20])).
% 5.97/5.97 tff(17936,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17935])).
% 5.97/5.97 tff(17937,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[17936, 19])).
% 5.97/5.97 tff(17938,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17937])).
% 5.97/5.97 tff(17939,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[17938, 18])).
% 5.97/5.97 tff(17940,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17939])).
% 5.97/5.97 tff(17941,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[17940, 17])).
% 5.97/5.97 tff(17942,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17941])).
% 5.97/5.97 tff(17943,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[17942, 16])).
% 5.97/5.97 tff(17944,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17943])).
% 5.97/5.97 tff(17945,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[17944, 15])).
% 5.97/5.97 tff(17946,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17945])).
% 5.97/5.97 tff(17947,plain,
% 5.97/5.97 (NPX6!15 = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[1523, 17946, 25])).
% 5.97/5.97 tff(17948,plain,
% 5.97/5.97 (succ(NPX6!15) = succ(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17947])).
% 5.97/5.97 tff(17949,plain,
% 5.97/5.97 (succ(NPX6!15) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[17948, 48])).
% 5.97/5.97 tff(17950,plain,
% 5.97/5.97 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n3, n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17949, 17919])).
% 5.97/5.97 tff(17951,plain,
% 5.97/5.97 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[17950, 786])).
% 5.97/5.97 tff(17952,plain,
% 5.97/5.97 (succ(X6!49) = succ(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17925])).
% 5.97/5.97 tff(17953,plain,
% 5.97/5.97 (succ(X6!49) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[17952, 48])).
% 5.97/5.97 tff(17954,plain,
% 5.97/5.97 (succ(succ(X6!49)) = succ(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17953])).
% 5.97/5.97 tff(17955,plain,
% 5.97/5.97 (succ(succ(X6!49)) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[17954, 14])).
% 5.97/5.97 tff(17956,plain,
% 5.97/5.97 (succ(succ(succ(X6!49))) = succ(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17955])).
% 5.97/5.97 tff(17957,plain,
% 5.97/5.97 (succ(succ(succ(X6!49))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[17956, 33])).
% 5.97/5.97 tff(17958,plain,
% 5.97/5.97 (succ(succ(succ(succ(X6!49)))) = succ(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17957])).
% 5.97/5.97 tff(17959,plain,
% 5.97/5.97 (succ(succ(succ(succ(X6!49)))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[17958, 30])).
% 5.97/5.97 tff(17960,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(X6!49))))) = succ(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17959])).
% 5.97/5.97 tff(17961,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(X6!49))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[17960, 39])).
% 5.97/5.97 tff(17962,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17961])).
% 5.97/5.97 tff(17963,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[17962, 53])).
% 5.97/5.97 tff(17964,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17963])).
% 5.97/5.97 tff(17965,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[17964, 45])).
% 5.97/5.97 tff(17966,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17965])).
% 5.97/5.97 tff(17967,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[17966, 28])).
% 5.97/5.97 tff(17968,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17967])).
% 5.97/5.97 tff(17969,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[17968, 42])).
% 5.97/5.97 tff(17970,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17969])).
% 5.97/5.97 tff(17971,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[17970, 58])).
% 5.97/5.97 tff(17972,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17971])).
% 5.97/5.97 tff(17973,plain,
% 5.97/5.97 (NSX6!13 = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[1550, 17972, 36])).
% 5.97/5.97 tff(17974,plain,
% 5.97/5.97 (pred(NSX6!13) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17973])).
% 5.97/5.97 tff(17975,plain,
% 5.97/5.97 (pred(NSX6!13) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[17974, 24])).
% 5.97/5.97 tff(17976,plain,
% 5.97/5.97 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n1, n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17975, 17951])).
% 5.97/5.97 tff(17977,plain,
% 5.97/5.97 (sum(n1, n7) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.97/5.97 inference(symmetry,[status(thm)],[17976])).
% 5.97/5.97 tff(17978,plain,
% 5.97/5.97 (sum(pred(Y6!48), succ(X6!49)) = sum(n1, n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17871, 17953])).
% 5.97/5.97 tff(17979,plain,
% 5.97/5.97 (sum(pred(Y6!48), succ(X6!49)) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[17978, 47])).
% 5.97/5.97 tff(17980,plain,
% 5.97/5.97 (sum(pred(X6!49), succ(Y6!48)) = sum(n1, n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17927, 17895])).
% 5.97/5.97 tff(17981,plain,
% 5.97/5.97 (sum(pred(X6!49), succ(Y6!48)) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[17980, 47])).
% 5.97/5.97 tff(17982,plain,
% 5.97/5.97 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n4, n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17981, 17979])).
% 5.97/5.97 tff(17983,plain,
% 5.97/5.97 (X7!47 = Y7!46),
% 5.97/5.97 inference(transitivity,[status(thm)],[785, 17982, 46, 6515, 17977, 794])).
% 5.97/5.97 tff(17984,plain,
% 5.97/5.97 ($false),
% 5.97/5.97 inference(unit_resolution,[status(thm)],[792, 17983])).
% 5.97/5.97 tff(17985,plain,((~(X0!61 = n10)) | (X7!47 = Y7!46) | (~(Y0!60 = n2))), inference(lemma,lemma(discharge,[]))).
% 5.97/5.97 tff(17986,plain,
% 5.97/5.97 (~(X0!61 = n10)),
% 5.97/5.97 inference(unit_resolution,[status(thm)],[17985, 14626, 792])).
% 5.97/5.97 tff(17987,assumption,(X0!61 = n3), introduced(assumption)).
% 5.97/5.97 tff(17988,plain,
% 5.97/5.97 (pred(X0!61) = pred(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17987])).
% 5.97/5.97 tff(17989,plain,
% 5.97/5.97 (pred(X0!61) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[17988, 25])).
% 5.97/5.97 tff(17990,plain,
% 5.97/5.97 (pred(pred(X0!61)) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17989])).
% 5.97/5.97 tff(17991,plain,
% 5.97/5.97 (pred(pred(X0!61)) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[17990, 24])).
% 5.97/5.97 tff(17992,plain,
% 5.97/5.97 (pred(pred(pred(X0!61))) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17991])).
% 5.97/5.97 tff(17993,plain,
% 5.97/5.97 (pred(pred(pred(X0!61))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[17992, 23])).
% 5.97/5.97 tff(17994,plain,
% 5.97/5.97 (pred(pred(pred(pred(X0!61)))) = pred(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17993])).
% 5.97/5.97 tff(17995,plain,
% 5.97/5.97 (pred(pred(pred(pred(X0!61)))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[17994, 22])).
% 5.97/5.97 tff(17996,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X0!61))))) = pred(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17995])).
% 5.97/5.97 tff(17997,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X0!61))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[17996, 21])).
% 5.97/5.97 tff(17998,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X0!61)))))) = pred(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17997])).
% 5.97/5.97 tff(17999,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X0!61)))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[17998, 20])).
% 5.97/5.97 tff(18000,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = pred(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17999])).
% 5.97/5.97 tff(18001,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X0!61))))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18000, 19])).
% 5.97/5.97 tff(18002,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = pred(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18001])).
% 5.97/5.97 tff(18003,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18002, 18])).
% 5.97/5.97 tff(18004,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = pred(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18003])).
% 5.97/5.97 tff(18005,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18004, 17])).
% 5.97/5.97 tff(18006,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = pred(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18005])).
% 5.97/5.97 tff(18007,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61)))))))))) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18006, 16])).
% 5.97/5.97 tff(18008,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X0!61))))))))))) = pred(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18007])).
% 5.97/5.97 tff(18009,plain,
% 5.97/5.97 (NPX0!39 = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[166, 18008, 15])).
% 5.97/5.97 tff(18010,plain,
% 5.97/5.97 (succ(NPX0!39) = succ(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18009])).
% 5.97/5.97 tff(18011,plain,
% 5.97/5.97 (succ(NPX0!39) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18010, 14])).
% 5.97/5.97 tff(18012,plain,
% 5.97/5.97 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n4, n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18011, 146])).
% 5.97/5.97 tff(18013,plain,
% 5.97/5.97 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18012, 12])).
% 5.97/5.97 tff(18014,plain,
% 5.97/5.97 (succ(X0!61) = succ(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17987])).
% 5.97/5.97 tff(18015,plain,
% 5.97/5.97 (succ(X0!61) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18014, 14])).
% 5.97/5.97 tff(18016,plain,
% 5.97/5.97 (succ(succ(X0!61)) = succ(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18015])).
% 5.97/5.97 tff(18017,plain,
% 5.97/5.97 (succ(succ(X0!61)) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18016, 33])).
% 5.97/5.97 tff(18018,plain,
% 5.97/5.97 (succ(succ(succ(X0!61))) = succ(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18017])).
% 5.97/5.97 tff(18019,plain,
% 5.97/5.97 (succ(succ(succ(X0!61))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18018, 30])).
% 5.97/5.97 tff(18020,plain,
% 5.97/5.97 (succ(succ(succ(succ(X0!61)))) = succ(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18019])).
% 5.97/5.97 tff(18021,plain,
% 5.97/5.97 (succ(succ(succ(succ(X0!61)))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18020, 39])).
% 5.97/5.97 tff(18022,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(X0!61))))) = succ(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18021])).
% 5.97/5.97 tff(18023,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(X0!61))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18022, 53])).
% 5.97/5.97 tff(18024,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(X0!61)))))) = succ(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18023])).
% 5.97/5.97 tff(18025,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(X0!61)))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18024, 45])).
% 5.97/5.97 tff(18026,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = succ(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18025])).
% 5.97/5.97 tff(18027,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(X0!61))))))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18026, 28])).
% 5.97/5.97 tff(18028,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = succ(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18027])).
% 5.97/5.97 tff(18029,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18028, 42])).
% 5.97/5.97 tff(18030,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = succ(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18029])).
% 5.97/5.97 tff(18031,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[18030, 58])).
% 5.97/5.97 tff(18032,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = succ(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18031])).
% 5.97/5.97 tff(18033,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61)))))))))) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18032, 36])).
% 5.97/5.97 tff(18034,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X0!61))))))))))) = succ(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18033])).
% 5.97/5.97 tff(18035,plain,
% 5.97/5.97 (NSX0!37 = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[191, 18034, 48])).
% 5.97/5.97 tff(18036,plain,
% 5.97/5.97 (pred(NSX0!37) = pred(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18035])).
% 5.97/5.97 tff(18037,plain,
% 5.97/5.97 (pred(NSX0!37) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18036, 25])).
% 5.97/5.97 tff(18038,plain,
% 5.97/5.97 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n2, n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18037, 18013])).
% 5.97/5.97 tff(18039,plain,
% 5.97/5.97 (Y1!58 = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[196, 18038, 327])).
% 5.97/5.97 tff(18040,plain,
% 5.97/5.97 (pred(Y1!58) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18039])).
% 5.97/5.97 tff(18041,plain,
% 5.97/5.97 (pred(Y1!58) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18040, 23])).
% 5.97/5.97 tff(18042,plain,
% 5.97/5.97 (pred(pred(Y1!58)) = pred(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18041])).
% 5.97/5.97 tff(18043,plain,
% 5.97/5.97 (pred(pred(Y1!58)) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18042, 22])).
% 5.97/5.97 tff(18044,plain,
% 5.97/5.97 (pred(pred(pred(Y1!58))) = pred(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18043])).
% 5.97/5.97 tff(18045,plain,
% 5.97/5.97 (pred(pred(pred(Y1!58))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18044, 21])).
% 5.97/5.97 tff(18046,plain,
% 5.97/5.97 (pred(pred(pred(pred(Y1!58)))) = pred(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18045])).
% 5.97/5.97 tff(18047,plain,
% 5.97/5.97 (pred(pred(pred(pred(Y1!58)))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18046, 20])).
% 5.97/5.97 tff(18048,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18047])).
% 5.97/5.97 tff(18049,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(Y1!58))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18048, 19])).
% 5.97/5.97 tff(18050,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18049])).
% 5.97/5.97 tff(18051,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18050, 18])).
% 5.97/5.97 tff(18052,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18051])).
% 5.97/5.97 tff(18053,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18052, 17])).
% 5.97/5.97 tff(18054,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18053])).
% 5.97/5.97 tff(18055,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18054, 16])).
% 5.97/5.97 tff(18056,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18055])).
% 5.97/5.97 tff(18057,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18056, 15])).
% 5.97/5.97 tff(18058,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18057])).
% 5.97/5.97 tff(18059,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18058, 25])).
% 5.97/5.97 tff(18060,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18059])).
% 5.97/5.97 tff(18061,plain,
% 5.97/5.97 (NPY1!34 = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[232, 18060, 24])).
% 5.97/5.97 tff(18062,plain,
% 5.97/5.97 (succ(NPY1!34) = succ(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18061])).
% 5.97/5.97 tff(18063,plain,
% 5.97/5.97 (succ(NPY1!34) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18062, 36])).
% 5.97/5.97 tff(18064,plain,
% 5.97/5.97 (succ(Y1!58) = succ(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18039])).
% 5.97/5.97 tff(18065,plain,
% 5.97/5.97 (succ(Y1!58) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18064, 36])).
% 5.97/5.97 tff(18066,plain,
% 5.97/5.97 (succ(succ(Y1!58)) = succ(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18065])).
% 5.97/5.97 tff(18067,plain,
% 5.97/5.97 (succ(succ(Y1!58)) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18066, 48])).
% 5.97/5.97 tff(18068,plain,
% 5.97/5.97 (succ(succ(succ(Y1!58))) = succ(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18067])).
% 5.97/5.97 tff(18069,plain,
% 5.97/5.97 (succ(succ(succ(Y1!58))) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18068, 14])).
% 5.97/5.97 tff(18070,plain,
% 5.97/5.97 (succ(succ(succ(succ(Y1!58)))) = succ(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18069])).
% 5.97/5.97 tff(18071,plain,
% 5.97/5.97 (succ(succ(succ(succ(Y1!58)))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18070, 33])).
% 5.97/5.97 tff(18072,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18071])).
% 5.97/5.97 tff(18073,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(Y1!58))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18072, 30])).
% 5.97/5.97 tff(18074,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18073])).
% 5.97/5.97 tff(18075,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18074, 39])).
% 5.97/5.97 tff(18076,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18075])).
% 5.97/5.97 tff(18077,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18076, 53])).
% 5.97/5.97 tff(18078,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18077])).
% 5.97/5.97 tff(18079,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18078, 45])).
% 5.97/5.97 tff(18080,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18079])).
% 5.97/5.97 tff(18081,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18080, 28])).
% 5.97/5.97 tff(18082,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18081])).
% 5.97/5.97 tff(18083,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18082, 42])).
% 5.97/5.97 tff(18084,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18083])).
% 5.97/5.97 tff(18085,plain,
% 5.97/5.97 (NSY1!32 = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[255, 18084, 58])).
% 5.97/5.97 tff(18086,plain,
% 5.97/5.97 (pred(NSY1!32) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18085])).
% 5.97/5.97 tff(18087,plain,
% 5.97/5.97 (pred(NSY1!32) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18086, 23])).
% 5.97/5.97 tff(18088,plain,
% 5.97/5.97 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n0, n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18087, 18063])).
% 5.97/5.97 tff(18089,plain,
% 5.97/5.97 (sum(pred(NSY1!32), succ(NPY1!34)) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18088, 35])).
% 5.97/5.97 tff(18090,plain,
% 5.97/5.97 (sum(pred(Y0!60), succ(X0!61)) = sum(n2, n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[82, 18015])).
% 5.97/5.97 tff(18091,plain,
% 5.97/5.97 (sum(pred(Y0!60), succ(X0!61)) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18090, 13])).
% 5.97/5.97 tff(18092,plain,
% 5.97/5.97 (sum(pred(X0!61), succ(Y0!60)) = sum(n2, n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[17989, 87])).
% 5.97/5.97 tff(18093,plain,
% 5.97/5.97 (sum(pred(X0!61), succ(Y0!60)) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18092, 13])).
% 5.97/5.97 tff(18094,plain,
% 5.97/5.97 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n6, n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18093, 18091])).
% 5.97/5.97 tff(18095,plain,
% 5.97/5.97 (X1!59 = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[93, 18094, 37])).
% 5.97/5.97 tff(18096,plain,
% 5.97/5.97 (pred(X1!59) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18095])).
% 5.97/5.97 tff(18097,plain,
% 5.97/5.97 (pred(X1!59) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18096, 23])).
% 5.97/5.97 tff(18098,plain,
% 5.97/5.97 (pred(pred(X1!59)) = pred(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18097])).
% 5.97/5.97 tff(18099,plain,
% 5.97/5.97 (pred(pred(X1!59)) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18098, 22])).
% 5.97/5.97 tff(18100,plain,
% 5.97/5.97 (pred(pred(pred(X1!59))) = pred(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18099])).
% 5.97/5.97 tff(18101,plain,
% 5.97/5.97 (pred(pred(pred(X1!59))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18100, 21])).
% 5.97/5.97 tff(18102,plain,
% 5.97/5.97 (pred(pred(pred(pred(X1!59)))) = pred(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18101])).
% 5.97/5.97 tff(18103,plain,
% 5.97/5.97 (pred(pred(pred(pred(X1!59)))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18102, 20])).
% 5.97/5.97 tff(18104,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X1!59))))) = pred(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18103])).
% 5.97/5.97 tff(18105,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X1!59))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18104, 19])).
% 5.97/5.97 tff(18106,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18105])).
% 5.97/5.97 tff(18107,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18106, 18])).
% 5.97/5.97 tff(18108,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18107])).
% 5.97/5.97 tff(18109,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18108, 17])).
% 5.97/5.97 tff(18110,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18109])).
% 5.97/5.97 tff(18111,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18110, 16])).
% 5.97/5.97 tff(18112,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18111])).
% 5.97/5.97 tff(18113,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18112, 15])).
% 5.97/5.97 tff(18114,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18113])).
% 5.97/5.97 tff(18115,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18114, 25])).
% 5.97/5.97 tff(18116,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18115])).
% 5.97/5.97 tff(18117,plain,
% 5.97/5.97 (NPX1!35 = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[280, 18116, 24])).
% 5.97/5.97 tff(18118,plain,
% 5.97/5.97 (succ(NPX1!35) = succ(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18117])).
% 5.97/5.97 tff(18119,plain,
% 5.97/5.97 (succ(NPX1!35) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18118, 36])).
% 5.97/5.97 tff(18120,plain,
% 5.97/5.97 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n2, n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18119, 18089])).
% 5.97/5.97 tff(18121,plain,
% 5.97/5.97 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18120, 34])).
% 5.97/5.97 tff(18122,plain,
% 5.97/5.97 (succ(X1!59) = succ(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18095])).
% 5.97/5.97 tff(18123,plain,
% 5.97/5.97 (succ(X1!59) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18122, 36])).
% 5.97/5.97 tff(18124,plain,
% 5.97/5.97 (succ(succ(X1!59)) = succ(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18123])).
% 5.97/5.97 tff(18125,plain,
% 5.97/5.97 (succ(succ(X1!59)) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18124, 48])).
% 5.97/5.97 tff(18126,plain,
% 5.97/5.97 (succ(succ(succ(X1!59))) = succ(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18125])).
% 5.97/5.97 tff(18127,plain,
% 5.97/5.97 (succ(succ(succ(X1!59))) = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[18126, 14])).
% 5.97/5.97 tff(18128,plain,
% 5.97/5.97 (succ(succ(succ(succ(X1!59)))) = succ(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18127])).
% 5.97/5.97 tff(18129,plain,
% 5.97/5.97 (succ(succ(succ(succ(X1!59)))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18128, 33])).
% 5.97/5.97 tff(18130,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(X1!59))))) = succ(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18129])).
% 5.97/5.97 tff(18131,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(X1!59))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18130, 30])).
% 5.97/5.97 tff(18132,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18131])).
% 5.97/5.97 tff(18133,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18132, 39])).
% 5.97/5.97 tff(18134,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18133])).
% 5.97/5.97 tff(18135,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18134, 53])).
% 5.97/5.97 tff(18136,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18135])).
% 5.97/5.97 tff(18137,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18136, 45])).
% 5.97/5.97 tff(18138,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18137])).
% 5.97/5.97 tff(18139,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18138, 28])).
% 5.97/5.97 tff(18140,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18139])).
% 5.97/5.97 tff(18141,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18140, 42])).
% 5.97/5.97 tff(18142,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18141])).
% 5.97/5.97 tff(18143,plain,
% 5.97/5.97 (NSX1!33 = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[305, 18142, 58])).
% 5.97/5.97 tff(18144,plain,
% 5.97/5.97 (pred(NSX1!33) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18143])).
% 5.97/5.97 tff(18145,plain,
% 5.97/5.97 (pred(NSX1!33) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18144, 23])).
% 5.97/5.97 tff(18146,plain,
% 5.97/5.97 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n0, n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18145, 18121])).
% 5.97/5.97 tff(18147,plain,
% 5.97/5.97 (Y2!56 = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[310, 18146, 442])).
% 5.97/5.97 tff(18148,plain,
% 5.97/5.97 (pred(Y2!56) = pred(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18147])).
% 5.97/5.97 tff(18149,plain,
% 5.97/5.97 (pred(Y2!56) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18148, 15])).
% 5.97/5.97 tff(18150,plain,
% 5.97/5.97 (pred(pred(Y2!56)) = pred(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18149])).
% 5.97/5.97 tff(18151,plain,
% 5.97/5.97 (pred(pred(Y2!56)) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18150, 25])).
% 5.97/5.97 tff(18152,plain,
% 5.97/5.97 (pred(pred(pred(Y2!56))) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18151])).
% 5.97/5.97 tff(18153,plain,
% 5.97/5.97 (pred(pred(pred(Y2!56))) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[18152, 24])).
% 5.97/5.97 tff(18154,plain,
% 5.97/5.97 (pred(pred(pred(pred(Y2!56)))) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18153])).
% 5.97/5.97 tff(18155,plain,
% 5.97/5.97 (pred(pred(pred(pred(Y2!56)))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18154, 23])).
% 5.97/5.97 tff(18156,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18155])).
% 5.97/5.97 tff(18157,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(Y2!56))))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18156, 22])).
% 5.97/5.97 tff(18158,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18157])).
% 5.97/5.97 tff(18159,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18158, 21])).
% 5.97/5.97 tff(18160,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18159])).
% 5.97/5.97 tff(18161,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18160, 20])).
% 5.97/5.97 tff(18162,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18161])).
% 5.97/5.97 tff(18163,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18162, 19])).
% 5.97/5.97 tff(18164,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18163])).
% 5.97/5.97 tff(18165,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18164, 18])).
% 5.97/5.97 tff(18166,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18165])).
% 5.97/5.97 tff(18167,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18166, 17])).
% 5.97/5.97 tff(18168,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18167])).
% 5.97/5.97 tff(18169,plain,
% 5.97/5.97 (NPY2!30 = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[347, 18168, 16])).
% 5.97/5.97 tff(18170,plain,
% 5.97/5.97 (succ(NPY2!30) = succ(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18169])).
% 5.97/5.97 tff(18171,plain,
% 5.97/5.97 (succ(NPY2!30) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18170, 33])).
% 5.97/5.97 tff(18172,plain,
% 5.97/5.97 (succ(Y2!56) = succ(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18147])).
% 5.97/5.97 tff(18173,plain,
% 5.97/5.97 (succ(Y2!56) = n5),
% 5.97/5.97 inference(transitivity,[status(thm)],[18172, 33])).
% 5.97/5.97 tff(18174,plain,
% 5.97/5.97 (succ(succ(Y2!56)) = succ(n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18173])).
% 5.97/5.97 tff(18175,plain,
% 5.97/5.97 (succ(succ(Y2!56)) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18174, 30])).
% 5.97/5.97 tff(18176,plain,
% 5.97/5.97 (succ(succ(succ(Y2!56))) = succ(n6)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18175])).
% 5.97/5.97 tff(18177,plain,
% 5.97/5.97 (succ(succ(succ(Y2!56))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18176, 39])).
% 5.97/5.97 tff(18178,plain,
% 5.97/5.97 (succ(succ(succ(succ(Y2!56)))) = succ(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18177])).
% 5.97/5.97 tff(18179,plain,
% 5.97/5.97 (succ(succ(succ(succ(Y2!56)))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18178, 53])).
% 5.97/5.97 tff(18180,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18179])).
% 5.97/5.97 tff(18181,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(Y2!56))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18180, 45])).
% 5.97/5.97 tff(18182,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18181])).
% 5.97/5.97 tff(18183,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18182, 28])).
% 5.97/5.97 tff(18184,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18183])).
% 5.97/5.97 tff(18185,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18184, 42])).
% 5.97/5.97 tff(18186,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18185])).
% 5.97/5.97 tff(18187,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[18186, 58])).
% 5.97/5.97 tff(18188,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18187])).
% 5.97/5.97 tff(18189,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18188, 36])).
% 5.97/5.97 tff(18190,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18189])).
% 5.97/5.97 tff(18191,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18190, 48])).
% 5.97/5.97 tff(18192,plain,
% 5.97/5.97 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18191])).
% 5.97/5.97 tff(18193,plain,
% 5.97/5.97 (NSY2!28 = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[370, 18192, 14])).
% 5.97/5.97 tff(18194,plain,
% 5.97/5.97 (pred(NSY2!28) = pred(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18193])).
% 5.97/5.97 tff(18195,plain,
% 5.97/5.97 (pred(NSY2!28) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18194, 15])).
% 5.97/5.97 tff(18196,plain,
% 5.97/5.97 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n3, n5)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18195, 18171])).
% 5.97/5.97 tff(18197,plain,
% 5.97/5.97 (sum(pred(NSY2!28), succ(NPY2!30)) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18196, 32])).
% 5.97/5.97 tff(18198,plain,
% 5.97/5.97 (sum(pred(Y1!58), succ(X1!59)) = sum(n0, n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18041, 18123])).
% 5.97/5.97 tff(18199,plain,
% 5.97/5.97 (sum(pred(Y1!58), succ(X1!59)) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18198, 35])).
% 5.97/5.97 tff(18200,plain,
% 5.97/5.97 (sum(pred(X1!59), succ(Y1!58)) = sum(n0, n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18097, 18065])).
% 5.97/5.97 tff(18201,plain,
% 5.97/5.97 (sum(pred(X1!59), succ(Y1!58)) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18200, 35])).
% 5.97/5.97 tff(18202,plain,
% 5.97/5.97 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n2, n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18201, 18199])).
% 5.97/5.97 tff(18203,plain,
% 5.97/5.97 (X2!57 = n4),
% 5.97/5.97 inference(transitivity,[status(thm)],[209, 18202, 34])).
% 5.97/5.97 tff(18204,plain,
% 5.97/5.97 (pred(X2!57) = pred(n4)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18203])).
% 5.97/5.97 tff(18205,plain,
% 5.97/5.97 (pred(X2!57) = n3),
% 5.97/5.97 inference(transitivity,[status(thm)],[18204, 15])).
% 5.97/5.97 tff(18206,plain,
% 5.97/5.97 (pred(pred(X2!57)) = pred(n3)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18205])).
% 5.97/5.97 tff(18207,plain,
% 5.97/5.97 (pred(pred(X2!57)) = n2),
% 5.97/5.97 inference(transitivity,[status(thm)],[18206, 25])).
% 5.97/5.97 tff(18208,plain,
% 5.97/5.97 (pred(pred(pred(X2!57))) = pred(n2)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18207])).
% 5.97/5.97 tff(18209,plain,
% 5.97/5.97 (pred(pred(pred(X2!57))) = n1),
% 5.97/5.97 inference(transitivity,[status(thm)],[18208, 24])).
% 5.97/5.97 tff(18210,plain,
% 5.97/5.97 (pred(pred(pred(pred(X2!57)))) = pred(n1)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18209])).
% 5.97/5.97 tff(18211,plain,
% 5.97/5.97 (pred(pred(pred(pred(X2!57)))) = n0),
% 5.97/5.97 inference(transitivity,[status(thm)],[18210, 23])).
% 5.97/5.97 tff(18212,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X2!57))))) = pred(n0)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18211])).
% 5.97/5.97 tff(18213,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(X2!57))))) = n10),
% 5.97/5.97 inference(transitivity,[status(thm)],[18212, 22])).
% 5.97/5.97 tff(18214,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n10)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18213])).
% 5.97/5.97 tff(18215,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n9),
% 5.97/5.97 inference(transitivity,[status(thm)],[18214, 21])).
% 5.97/5.97 tff(18216,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n9)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18215])).
% 5.97/5.97 tff(18217,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n8),
% 5.97/5.97 inference(transitivity,[status(thm)],[18216, 20])).
% 5.97/5.97 tff(18218,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n8)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18217])).
% 5.97/5.97 tff(18219,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n7),
% 5.97/5.97 inference(transitivity,[status(thm)],[18218, 19])).
% 5.97/5.97 tff(18220,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n7)),
% 5.97/5.97 inference(monotonicity,[status(thm)],[18219])).
% 5.97/5.97 tff(18221,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n6),
% 5.97/5.97 inference(transitivity,[status(thm)],[18220, 18])).
% 5.97/5.97 tff(18222,plain,
% 5.97/5.97 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18221])).
% 5.97/5.98 tff(18223,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18222, 17])).
% 5.97/5.98 tff(18224,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18223])).
% 5.97/5.98 tff(18225,plain,
% 5.97/5.98 (NPX2!31 = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[395, 18224, 16])).
% 5.97/5.98 tff(18226,plain,
% 5.97/5.98 (succ(NPX2!31) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18225])).
% 5.97/5.98 tff(18227,plain,
% 5.97/5.98 (succ(NPX2!31) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18226, 33])).
% 5.97/5.98 tff(18228,plain,
% 5.97/5.98 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n5, n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18227, 18197])).
% 5.97/5.98 tff(18229,plain,
% 5.97/5.98 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18228, 558])).
% 5.97/5.98 tff(18230,plain,
% 5.97/5.98 (succ(X2!57) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18203])).
% 5.97/5.98 tff(18231,plain,
% 5.97/5.98 (succ(X2!57) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18230, 33])).
% 5.97/5.98 tff(18232,plain,
% 5.97/5.98 (succ(succ(X2!57)) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18231])).
% 5.97/5.98 tff(18233,plain,
% 5.97/5.98 (succ(succ(X2!57)) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18232, 30])).
% 5.97/5.98 tff(18234,plain,
% 5.97/5.98 (succ(succ(succ(X2!57))) = succ(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18233])).
% 5.97/5.98 tff(18235,plain,
% 5.97/5.98 (succ(succ(succ(X2!57))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18234, 39])).
% 5.97/5.98 tff(18236,plain,
% 5.97/5.98 (succ(succ(succ(succ(X2!57)))) = succ(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18235])).
% 5.97/5.98 tff(18237,plain,
% 5.97/5.98 (succ(succ(succ(succ(X2!57)))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18236, 53])).
% 5.97/5.98 tff(18238,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X2!57))))) = succ(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18237])).
% 5.97/5.98 tff(18239,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X2!57))))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18238, 45])).
% 5.97/5.98 tff(18240,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18239])).
% 5.97/5.98 tff(18241,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18240, 28])).
% 5.97/5.98 tff(18242,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18241])).
% 5.97/5.98 tff(18243,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18242, 42])).
% 5.97/5.98 tff(18244,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18243])).
% 5.97/5.98 tff(18245,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18244, 58])).
% 5.97/5.98 tff(18246,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18245])).
% 5.97/5.98 tff(18247,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18246, 36])).
% 5.97/5.98 tff(18248,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18247])).
% 5.97/5.98 tff(18249,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18248, 48])).
% 5.97/5.98 tff(18250,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18249])).
% 5.97/5.98 tff(18251,plain,
% 5.97/5.98 (NSX2!29 = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[420, 18250, 14])).
% 5.97/5.98 tff(18252,plain,
% 5.97/5.98 (pred(NSX2!29) = pred(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18251])).
% 5.97/5.98 tff(18253,plain,
% 5.97/5.98 (pred(NSX2!29) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18252, 15])).
% 5.97/5.98 tff(18254,plain,
% 5.97/5.98 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n3, n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18253, 18229])).
% 5.97/5.98 tff(18255,plain,
% 5.97/5.98 (Y3!54 = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[425, 18254, 557])).
% 5.97/5.98 tff(18256,plain,
% 5.97/5.98 (pred(Y3!54) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18255])).
% 5.97/5.98 tff(18257,plain,
% 5.97/5.98 (pred(Y3!54) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18256, 16])).
% 5.97/5.98 tff(18258,plain,
% 5.97/5.98 (pred(pred(Y3!54)) = pred(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18257])).
% 5.97/5.98 tff(18259,plain,
% 5.97/5.98 (pred(pred(Y3!54)) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18258, 15])).
% 5.97/5.98 tff(18260,plain,
% 5.97/5.98 (pred(pred(pred(Y3!54))) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18259])).
% 5.97/5.98 tff(18261,plain,
% 5.97/5.98 (pred(pred(pred(Y3!54))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18260, 25])).
% 5.97/5.98 tff(18262,plain,
% 5.97/5.98 (pred(pred(pred(pred(Y3!54)))) = pred(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18261])).
% 5.97/5.98 tff(18263,plain,
% 5.97/5.98 (pred(pred(pred(pred(Y3!54)))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18262, 24])).
% 5.97/5.98 tff(18264,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18263])).
% 5.97/5.98 tff(18265,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(Y3!54))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18264, 23])).
% 5.97/5.98 tff(18266,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18265])).
% 5.97/5.98 tff(18267,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18266, 22])).
% 5.97/5.98 tff(18268,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18267])).
% 5.97/5.98 tff(18269,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18268, 21])).
% 5.97/5.98 tff(18270,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18269])).
% 5.97/5.98 tff(18271,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18270, 20])).
% 5.97/5.98 tff(18272,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18271])).
% 5.97/5.98 tff(18273,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18272, 19])).
% 5.97/5.98 tff(18274,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18273])).
% 5.97/5.98 tff(18275,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18274, 18])).
% 5.97/5.98 tff(18276,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18275])).
% 5.97/5.98 tff(18277,plain,
% 5.97/5.98 (NPY3!26 = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[462, 18276, 17])).
% 5.97/5.98 tff(18278,plain,
% 5.97/5.98 (succ(NPY3!26) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18277])).
% 5.97/5.98 tff(18279,plain,
% 5.97/5.98 (succ(NPY3!26) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18278, 30])).
% 5.97/5.98 tff(18280,plain,
% 5.97/5.98 (succ(Y3!54) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18255])).
% 5.97/5.98 tff(18281,plain,
% 5.97/5.98 (succ(Y3!54) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18280, 30])).
% 5.97/5.98 tff(18282,plain,
% 5.97/5.98 (succ(succ(Y3!54)) = succ(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18281])).
% 5.97/5.98 tff(18283,plain,
% 5.97/5.98 (succ(succ(Y3!54)) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18282, 39])).
% 5.97/5.98 tff(18284,plain,
% 5.97/5.98 (succ(succ(succ(Y3!54))) = succ(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18283])).
% 5.97/5.98 tff(18285,plain,
% 5.97/5.98 (succ(succ(succ(Y3!54))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18284, 53])).
% 5.97/5.98 tff(18286,plain,
% 5.97/5.98 (succ(succ(succ(succ(Y3!54)))) = succ(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18285])).
% 5.97/5.98 tff(18287,plain,
% 5.97/5.98 (succ(succ(succ(succ(Y3!54)))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18286, 45])).
% 5.97/5.98 tff(18288,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18287])).
% 5.97/5.98 tff(18289,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(Y3!54))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18288, 28])).
% 5.97/5.98 tff(18290,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18289])).
% 5.97/5.98 tff(18291,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18290, 42])).
% 5.97/5.98 tff(18292,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18291])).
% 5.97/5.98 tff(18293,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18292, 58])).
% 5.97/5.98 tff(18294,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18293])).
% 5.97/5.98 tff(18295,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18294, 36])).
% 5.97/5.98 tff(18296,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18295])).
% 5.97/5.98 tff(18297,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18296, 48])).
% 5.97/5.98 tff(18298,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18297])).
% 5.97/5.98 tff(18299,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18298, 14])).
% 5.97/5.98 tff(18300,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18299])).
% 5.97/5.98 tff(18301,plain,
% 5.97/5.98 (NSY3!24 = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[485, 18300, 33])).
% 5.97/5.98 tff(18302,plain,
% 5.97/5.98 (pred(NSY3!24) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18301])).
% 5.97/5.98 tff(18303,plain,
% 5.97/5.98 (pred(NSY3!24) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18302, 16])).
% 5.97/5.98 tff(18304,plain,
% 5.97/5.98 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n4, n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18303, 18279])).
% 5.97/5.98 tff(18305,plain,
% 5.97/5.98 (sum(pred(NSY3!24), succ(NPY3!26)) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18304, 12])).
% 5.97/5.98 tff(18306,plain,
% 5.97/5.98 (sum(pred(Y2!56), succ(X2!57)) = sum(n3, n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18149, 18231])).
% 5.97/5.98 tff(18307,plain,
% 5.97/5.98 (sum(pred(Y2!56), succ(X2!57)) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18306, 32])).
% 5.97/5.98 tff(18308,plain,
% 5.97/5.98 (sum(pred(X2!57), succ(Y2!56)) = sum(n3, n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18205, 18173])).
% 5.97/5.98 tff(18309,plain,
% 5.97/5.98 (sum(pred(X2!57), succ(Y2!56)) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18308, 32])).
% 5.97/5.98 tff(18310,plain,
% 5.97/5.98 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n8, n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18309, 18307])).
% 5.97/5.98 tff(18311,plain,
% 5.97/5.98 (X3!55 = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[323, 18310, 31])).
% 5.97/5.98 tff(18312,plain,
% 5.97/5.98 (pred(X3!55) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18311])).
% 5.97/5.98 tff(18313,plain,
% 5.97/5.98 (pred(X3!55) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18312, 16])).
% 5.97/5.98 tff(18314,plain,
% 5.97/5.98 (pred(pred(X3!55)) = pred(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18313])).
% 5.97/5.98 tff(18315,plain,
% 5.97/5.98 (pred(pred(X3!55)) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18314, 15])).
% 5.97/5.98 tff(18316,plain,
% 5.97/5.98 (pred(pred(pred(X3!55))) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18315])).
% 5.97/5.98 tff(18317,plain,
% 5.97/5.98 (pred(pred(pred(X3!55))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18316, 25])).
% 5.97/5.98 tff(18318,plain,
% 5.97/5.98 (pred(pred(pred(pred(X3!55)))) = pred(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18317])).
% 5.97/5.98 tff(18319,plain,
% 5.97/5.98 (pred(pred(pred(pred(X3!55)))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18318, 24])).
% 5.97/5.98 tff(18320,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(X3!55))))) = pred(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18319])).
% 5.97/5.98 tff(18321,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(X3!55))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18320, 23])).
% 5.97/5.98 tff(18322,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18321])).
% 5.97/5.98 tff(18323,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18322, 22])).
% 5.97/5.98 tff(18324,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18323])).
% 5.97/5.98 tff(18325,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18324, 21])).
% 5.97/5.98 tff(18326,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18325])).
% 5.97/5.98 tff(18327,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18326, 20])).
% 5.97/5.98 tff(18328,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18327])).
% 5.97/5.98 tff(18329,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18328, 19])).
% 5.97/5.98 tff(18330,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18329])).
% 5.97/5.98 tff(18331,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18330, 18])).
% 5.97/5.98 tff(18332,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18331])).
% 5.97/5.98 tff(18333,plain,
% 5.97/5.98 (NPX3!27 = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[510, 18332, 17])).
% 5.97/5.98 tff(18334,plain,
% 5.97/5.98 (succ(NPX3!27) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18333])).
% 5.97/5.98 tff(18335,plain,
% 5.97/5.98 (succ(NPX3!27) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18334, 30])).
% 5.97/5.98 tff(18336,plain,
% 5.97/5.98 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n6, n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18335, 18305])).
% 5.97/5.98 tff(18337,plain,
% 5.97/5.98 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18336, 674])).
% 5.97/5.98 tff(18338,plain,
% 5.97/5.98 (succ(X3!55) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18311])).
% 5.97/5.98 tff(18339,plain,
% 5.97/5.98 (succ(X3!55) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18338, 30])).
% 5.97/5.98 tff(18340,plain,
% 5.97/5.98 (succ(succ(X3!55)) = succ(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18339])).
% 5.97/5.98 tff(18341,plain,
% 5.97/5.98 (succ(succ(X3!55)) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18340, 39])).
% 5.97/5.98 tff(18342,plain,
% 5.97/5.98 (succ(succ(succ(X3!55))) = succ(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18341])).
% 5.97/5.98 tff(18343,plain,
% 5.97/5.98 (succ(succ(succ(X3!55))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18342, 53])).
% 5.97/5.98 tff(18344,plain,
% 5.97/5.98 (succ(succ(succ(succ(X3!55)))) = succ(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18343])).
% 5.97/5.98 tff(18345,plain,
% 5.97/5.98 (succ(succ(succ(succ(X3!55)))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18344, 45])).
% 5.97/5.98 tff(18346,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X3!55))))) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18345])).
% 5.97/5.98 tff(18347,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X3!55))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18346, 28])).
% 5.97/5.98 tff(18348,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18347])).
% 5.97/5.98 tff(18349,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18348, 42])).
% 5.97/5.98 tff(18350,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18349])).
% 5.97/5.98 tff(18351,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18350, 58])).
% 5.97/5.98 tff(18352,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18351])).
% 5.97/5.98 tff(18353,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18352, 36])).
% 5.97/5.98 tff(18354,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18353])).
% 5.97/5.98 tff(18355,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18354, 48])).
% 5.97/5.98 tff(18356,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18355])).
% 5.97/5.98 tff(18357,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18356, 14])).
% 5.97/5.98 tff(18358,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18357])).
% 5.97/5.98 tff(18359,plain,
% 5.97/5.98 (NSX3!25 = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[535, 18358, 33])).
% 5.97/5.98 tff(18360,plain,
% 5.97/5.98 (pred(NSX3!25) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18359])).
% 5.97/5.98 tff(18361,plain,
% 5.97/5.98 (pred(NSX3!25) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18360, 16])).
% 5.97/5.98 tff(18362,plain,
% 5.97/5.98 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n4, n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18361, 18337])).
% 5.97/5.98 tff(18363,plain,
% 5.97/5.98 (Y4!52 = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[540, 18362, 673])).
% 5.97/5.98 tff(18364,plain,
% 5.97/5.98 (pred(Y4!52) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18363])).
% 5.97/5.98 tff(18365,plain,
% 5.97/5.98 (pred(Y4!52) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18364, 20])).
% 5.97/5.98 tff(18366,plain,
% 5.97/5.98 (pred(pred(Y4!52)) = pred(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18365])).
% 5.97/5.98 tff(18367,plain,
% 5.97/5.98 (pred(pred(Y4!52)) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18366, 19])).
% 5.97/5.98 tff(18368,plain,
% 5.97/5.98 (pred(pred(pred(Y4!52))) = pred(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18367])).
% 5.97/5.98 tff(18369,plain,
% 5.97/5.98 (pred(pred(pred(Y4!52))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18368, 18])).
% 5.97/5.98 tff(18370,plain,
% 5.97/5.98 (pred(pred(pred(pred(Y4!52)))) = pred(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18369])).
% 5.97/5.98 tff(18371,plain,
% 5.97/5.98 (pred(pred(pred(pred(Y4!52)))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18370, 17])).
% 5.97/5.98 tff(18372,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18371])).
% 5.97/5.98 tff(18373,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(Y4!52))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18372, 16])).
% 5.97/5.98 tff(18374,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18373])).
% 5.97/5.98 tff(18375,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18374, 15])).
% 5.97/5.98 tff(18376,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18375])).
% 5.97/5.98 tff(18377,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18376, 25])).
% 5.97/5.98 tff(18378,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18377])).
% 5.97/5.98 tff(18379,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18378, 24])).
% 5.97/5.98 tff(18380,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18379])).
% 5.97/5.98 tff(18381,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18380, 23])).
% 5.97/5.98 tff(18382,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18381])).
% 5.97/5.98 tff(18383,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18382, 22])).
% 5.97/5.98 tff(18384,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18383])).
% 5.97/5.98 tff(18385,plain,
% 5.97/5.98 (NPY4!22 = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[578, 18384, 21])).
% 5.97/5.98 tff(18386,plain,
% 5.97/5.98 (succ(NPY4!22) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18385])).
% 5.97/5.98 tff(18387,plain,
% 5.97/5.98 (succ(NPY4!22) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18386, 28])).
% 5.97/5.98 tff(18388,plain,
% 5.97/5.98 (succ(Y4!52) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18363])).
% 5.97/5.98 tff(18389,plain,
% 5.97/5.98 (succ(Y4!52) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18388, 28])).
% 5.97/5.98 tff(18390,plain,
% 5.97/5.98 (succ(succ(Y4!52)) = succ(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18389])).
% 5.97/5.98 tff(18391,plain,
% 5.97/5.98 (succ(succ(Y4!52)) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18390, 42])).
% 5.97/5.98 tff(18392,plain,
% 5.97/5.98 (succ(succ(succ(Y4!52))) = succ(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18391])).
% 5.97/5.98 tff(18393,plain,
% 5.97/5.98 (succ(succ(succ(Y4!52))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18392, 58])).
% 5.97/5.98 tff(18394,plain,
% 5.97/5.98 (succ(succ(succ(succ(Y4!52)))) = succ(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18393])).
% 5.97/5.98 tff(18395,plain,
% 5.97/5.98 (succ(succ(succ(succ(Y4!52)))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18394, 36])).
% 5.97/5.98 tff(18396,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18395])).
% 5.97/5.98 tff(18397,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(Y4!52))))) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18396, 48])).
% 5.97/5.98 tff(18398,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18397])).
% 5.97/5.98 tff(18399,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18398, 14])).
% 5.97/5.98 tff(18400,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18399])).
% 5.97/5.98 tff(18401,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18400, 33])).
% 5.97/5.98 tff(18402,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18401])).
% 5.97/5.98 tff(18403,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18402, 30])).
% 5.97/5.98 tff(18404,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18403])).
% 5.97/5.98 tff(18405,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18404, 39])).
% 5.97/5.98 tff(18406,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18405])).
% 5.97/5.98 tff(18407,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18406, 53])).
% 5.97/5.98 tff(18408,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18407])).
% 5.97/5.98 tff(18409,plain,
% 5.97/5.98 (NSY4!20 = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[601, 18408, 45])).
% 5.97/5.98 tff(18410,plain,
% 5.97/5.98 (pred(NSY4!20) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18409])).
% 5.97/5.98 tff(18411,plain,
% 5.97/5.98 (pred(NSY4!20) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18410, 20])).
% 5.97/5.98 tff(18412,plain,
% 5.97/5.98 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n8, n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18411, 18387])).
% 5.97/5.98 tff(18413,plain,
% 5.97/5.98 (sum(pred(NSY4!20), succ(NPY4!22)) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18412, 27])).
% 5.97/5.98 tff(18414,plain,
% 5.97/5.98 (sum(pred(Y3!54), succ(X3!55)) = sum(n4, n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18257, 18339])).
% 5.97/5.98 tff(18415,plain,
% 5.97/5.98 (sum(pred(Y3!54), succ(X3!55)) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18414, 12])).
% 5.97/5.98 tff(18416,plain,
% 5.97/5.98 (sum(pred(X3!55), succ(Y3!54)) = sum(n4, n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18313, 18281])).
% 5.97/5.98 tff(18417,plain,
% 5.97/5.98 (sum(pred(X3!55), succ(Y3!54)) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18416, 12])).
% 5.97/5.98 tff(18418,plain,
% 5.97/5.98 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n10, n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18417, 18415])).
% 5.97/5.98 tff(18419,plain,
% 5.97/5.98 (X4!53 = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[438, 18418, 29])).
% 5.97/5.98 tff(18420,plain,
% 5.97/5.98 (pred(X4!53) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18419])).
% 5.97/5.98 tff(18421,plain,
% 5.97/5.98 (pred(X4!53) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18420, 20])).
% 5.97/5.98 tff(18422,plain,
% 5.97/5.98 (pred(pred(X4!53)) = pred(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18421])).
% 5.97/5.98 tff(18423,plain,
% 5.97/5.98 (pred(pred(X4!53)) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18422, 19])).
% 5.97/5.98 tff(18424,plain,
% 5.97/5.98 (pred(pred(pred(X4!53))) = pred(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18423])).
% 5.97/5.98 tff(18425,plain,
% 5.97/5.98 (pred(pred(pred(X4!53))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18424, 18])).
% 5.97/5.98 tff(18426,plain,
% 5.97/5.98 (pred(pred(pred(pred(X4!53)))) = pred(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18425])).
% 5.97/5.98 tff(18427,plain,
% 5.97/5.98 (pred(pred(pred(pred(X4!53)))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18426, 17])).
% 5.97/5.98 tff(18428,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(X4!53))))) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18427])).
% 5.97/5.98 tff(18429,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(X4!53))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18428, 16])).
% 5.97/5.98 tff(18430,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18429])).
% 5.97/5.98 tff(18431,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18430, 15])).
% 5.97/5.98 tff(18432,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18431])).
% 5.97/5.98 tff(18433,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18432, 25])).
% 5.97/5.98 tff(18434,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18433])).
% 5.97/5.98 tff(18435,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18434, 24])).
% 5.97/5.98 tff(18436,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18435])).
% 5.97/5.98 tff(18437,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18436, 23])).
% 5.97/5.98 tff(18438,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18437])).
% 5.97/5.98 tff(18439,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18438, 22])).
% 5.97/5.98 tff(18440,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18439])).
% 5.97/5.98 tff(18441,plain,
% 5.97/5.98 (NPX4!23 = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[626, 18440, 21])).
% 5.97/5.98 tff(18442,plain,
% 5.97/5.98 (succ(NPX4!23) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18441])).
% 5.97/5.98 tff(18443,plain,
% 5.97/5.98 (succ(NPX4!23) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18442, 28])).
% 5.97/5.98 tff(18444,plain,
% 5.97/5.98 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n10, n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18443, 18413])).
% 5.97/5.98 tff(18445,plain,
% 5.97/5.98 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18444, 69])).
% 5.97/5.98 tff(18446,plain,
% 5.97/5.98 (succ(X4!53) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18419])).
% 5.97/5.98 tff(18447,plain,
% 5.97/5.98 (succ(X4!53) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18446, 28])).
% 5.97/5.98 tff(18448,plain,
% 5.97/5.98 (succ(succ(X4!53)) = succ(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18447])).
% 5.97/5.98 tff(18449,plain,
% 5.97/5.98 (succ(succ(X4!53)) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18448, 42])).
% 5.97/5.98 tff(18450,plain,
% 5.97/5.98 (succ(succ(succ(X4!53))) = succ(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18449])).
% 5.97/5.98 tff(18451,plain,
% 5.97/5.98 (succ(succ(succ(X4!53))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18450, 58])).
% 5.97/5.98 tff(18452,plain,
% 5.97/5.98 (succ(succ(succ(succ(X4!53)))) = succ(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18451])).
% 5.97/5.98 tff(18453,plain,
% 5.97/5.98 (succ(succ(succ(succ(X4!53)))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18452, 36])).
% 5.97/5.98 tff(18454,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X4!53))))) = succ(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18453])).
% 5.97/5.98 tff(18455,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X4!53))))) = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[18454, 48])).
% 5.97/5.98 tff(18456,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18455])).
% 5.97/5.98 tff(18457,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18456, 14])).
% 5.97/5.98 tff(18458,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18457])).
% 5.97/5.98 tff(18459,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18458, 33])).
% 5.97/5.98 tff(18460,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18459])).
% 5.97/5.98 tff(18461,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18460, 30])).
% 5.97/5.98 tff(18462,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18461])).
% 5.97/5.98 tff(18463,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18462, 39])).
% 5.97/5.98 tff(18464,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18463])).
% 5.97/5.98 tff(18465,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18464, 53])).
% 5.97/5.98 tff(18466,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18465])).
% 5.97/5.98 tff(18467,plain,
% 5.97/5.98 (NSX4!21 = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[651, 18466, 45])).
% 5.97/5.98 tff(18468,plain,
% 5.97/5.98 (pred(NSX4!21) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18467])).
% 5.97/5.98 tff(18469,plain,
% 5.97/5.98 (pred(NSX4!21) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18468, 20])).
% 5.97/5.98 tff(18470,plain,
% 5.97/5.98 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n8, n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18469, 18445])).
% 5.97/5.98 tff(18471,plain,
% 5.97/5.98 (Y5!50 = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[656, 18470, 98])).
% 5.97/5.98 tff(18472,plain,
% 5.97/5.98 (pred(Y5!50) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18471])).
% 5.97/5.98 tff(18473,plain,
% 5.97/5.98 (pred(Y5!50) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18472, 25])).
% 5.97/5.98 tff(18474,plain,
% 5.97/5.98 (pred(pred(Y5!50)) = pred(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18473])).
% 5.97/5.98 tff(18475,plain,
% 5.97/5.98 (pred(pred(Y5!50)) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18474, 24])).
% 5.97/5.98 tff(18476,plain,
% 5.97/5.98 (pred(pred(pred(Y5!50))) = pred(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18475])).
% 5.97/5.98 tff(18477,plain,
% 5.97/5.98 (pred(pred(pred(Y5!50))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18476, 23])).
% 5.97/5.98 tff(18478,plain,
% 5.97/5.98 (pred(pred(pred(pred(Y5!50)))) = pred(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18477])).
% 5.97/5.98 tff(18479,plain,
% 5.97/5.98 (pred(pred(pred(pred(Y5!50)))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18478, 22])).
% 5.97/5.98 tff(18480,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18479])).
% 5.97/5.98 tff(18481,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(Y5!50))))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18480, 21])).
% 5.97/5.98 tff(18482,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18481])).
% 5.97/5.98 tff(18483,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18482, 20])).
% 5.97/5.98 tff(18484,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18483])).
% 5.97/5.98 tff(18485,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18484, 19])).
% 5.97/5.98 tff(18486,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18485])).
% 5.97/5.98 tff(18487,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18486, 18])).
% 5.97/5.98 tff(18488,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18487])).
% 5.97/5.98 tff(18489,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18488, 17])).
% 5.97/5.98 tff(18490,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18489])).
% 5.97/5.98 tff(18491,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18490, 16])).
% 5.97/5.98 tff(18492,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18491])).
% 5.97/5.98 tff(18493,plain,
% 5.97/5.98 (NPY5!18 = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[694, 18492, 15])).
% 5.97/5.98 tff(18494,plain,
% 5.97/5.98 (succ(NPY5!18) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18493])).
% 5.97/5.98 tff(18495,plain,
% 5.97/5.98 (succ(NPY5!18) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18494, 14])).
% 5.97/5.98 tff(18496,plain,
% 5.97/5.98 (succ(Y5!50) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18471])).
% 5.97/5.98 tff(18497,plain,
% 5.97/5.98 (succ(Y5!50) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18496, 14])).
% 5.97/5.98 tff(18498,plain,
% 5.97/5.98 (succ(succ(Y5!50)) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18497])).
% 5.97/5.98 tff(18499,plain,
% 5.97/5.98 (succ(succ(Y5!50)) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18498, 33])).
% 5.97/5.98 tff(18500,plain,
% 5.97/5.98 (succ(succ(succ(Y5!50))) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18499])).
% 5.97/5.98 tff(18501,plain,
% 5.97/5.98 (succ(succ(succ(Y5!50))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18500, 30])).
% 5.97/5.98 tff(18502,plain,
% 5.97/5.98 (succ(succ(succ(succ(Y5!50)))) = succ(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18501])).
% 5.97/5.98 tff(18503,plain,
% 5.97/5.98 (succ(succ(succ(succ(Y5!50)))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18502, 39])).
% 5.97/5.98 tff(18504,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18503])).
% 5.97/5.98 tff(18505,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(Y5!50))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18504, 53])).
% 5.97/5.98 tff(18506,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18505])).
% 5.97/5.98 tff(18507,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18506, 45])).
% 5.97/5.98 tff(18508,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18507])).
% 5.97/5.98 tff(18509,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18508, 28])).
% 5.97/5.98 tff(18510,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18509])).
% 5.97/5.98 tff(18511,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18510, 42])).
% 5.97/5.98 tff(18512,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18511])).
% 5.97/5.98 tff(18513,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18512, 58])).
% 5.97/5.98 tff(18514,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18513])).
% 5.97/5.98 tff(18515,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18514, 36])).
% 5.97/5.98 tff(18516,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18515])).
% 5.97/5.98 tff(18517,plain,
% 5.97/5.98 (NSY5!16 = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[717, 18516, 48])).
% 5.97/5.98 tff(18518,plain,
% 5.97/5.98 (pred(NSY5!16) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18517])).
% 5.97/5.98 tff(18519,plain,
% 5.97/5.98 (pred(NSY5!16) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18518, 25])).
% 5.97/5.98 tff(18520,plain,
% 5.97/5.98 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n2, n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18519, 18495])).
% 5.97/5.98 tff(18521,plain,
% 5.97/5.98 (sum(pred(NSY5!16), succ(NPY5!18)) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18520, 13])).
% 5.97/5.98 tff(18522,plain,
% 5.97/5.98 (sum(pred(Y4!52), succ(X4!53)) = sum(n8, n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18365, 18447])).
% 5.97/5.98 tff(18523,plain,
% 5.97/5.98 (sum(pred(Y4!52), succ(X4!53)) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18522, 27])).
% 5.97/5.98 tff(18524,plain,
% 5.97/5.98 (sum(pred(X4!53), succ(Y4!52)) = sum(n8, n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18421, 18389])).
% 5.97/5.98 tff(18525,plain,
% 5.97/5.98 (sum(pred(X4!53), succ(Y4!52)) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18524, 27])).
% 5.97/5.98 tff(18526,plain,
% 5.97/5.98 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n7, n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18525, 18523])).
% 5.97/5.98 tff(18527,plain,
% 5.97/5.98 (X5!51 = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[553, 18526, 26])).
% 5.97/5.98 tff(18528,plain,
% 5.97/5.98 (pred(X5!51) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18527])).
% 5.97/5.98 tff(18529,plain,
% 5.97/5.98 (pred(X5!51) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18528, 25])).
% 5.97/5.98 tff(18530,plain,
% 5.97/5.98 (pred(pred(X5!51)) = pred(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18529])).
% 5.97/5.98 tff(18531,plain,
% 5.97/5.98 (pred(pred(X5!51)) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18530, 24])).
% 5.97/5.98 tff(18532,plain,
% 5.97/5.98 (pred(pred(pred(X5!51))) = pred(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18531])).
% 5.97/5.98 tff(18533,plain,
% 5.97/5.98 (pred(pred(pred(X5!51))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18532, 23])).
% 5.97/5.98 tff(18534,plain,
% 5.97/5.98 (pred(pred(pred(pred(X5!51)))) = pred(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18533])).
% 5.97/5.98 tff(18535,plain,
% 5.97/5.98 (pred(pred(pred(pred(X5!51)))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18534, 22])).
% 5.97/5.98 tff(18536,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(X5!51))))) = pred(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18535])).
% 5.97/5.98 tff(18537,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(X5!51))))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18536, 21])).
% 5.97/5.98 tff(18538,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18537])).
% 5.97/5.98 tff(18539,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18538, 20])).
% 5.97/5.98 tff(18540,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18539])).
% 5.97/5.98 tff(18541,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18540, 19])).
% 5.97/5.98 tff(18542,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18541])).
% 5.97/5.98 tff(18543,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18542, 18])).
% 5.97/5.98 tff(18544,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18543])).
% 5.97/5.98 tff(18545,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18544, 17])).
% 5.97/5.98 tff(18546,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18545])).
% 5.97/5.98 tff(18547,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18546, 16])).
% 5.97/5.98 tff(18548,plain,
% 5.97/5.98 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18547])).
% 5.97/5.98 tff(18549,plain,
% 5.97/5.98 (NPX5!19 = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[742, 18548, 15])).
% 5.97/5.98 tff(18550,plain,
% 5.97/5.98 (succ(NPX5!19) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18549])).
% 5.97/5.98 tff(18551,plain,
% 5.97/5.98 (succ(NPX5!19) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18550, 14])).
% 5.97/5.98 tff(18552,plain,
% 5.97/5.98 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n4, n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18551, 18521])).
% 5.97/5.98 tff(18553,plain,
% 5.97/5.98 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18552, 12])).
% 5.97/5.98 tff(18554,plain,
% 5.97/5.98 (succ(X5!51) = succ(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18527])).
% 5.97/5.98 tff(18555,plain,
% 5.97/5.98 (succ(X5!51) = n4),
% 5.97/5.98 inference(transitivity,[status(thm)],[18554, 14])).
% 5.97/5.98 tff(18556,plain,
% 5.97/5.98 (succ(succ(X5!51)) = succ(n4)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18555])).
% 5.97/5.98 tff(18557,plain,
% 5.97/5.98 (succ(succ(X5!51)) = n5),
% 5.97/5.98 inference(transitivity,[status(thm)],[18556, 33])).
% 5.97/5.98 tff(18558,plain,
% 5.97/5.98 (succ(succ(succ(X5!51))) = succ(n5)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18557])).
% 5.97/5.98 tff(18559,plain,
% 5.97/5.98 (succ(succ(succ(X5!51))) = n6),
% 5.97/5.98 inference(transitivity,[status(thm)],[18558, 30])).
% 5.97/5.98 tff(18560,plain,
% 5.97/5.98 (succ(succ(succ(succ(X5!51)))) = succ(n6)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18559])).
% 5.97/5.98 tff(18561,plain,
% 5.97/5.98 (succ(succ(succ(succ(X5!51)))) = n7),
% 5.97/5.98 inference(transitivity,[status(thm)],[18560, 39])).
% 5.97/5.98 tff(18562,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X5!51))))) = succ(n7)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18561])).
% 5.97/5.98 tff(18563,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(X5!51))))) = n8),
% 5.97/5.98 inference(transitivity,[status(thm)],[18562, 53])).
% 5.97/5.98 tff(18564,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n8)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18563])).
% 5.97/5.98 tff(18565,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18564, 45])).
% 5.97/5.98 tff(18566,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n9)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18565])).
% 5.97/5.98 tff(18567,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18566, 28])).
% 5.97/5.98 tff(18568,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18567])).
% 5.97/5.98 tff(18569,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18568, 42])).
% 5.97/5.98 tff(18570,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18569])).
% 5.97/5.98 tff(18571,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[18570, 58])).
% 5.97/5.98 tff(18572,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18571])).
% 5.97/5.98 tff(18573,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18572, 36])).
% 5.97/5.98 tff(18574,plain,
% 5.97/5.98 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n2)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18573])).
% 5.97/5.98 tff(18575,plain,
% 5.97/5.98 (NSX5!17 = n3),
% 5.97/5.98 inference(transitivity,[status(thm)],[767, 18574, 48])).
% 5.97/5.98 tff(18576,plain,
% 5.97/5.98 (pred(NSX5!17) = pred(n3)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18575])).
% 5.97/5.98 tff(18577,plain,
% 5.97/5.98 (pred(NSX5!17) = n2),
% 5.97/5.98 inference(transitivity,[status(thm)],[18576, 25])).
% 5.97/5.98 tff(18578,plain,
% 5.97/5.98 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n2, n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18577, 18553])).
% 5.97/5.98 tff(18579,plain,
% 5.97/5.98 (Y6!48 = n1),
% 5.97/5.98 inference(transitivity,[status(thm)],[772, 18578, 327])).
% 5.97/5.98 tff(18580,plain,
% 5.97/5.98 (pred(Y6!48) = pred(n1)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18579])).
% 5.97/5.98 tff(18581,plain,
% 5.97/5.98 (pred(Y6!48) = n0),
% 5.97/5.98 inference(transitivity,[status(thm)],[18580, 23])).
% 5.97/5.98 tff(18582,plain,
% 5.97/5.98 (pred(pred(Y6!48)) = pred(n0)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18581])).
% 5.97/5.98 tff(18583,plain,
% 5.97/5.98 (pred(pred(Y6!48)) = n10),
% 5.97/5.98 inference(transitivity,[status(thm)],[18582, 22])).
% 5.97/5.98 tff(18584,plain,
% 5.97/5.98 (pred(pred(pred(Y6!48))) = pred(n10)),
% 5.97/5.98 inference(monotonicity,[status(thm)],[18583])).
% 5.97/5.98 tff(18585,plain,
% 5.97/5.98 (pred(pred(pred(Y6!48))) = n9),
% 5.97/5.98 inference(transitivity,[status(thm)],[18584, 21])).
% 5.97/5.98 tff(18586,plain,
% 5.97/5.99 (pred(pred(pred(pred(Y6!48)))) = pred(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18585])).
% 5.97/5.99 tff(18587,plain,
% 5.97/5.99 (pred(pred(pred(pred(Y6!48)))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18586, 20])).
% 5.97/5.99 tff(18588,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18587])).
% 5.97/5.99 tff(18589,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(Y6!48))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18588, 19])).
% 5.97/5.99 tff(18590,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18589])).
% 5.97/5.99 tff(18591,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18590, 18])).
% 5.97/5.99 tff(18592,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18591])).
% 5.97/5.99 tff(18593,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18592, 17])).
% 5.97/5.99 tff(18594,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18593])).
% 5.97/5.99 tff(18595,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18594, 16])).
% 5.97/5.99 tff(18596,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18595])).
% 5.97/5.99 tff(18597,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18596, 15])).
% 5.97/5.99 tff(18598,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18597])).
% 5.97/5.99 tff(18599,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18598, 25])).
% 5.97/5.99 tff(18600,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18599])).
% 5.97/5.99 tff(18601,plain,
% 5.97/5.99 (NPY6!14 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[1465, 18600, 24])).
% 5.97/5.99 tff(18602,plain,
% 5.97/5.99 (succ(NPY6!14) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18601])).
% 5.97/5.99 tff(18603,plain,
% 5.97/5.99 (succ(NPY6!14) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18602, 36])).
% 5.97/5.99 tff(18604,plain,
% 5.97/5.99 (succ(Y6!48) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18579])).
% 5.97/5.99 tff(18605,plain,
% 5.97/5.99 (succ(Y6!48) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18604, 36])).
% 5.97/5.99 tff(18606,plain,
% 5.97/5.99 (succ(succ(Y6!48)) = succ(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18605])).
% 5.97/5.99 tff(18607,plain,
% 5.97/5.99 (succ(succ(Y6!48)) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18606, 48])).
% 5.97/5.99 tff(18608,plain,
% 5.97/5.99 (succ(succ(succ(Y6!48))) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18607])).
% 5.97/5.99 tff(18609,plain,
% 5.97/5.99 (succ(succ(succ(Y6!48))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18608, 14])).
% 5.97/5.99 tff(18610,plain,
% 5.97/5.99 (succ(succ(succ(succ(Y6!48)))) = succ(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18609])).
% 5.97/5.99 tff(18611,plain,
% 5.97/5.99 (succ(succ(succ(succ(Y6!48)))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18610, 33])).
% 5.97/5.99 tff(18612,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18611])).
% 5.97/5.99 tff(18613,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(Y6!48))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18612, 30])).
% 5.97/5.99 tff(18614,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18613])).
% 5.97/5.99 tff(18615,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18614, 39])).
% 5.97/5.99 tff(18616,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18615])).
% 5.97/5.99 tff(18617,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18616, 53])).
% 5.97/5.99 tff(18618,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18617])).
% 5.97/5.99 tff(18619,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18618, 45])).
% 5.97/5.99 tff(18620,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18619])).
% 5.97/5.99 tff(18621,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18620, 28])).
% 5.97/5.99 tff(18622,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18621])).
% 5.97/5.99 tff(18623,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18622, 42])).
% 5.97/5.99 tff(18624,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18623])).
% 5.97/5.99 tff(18625,plain,
% 5.97/5.99 (NSY6!12 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[1490, 18624, 58])).
% 5.97/5.99 tff(18626,plain,
% 5.97/5.99 (pred(NSY6!12) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18625])).
% 5.97/5.99 tff(18627,plain,
% 5.97/5.99 (pred(NSY6!12) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18626, 23])).
% 5.97/5.99 tff(18628,plain,
% 5.97/5.99 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n0, n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18627, 18603])).
% 5.97/5.99 tff(18629,plain,
% 5.97/5.99 (sum(pred(NSY6!12), succ(NPY6!14)) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18628, 35])).
% 5.97/5.99 tff(18630,plain,
% 5.97/5.99 (sum(pred(Y5!50), succ(X5!51)) = sum(n2, n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18473, 18555])).
% 5.97/5.99 tff(18631,plain,
% 5.97/5.99 (sum(pred(Y5!50), succ(X5!51)) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18630, 13])).
% 5.97/5.99 tff(18632,plain,
% 5.97/5.99 (sum(pred(X5!51), succ(Y5!50)) = sum(n2, n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18529, 18497])).
% 5.97/5.99 tff(18633,plain,
% 5.97/5.99 (sum(pred(X5!51), succ(Y5!50)) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18632, 13])).
% 5.97/5.99 tff(18634,plain,
% 5.97/5.99 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n6, n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18633, 18631])).
% 5.97/5.99 tff(18635,plain,
% 5.97/5.99 (X6!49 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[669, 18634, 37])).
% 5.97/5.99 tff(18636,plain,
% 5.97/5.99 (pred(X6!49) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18635])).
% 5.97/5.99 tff(18637,plain,
% 5.97/5.99 (pred(X6!49) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18636, 23])).
% 5.97/5.99 tff(18638,plain,
% 5.97/5.99 (pred(pred(X6!49)) = pred(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18637])).
% 5.97/5.99 tff(18639,plain,
% 5.97/5.99 (pred(pred(X6!49)) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18638, 22])).
% 5.97/5.99 tff(18640,plain,
% 5.97/5.99 (pred(pred(pred(X6!49))) = pred(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18639])).
% 5.97/5.99 tff(18641,plain,
% 5.97/5.99 (pred(pred(pred(X6!49))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18640, 21])).
% 5.97/5.99 tff(18642,plain,
% 5.97/5.99 (pred(pred(pred(pred(X6!49)))) = pred(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18641])).
% 5.97/5.99 tff(18643,plain,
% 5.97/5.99 (pred(pred(pred(pred(X6!49)))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18642, 20])).
% 5.97/5.99 tff(18644,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(X6!49))))) = pred(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18643])).
% 5.97/5.99 tff(18645,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(X6!49))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18644, 19])).
% 5.97/5.99 tff(18646,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18645])).
% 5.97/5.99 tff(18647,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18646, 18])).
% 5.97/5.99 tff(18648,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18647])).
% 5.97/5.99 tff(18649,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18648, 17])).
% 5.97/5.99 tff(18650,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18649])).
% 5.97/5.99 tff(18651,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18650, 16])).
% 5.97/5.99 tff(18652,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18651])).
% 5.97/5.99 tff(18653,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18652, 15])).
% 5.97/5.99 tff(18654,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18653])).
% 5.97/5.99 tff(18655,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18654, 25])).
% 5.97/5.99 tff(18656,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18655])).
% 5.97/5.99 tff(18657,plain,
% 5.97/5.99 (NPX6!15 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[1523, 18656, 24])).
% 5.97/5.99 tff(18658,plain,
% 5.97/5.99 (succ(NPX6!15) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18657])).
% 5.97/5.99 tff(18659,plain,
% 5.97/5.99 (succ(NPX6!15) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18658, 36])).
% 5.97/5.99 tff(18660,plain,
% 5.97/5.99 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n2, n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18659, 18629])).
% 5.97/5.99 tff(18661,plain,
% 5.97/5.99 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18660, 34])).
% 5.97/5.99 tff(18662,plain,
% 5.97/5.99 (succ(X6!49) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18635])).
% 5.97/5.99 tff(18663,plain,
% 5.97/5.99 (succ(X6!49) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18662, 36])).
% 5.97/5.99 tff(18664,plain,
% 5.97/5.99 (succ(succ(X6!49)) = succ(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18663])).
% 5.97/5.99 tff(18665,plain,
% 5.97/5.99 (succ(succ(X6!49)) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18664, 48])).
% 5.97/5.99 tff(18666,plain,
% 5.97/5.99 (succ(succ(succ(X6!49))) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18665])).
% 5.97/5.99 tff(18667,plain,
% 5.97/5.99 (succ(succ(succ(X6!49))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18666, 14])).
% 5.97/5.99 tff(18668,plain,
% 5.97/5.99 (succ(succ(succ(succ(X6!49)))) = succ(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18667])).
% 5.97/5.99 tff(18669,plain,
% 5.97/5.99 (succ(succ(succ(succ(X6!49)))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18668, 33])).
% 5.97/5.99 tff(18670,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(X6!49))))) = succ(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18669])).
% 5.97/5.99 tff(18671,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(X6!49))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18670, 30])).
% 5.97/5.99 tff(18672,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18671])).
% 5.97/5.99 tff(18673,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18672, 39])).
% 5.97/5.99 tff(18674,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18673])).
% 5.97/5.99 tff(18675,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18674, 53])).
% 5.97/5.99 tff(18676,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18675])).
% 5.97/5.99 tff(18677,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18676, 45])).
% 5.97/5.99 tff(18678,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18677])).
% 5.97/5.99 tff(18679,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18678, 28])).
% 5.97/5.99 tff(18680,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18679])).
% 5.97/5.99 tff(18681,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18680, 42])).
% 5.97/5.99 tff(18682,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18681])).
% 5.97/5.99 tff(18683,plain,
% 5.97/5.99 (NSX6!13 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[1550, 18682, 58])).
% 5.97/5.99 tff(18684,plain,
% 5.97/5.99 (pred(NSX6!13) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18683])).
% 5.97/5.99 tff(18685,plain,
% 5.97/5.99 (pred(NSX6!13) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18684, 23])).
% 5.97/5.99 tff(18686,plain,
% 5.97/5.99 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n0, n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18685, 18661])).
% 5.97/5.99 tff(18687,plain,
% 5.97/5.99 (sum(n0, n4) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 5.97/5.99 inference(symmetry,[status(thm)],[18686])).
% 5.97/5.99 tff(18688,plain,
% 5.97/5.99 (n4 = sum(n0, n4)),
% 5.97/5.99 inference(symmetry,[status(thm)],[442])).
% 5.97/5.99 tff(18689,plain,
% 5.97/5.99 (sum(pred(Y6!48), succ(X6!49)) = sum(n0, n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18581, 18663])).
% 5.97/5.99 tff(18690,plain,
% 5.97/5.99 (sum(pred(Y6!48), succ(X6!49)) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18689, 35])).
% 5.97/5.99 tff(18691,plain,
% 5.97/5.99 (sum(pred(X6!49), succ(Y6!48)) = sum(n0, n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18637, 18605])).
% 5.97/5.99 tff(18692,plain,
% 5.97/5.99 (sum(pred(X6!49), succ(Y6!48)) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18691, 35])).
% 5.97/5.99 tff(18693,plain,
% 5.97/5.99 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n2, n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18692, 18690])).
% 5.97/5.99 tff(18694,plain,
% 5.97/5.99 (X7!47 = Y7!46),
% 5.97/5.99 inference(transitivity,[status(thm)],[785, 18693, 34, 18688, 18687, 794])).
% 5.97/5.99 tff(18695,plain,
% 5.97/5.99 ($false),
% 5.97/5.99 inference(unit_resolution,[status(thm)],[792, 18694])).
% 5.97/5.99 tff(18696,plain,((~(Y0!60 = n3)) | (X7!47 = Y7!46) | (~(X0!61 = n3))), inference(lemma,lemma(discharge,[]))).
% 5.97/5.99 tff(18697,plain,
% 5.97/5.99 (~(Y0!60 = n3)),
% 5.97/5.99 inference(unit_resolution,[status(thm)],[18696, 17987, 792])).
% 5.97/5.99 tff(18698,plain,
% 5.97/5.99 (sum(n2, n1) = n3),
% 5.97/5.99 inference(and_elim,[status(thm)],[9])).
% 5.97/5.99 tff(18699,plain,
% 5.97/5.99 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n4, n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18011, 847])).
% 5.97/5.99 tff(18700,plain,
% 5.97/5.99 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[18699, 8619])).
% 5.97/5.99 tff(18701,plain,
% 5.97/5.99 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n2, n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18037, 18700])).
% 5.97/5.99 tff(18702,plain,
% 5.97/5.99 (Y1!58 = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[196, 18701, 18698])).
% 5.97/5.99 tff(18703,plain,
% 5.97/5.99 (pred(Y1!58) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18702])).
% 5.97/5.99 tff(18704,plain,
% 5.97/5.99 (pred(Y1!58) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18703, 25])).
% 5.97/5.99 tff(18705,plain,
% 5.97/5.99 (pred(pred(Y1!58)) = pred(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18704])).
% 5.97/5.99 tff(18706,plain,
% 5.97/5.99 (pred(pred(Y1!58)) = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[18705, 24])).
% 5.97/5.99 tff(18707,plain,
% 5.97/5.99 (pred(pred(pred(Y1!58))) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18706])).
% 5.97/5.99 tff(18708,plain,
% 5.97/5.99 (pred(pred(pred(Y1!58))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18707, 23])).
% 5.97/5.99 tff(18709,plain,
% 5.97/5.99 (pred(pred(pred(pred(Y1!58)))) = pred(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18708])).
% 5.97/5.99 tff(18710,plain,
% 5.97/5.99 (pred(pred(pred(pred(Y1!58)))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18709, 22])).
% 5.97/5.99 tff(18711,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18710])).
% 5.97/5.99 tff(18712,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(Y1!58))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18711, 21])).
% 5.97/5.99 tff(18713,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18712])).
% 5.97/5.99 tff(18714,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18713, 20])).
% 5.97/5.99 tff(18715,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18714])).
% 5.97/5.99 tff(18716,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18715, 19])).
% 5.97/5.99 tff(18717,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18716])).
% 5.97/5.99 tff(18718,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18717, 18])).
% 5.97/5.99 tff(18719,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18718])).
% 5.97/5.99 tff(18720,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18719, 17])).
% 5.97/5.99 tff(18721,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18720])).
% 5.97/5.99 tff(18722,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18721, 16])).
% 5.97/5.99 tff(18723,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18722])).
% 5.97/5.99 tff(18724,plain,
% 5.97/5.99 (NPY1!34 = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[232, 18723, 15])).
% 5.97/5.99 tff(18725,plain,
% 5.97/5.99 (succ(NPY1!34) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18724])).
% 5.97/5.99 tff(18726,plain,
% 5.97/5.99 (succ(NPY1!34) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18725, 14])).
% 5.97/5.99 tff(18727,plain,
% 5.97/5.99 (succ(Y1!58) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18702])).
% 5.97/5.99 tff(18728,plain,
% 5.97/5.99 (succ(Y1!58) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18727, 14])).
% 5.97/5.99 tff(18729,plain,
% 5.97/5.99 (succ(succ(Y1!58)) = succ(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18728])).
% 5.97/5.99 tff(18730,plain,
% 5.97/5.99 (succ(succ(Y1!58)) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18729, 33])).
% 5.97/5.99 tff(18731,plain,
% 5.97/5.99 (succ(succ(succ(Y1!58))) = succ(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18730])).
% 5.97/5.99 tff(18732,plain,
% 5.97/5.99 (succ(succ(succ(Y1!58))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18731, 30])).
% 5.97/5.99 tff(18733,plain,
% 5.97/5.99 (succ(succ(succ(succ(Y1!58)))) = succ(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18732])).
% 5.97/5.99 tff(18734,plain,
% 5.97/5.99 (succ(succ(succ(succ(Y1!58)))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18733, 39])).
% 5.97/5.99 tff(18735,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18734])).
% 5.97/5.99 tff(18736,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(Y1!58))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18735, 53])).
% 5.97/5.99 tff(18737,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18736])).
% 5.97/5.99 tff(18738,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18737, 45])).
% 5.97/5.99 tff(18739,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18738])).
% 5.97/5.99 tff(18740,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18739, 28])).
% 5.97/5.99 tff(18741,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18740])).
% 5.97/5.99 tff(18742,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18741, 42])).
% 5.97/5.99 tff(18743,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18742])).
% 5.97/5.99 tff(18744,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[18743, 58])).
% 5.97/5.99 tff(18745,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18744])).
% 5.97/5.99 tff(18746,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18745, 36])).
% 5.97/5.99 tff(18747,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18746])).
% 5.97/5.99 tff(18748,plain,
% 5.97/5.99 (NSY1!32 = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[255, 18747, 48])).
% 5.97/5.99 tff(18749,plain,
% 5.97/5.99 (pred(NSY1!32) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18748])).
% 5.97/5.99 tff(18750,plain,
% 5.97/5.99 (pred(NSY1!32) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18749, 25])).
% 5.97/5.99 tff(18751,plain,
% 5.97/5.99 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n2, n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18750, 18726])).
% 5.97/5.99 tff(18752,plain,
% 5.97/5.99 (sum(pred(NSY1!32), succ(NPY1!34)) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18751, 13])).
% 5.97/5.99 tff(18753,plain,
% 5.97/5.99 (sum(pred(Y0!60), succ(X0!61)) = sum(n3, n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[799, 18015])).
% 5.97/5.99 tff(18754,plain,
% 5.97/5.99 (sum(pred(Y0!60), succ(X0!61)) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18753, 786])).
% 5.97/5.99 tff(18755,plain,
% 5.97/5.99 (sum(n2, n5) = n7),
% 5.97/5.99 inference(and_elim,[status(thm)],[9])).
% 5.97/5.99 tff(18756,plain,
% 5.97/5.99 (sum(pred(X0!61), succ(Y0!60)) = sum(n2, n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[17989, 823])).
% 5.97/5.99 tff(18757,plain,
% 5.97/5.99 (sum(pred(X0!61), succ(Y0!60)) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18756, 18755])).
% 5.97/5.99 tff(18758,plain,
% 5.97/5.99 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n7, n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18757, 18754])).
% 5.97/5.99 tff(18759,plain,
% 5.97/5.99 (X1!59 = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[93, 18758, 26])).
% 5.97/5.99 tff(18760,plain,
% 5.97/5.99 (pred(X1!59) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18759])).
% 5.97/5.99 tff(18761,plain,
% 5.97/5.99 (pred(X1!59) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18760, 25])).
% 5.97/5.99 tff(18762,plain,
% 5.97/5.99 (pred(pred(X1!59)) = pred(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18761])).
% 5.97/5.99 tff(18763,plain,
% 5.97/5.99 (pred(pred(X1!59)) = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[18762, 24])).
% 5.97/5.99 tff(18764,plain,
% 5.97/5.99 (pred(pred(pred(X1!59))) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18763])).
% 5.97/5.99 tff(18765,plain,
% 5.97/5.99 (pred(pred(pred(X1!59))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18764, 23])).
% 5.97/5.99 tff(18766,plain,
% 5.97/5.99 (pred(pred(pred(pred(X1!59)))) = pred(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18765])).
% 5.97/5.99 tff(18767,plain,
% 5.97/5.99 (pred(pred(pred(pred(X1!59)))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18766, 22])).
% 5.97/5.99 tff(18768,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(X1!59))))) = pred(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18767])).
% 5.97/5.99 tff(18769,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(X1!59))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18768, 21])).
% 5.97/5.99 tff(18770,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18769])).
% 5.97/5.99 tff(18771,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18770, 20])).
% 5.97/5.99 tff(18772,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18771])).
% 5.97/5.99 tff(18773,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18772, 19])).
% 5.97/5.99 tff(18774,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18773])).
% 5.97/5.99 tff(18775,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18774, 18])).
% 5.97/5.99 tff(18776,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18775])).
% 5.97/5.99 tff(18777,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18776, 17])).
% 5.97/5.99 tff(18778,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18777])).
% 5.97/5.99 tff(18779,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18778, 16])).
% 5.97/5.99 tff(18780,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18779])).
% 5.97/5.99 tff(18781,plain,
% 5.97/5.99 (NPX1!35 = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[280, 18780, 15])).
% 5.97/5.99 tff(18782,plain,
% 5.97/5.99 (succ(NPX1!35) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18781])).
% 5.97/5.99 tff(18783,plain,
% 5.97/5.99 (succ(NPX1!35) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18782, 14])).
% 5.97/5.99 tff(18784,plain,
% 5.97/5.99 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n4, n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18783, 18752])).
% 5.97/5.99 tff(18785,plain,
% 5.97/5.99 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18784, 12])).
% 5.97/5.99 tff(18786,plain,
% 5.97/5.99 (succ(X1!59) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18759])).
% 5.97/5.99 tff(18787,plain,
% 5.97/5.99 (succ(X1!59) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18786, 14])).
% 5.97/5.99 tff(18788,plain,
% 5.97/5.99 (succ(succ(X1!59)) = succ(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18787])).
% 5.97/5.99 tff(18789,plain,
% 5.97/5.99 (succ(succ(X1!59)) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18788, 33])).
% 5.97/5.99 tff(18790,plain,
% 5.97/5.99 (succ(succ(succ(X1!59))) = succ(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18789])).
% 5.97/5.99 tff(18791,plain,
% 5.97/5.99 (succ(succ(succ(X1!59))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18790, 30])).
% 5.97/5.99 tff(18792,plain,
% 5.97/5.99 (succ(succ(succ(succ(X1!59)))) = succ(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18791])).
% 5.97/5.99 tff(18793,plain,
% 5.97/5.99 (succ(succ(succ(succ(X1!59)))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18792, 39])).
% 5.97/5.99 tff(18794,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(X1!59))))) = succ(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18793])).
% 5.97/5.99 tff(18795,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(X1!59))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18794, 53])).
% 5.97/5.99 tff(18796,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18795])).
% 5.97/5.99 tff(18797,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18796, 45])).
% 5.97/5.99 tff(18798,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18797])).
% 5.97/5.99 tff(18799,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18798, 28])).
% 5.97/5.99 tff(18800,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18799])).
% 5.97/5.99 tff(18801,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18800, 42])).
% 5.97/5.99 tff(18802,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18801])).
% 5.97/5.99 tff(18803,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[18802, 58])).
% 5.97/5.99 tff(18804,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18803])).
% 5.97/5.99 tff(18805,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18804, 36])).
% 5.97/5.99 tff(18806,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18805])).
% 5.97/5.99 tff(18807,plain,
% 5.97/5.99 (NSX1!33 = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[305, 18806, 48])).
% 5.97/5.99 tff(18808,plain,
% 5.97/5.99 (pred(NSX1!33) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18807])).
% 5.97/5.99 tff(18809,plain,
% 5.97/5.99 (pred(NSX1!33) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18808, 25])).
% 5.97/5.99 tff(18810,plain,
% 5.97/5.99 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n2, n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18809, 18785])).
% 5.97/5.99 tff(18811,plain,
% 5.97/5.99 (Y2!56 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[310, 18810, 327])).
% 5.97/5.99 tff(18812,plain,
% 5.97/5.99 (pred(Y2!56) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18811])).
% 5.97/5.99 tff(18813,plain,
% 5.97/5.99 (pred(Y2!56) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18812, 23])).
% 5.97/5.99 tff(18814,plain,
% 5.97/5.99 (pred(pred(Y2!56)) = pred(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18813])).
% 5.97/5.99 tff(18815,plain,
% 5.97/5.99 (pred(pred(Y2!56)) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18814, 22])).
% 5.97/5.99 tff(18816,plain,
% 5.97/5.99 (pred(pred(pred(Y2!56))) = pred(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18815])).
% 5.97/5.99 tff(18817,plain,
% 5.97/5.99 (pred(pred(pred(Y2!56))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18816, 21])).
% 5.97/5.99 tff(18818,plain,
% 5.97/5.99 (pred(pred(pred(pred(Y2!56)))) = pred(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18817])).
% 5.97/5.99 tff(18819,plain,
% 5.97/5.99 (pred(pred(pred(pred(Y2!56)))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18818, 20])).
% 5.97/5.99 tff(18820,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18819])).
% 5.97/5.99 tff(18821,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(Y2!56))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18820, 19])).
% 5.97/5.99 tff(18822,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18821])).
% 5.97/5.99 tff(18823,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18822, 18])).
% 5.97/5.99 tff(18824,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18823])).
% 5.97/5.99 tff(18825,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18824, 17])).
% 5.97/5.99 tff(18826,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18825])).
% 5.97/5.99 tff(18827,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18826, 16])).
% 5.97/5.99 tff(18828,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18827])).
% 5.97/5.99 tff(18829,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18828, 15])).
% 5.97/5.99 tff(18830,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18829])).
% 5.97/5.99 tff(18831,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18830, 25])).
% 5.97/5.99 tff(18832,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18831])).
% 5.97/5.99 tff(18833,plain,
% 5.97/5.99 (NPY2!30 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[347, 18832, 24])).
% 5.97/5.99 tff(18834,plain,
% 5.97/5.99 (succ(NPY2!30) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18833])).
% 5.97/5.99 tff(18835,plain,
% 5.97/5.99 (succ(NPY2!30) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18834, 36])).
% 5.97/5.99 tff(18836,plain,
% 5.97/5.99 (succ(Y2!56) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18811])).
% 5.97/5.99 tff(18837,plain,
% 5.97/5.99 (succ(Y2!56) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18836, 36])).
% 5.97/5.99 tff(18838,plain,
% 5.97/5.99 (succ(succ(Y2!56)) = succ(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18837])).
% 5.97/5.99 tff(18839,plain,
% 5.97/5.99 (succ(succ(Y2!56)) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18838, 48])).
% 5.97/5.99 tff(18840,plain,
% 5.97/5.99 (succ(succ(succ(Y2!56))) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18839])).
% 5.97/5.99 tff(18841,plain,
% 5.97/5.99 (succ(succ(succ(Y2!56))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18840, 14])).
% 5.97/5.99 tff(18842,plain,
% 5.97/5.99 (succ(succ(succ(succ(Y2!56)))) = succ(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18841])).
% 5.97/5.99 tff(18843,plain,
% 5.97/5.99 (succ(succ(succ(succ(Y2!56)))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18842, 33])).
% 5.97/5.99 tff(18844,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18843])).
% 5.97/5.99 tff(18845,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(Y2!56))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18844, 30])).
% 5.97/5.99 tff(18846,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18845])).
% 5.97/5.99 tff(18847,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18846, 39])).
% 5.97/5.99 tff(18848,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18847])).
% 5.97/5.99 tff(18849,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18848, 53])).
% 5.97/5.99 tff(18850,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18849])).
% 5.97/5.99 tff(18851,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18850, 45])).
% 5.97/5.99 tff(18852,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18851])).
% 5.97/5.99 tff(18853,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18852, 28])).
% 5.97/5.99 tff(18854,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18853])).
% 5.97/5.99 tff(18855,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18854, 42])).
% 5.97/5.99 tff(18856,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18855])).
% 5.97/5.99 tff(18857,plain,
% 5.97/5.99 (NSY2!28 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[370, 18856, 58])).
% 5.97/5.99 tff(18858,plain,
% 5.97/5.99 (pred(NSY2!28) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18857])).
% 5.97/5.99 tff(18859,plain,
% 5.97/5.99 (pred(NSY2!28) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18858, 23])).
% 5.97/5.99 tff(18860,plain,
% 5.97/5.99 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n0, n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18859, 18835])).
% 5.97/5.99 tff(18861,plain,
% 5.97/5.99 (sum(pred(NSY2!28), succ(NPY2!30)) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18860, 35])).
% 5.97/5.99 tff(18862,plain,
% 5.97/5.99 (sum(pred(Y1!58), succ(X1!59)) = sum(n2, n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18704, 18787])).
% 5.97/5.99 tff(18863,plain,
% 5.97/5.99 (sum(pred(Y1!58), succ(X1!59)) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18862, 13])).
% 5.97/5.99 tff(18864,plain,
% 5.97/5.99 (sum(pred(X1!59), succ(Y1!58)) = sum(n2, n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18761, 18728])).
% 5.97/5.99 tff(18865,plain,
% 5.97/5.99 (sum(pred(X1!59), succ(Y1!58)) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18864, 13])).
% 5.97/5.99 tff(18866,plain,
% 5.97/5.99 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n6, n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18865, 18863])).
% 5.97/5.99 tff(18867,plain,
% 5.97/5.99 (X2!57 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[209, 18866, 37])).
% 5.97/5.99 tff(18868,plain,
% 5.97/5.99 (pred(X2!57) = pred(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18867])).
% 5.97/5.99 tff(18869,plain,
% 5.97/5.99 (pred(X2!57) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18868, 23])).
% 5.97/5.99 tff(18870,plain,
% 5.97/5.99 (pred(pred(X2!57)) = pred(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18869])).
% 5.97/5.99 tff(18871,plain,
% 5.97/5.99 (pred(pred(X2!57)) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18870, 22])).
% 5.97/5.99 tff(18872,plain,
% 5.97/5.99 (pred(pred(pred(X2!57))) = pred(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18871])).
% 5.97/5.99 tff(18873,plain,
% 5.97/5.99 (pred(pred(pred(X2!57))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18872, 21])).
% 5.97/5.99 tff(18874,plain,
% 5.97/5.99 (pred(pred(pred(pred(X2!57)))) = pred(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18873])).
% 5.97/5.99 tff(18875,plain,
% 5.97/5.99 (pred(pred(pred(pred(X2!57)))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18874, 20])).
% 5.97/5.99 tff(18876,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(X2!57))))) = pred(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18875])).
% 5.97/5.99 tff(18877,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(X2!57))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18876, 19])).
% 5.97/5.99 tff(18878,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18877])).
% 5.97/5.99 tff(18879,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18878, 18])).
% 5.97/5.99 tff(18880,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18879])).
% 5.97/5.99 tff(18881,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18880, 17])).
% 5.97/5.99 tff(18882,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18881])).
% 5.97/5.99 tff(18883,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18882, 16])).
% 5.97/5.99 tff(18884,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18883])).
% 5.97/5.99 tff(18885,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18884, 15])).
% 5.97/5.99 tff(18886,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18885])).
% 5.97/5.99 tff(18887,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18886, 25])).
% 5.97/5.99 tff(18888,plain,
% 5.97/5.99 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18887])).
% 5.97/5.99 tff(18889,plain,
% 5.97/5.99 (NPX2!31 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[395, 18888, 24])).
% 5.97/5.99 tff(18890,plain,
% 5.97/5.99 (succ(NPX2!31) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18889])).
% 5.97/5.99 tff(18891,plain,
% 5.97/5.99 (succ(NPX2!31) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18890, 36])).
% 5.97/5.99 tff(18892,plain,
% 5.97/5.99 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n2, n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18891, 18861])).
% 5.97/5.99 tff(18893,plain,
% 5.97/5.99 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18892, 34])).
% 5.97/5.99 tff(18894,plain,
% 5.97/5.99 (succ(X2!57) = succ(n1)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18867])).
% 5.97/5.99 tff(18895,plain,
% 5.97/5.99 (succ(X2!57) = n2),
% 5.97/5.99 inference(transitivity,[status(thm)],[18894, 36])).
% 5.97/5.99 tff(18896,plain,
% 5.97/5.99 (succ(succ(X2!57)) = succ(n2)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18895])).
% 5.97/5.99 tff(18897,plain,
% 5.97/5.99 (succ(succ(X2!57)) = n3),
% 5.97/5.99 inference(transitivity,[status(thm)],[18896, 48])).
% 5.97/5.99 tff(18898,plain,
% 5.97/5.99 (succ(succ(succ(X2!57))) = succ(n3)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18897])).
% 5.97/5.99 tff(18899,plain,
% 5.97/5.99 (succ(succ(succ(X2!57))) = n4),
% 5.97/5.99 inference(transitivity,[status(thm)],[18898, 14])).
% 5.97/5.99 tff(18900,plain,
% 5.97/5.99 (succ(succ(succ(succ(X2!57)))) = succ(n4)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18899])).
% 5.97/5.99 tff(18901,plain,
% 5.97/5.99 (succ(succ(succ(succ(X2!57)))) = n5),
% 5.97/5.99 inference(transitivity,[status(thm)],[18900, 33])).
% 5.97/5.99 tff(18902,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(X2!57))))) = succ(n5)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18901])).
% 5.97/5.99 tff(18903,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(X2!57))))) = n6),
% 5.97/5.99 inference(transitivity,[status(thm)],[18902, 30])).
% 5.97/5.99 tff(18904,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n6)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18903])).
% 5.97/5.99 tff(18905,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n7),
% 5.97/5.99 inference(transitivity,[status(thm)],[18904, 39])).
% 5.97/5.99 tff(18906,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n7)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18905])).
% 5.97/5.99 tff(18907,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n8),
% 5.97/5.99 inference(transitivity,[status(thm)],[18906, 53])).
% 5.97/5.99 tff(18908,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n8)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18907])).
% 5.97/5.99 tff(18909,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n9),
% 5.97/5.99 inference(transitivity,[status(thm)],[18908, 45])).
% 5.97/5.99 tff(18910,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n9)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18909])).
% 5.97/5.99 tff(18911,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n10),
% 5.97/5.99 inference(transitivity,[status(thm)],[18910, 28])).
% 5.97/5.99 tff(18912,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n10)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18911])).
% 5.97/5.99 tff(18913,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n0),
% 5.97/5.99 inference(transitivity,[status(thm)],[18912, 42])).
% 5.97/5.99 tff(18914,plain,
% 5.97/5.99 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n0)),
% 5.97/5.99 inference(monotonicity,[status(thm)],[18913])).
% 5.97/5.99 tff(18915,plain,
% 5.97/5.99 (NSX2!29 = n1),
% 5.97/5.99 inference(transitivity,[status(thm)],[420, 18914, 58])).
% 5.97/6.00 tff(18916,plain,
% 5.97/6.00 (pred(NSX2!29) = pred(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18915])).
% 5.97/6.00 tff(18917,plain,
% 5.97/6.00 (pred(NSX2!29) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[18916, 23])).
% 5.97/6.00 tff(18918,plain,
% 5.97/6.00 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n0, n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18917, 18893])).
% 5.97/6.00 tff(18919,plain,
% 5.97/6.00 (Y3!54 = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[425, 18918, 442])).
% 5.97/6.00 tff(18920,plain,
% 5.97/6.00 (pred(Y3!54) = pred(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18919])).
% 5.97/6.00 tff(18921,plain,
% 5.97/6.00 (pred(Y3!54) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[18920, 15])).
% 5.97/6.00 tff(18922,plain,
% 5.97/6.00 (pred(pred(Y3!54)) = pred(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18921])).
% 5.97/6.00 tff(18923,plain,
% 5.97/6.00 (pred(pred(Y3!54)) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[18922, 25])).
% 5.97/6.00 tff(18924,plain,
% 5.97/6.00 (pred(pred(pred(Y3!54))) = pred(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18923])).
% 5.97/6.00 tff(18925,plain,
% 5.97/6.00 (pred(pred(pred(Y3!54))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[18924, 24])).
% 5.97/6.00 tff(18926,plain,
% 5.97/6.00 (pred(pred(pred(pred(Y3!54)))) = pred(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18925])).
% 5.97/6.00 tff(18927,plain,
% 5.97/6.00 (pred(pred(pred(pred(Y3!54)))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[18926, 23])).
% 5.97/6.00 tff(18928,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18927])).
% 5.97/6.00 tff(18929,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(Y3!54))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[18928, 22])).
% 5.97/6.00 tff(18930,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18929])).
% 5.97/6.00 tff(18931,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[18930, 21])).
% 5.97/6.00 tff(18932,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18931])).
% 5.97/6.00 tff(18933,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[18932, 20])).
% 5.97/6.00 tff(18934,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18933])).
% 5.97/6.00 tff(18935,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[18934, 19])).
% 5.97/6.00 tff(18936,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18935])).
% 5.97/6.00 tff(18937,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[18936, 18])).
% 5.97/6.00 tff(18938,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18937])).
% 5.97/6.00 tff(18939,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[18938, 17])).
% 5.97/6.00 tff(18940,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18939])).
% 5.97/6.00 tff(18941,plain,
% 5.97/6.00 (NPY3!26 = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[462, 18940, 16])).
% 5.97/6.00 tff(18942,plain,
% 5.97/6.00 (succ(NPY3!26) = succ(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18941])).
% 5.97/6.00 tff(18943,plain,
% 5.97/6.00 (succ(NPY3!26) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[18942, 33])).
% 5.97/6.00 tff(18944,plain,
% 5.97/6.00 (succ(Y3!54) = succ(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18919])).
% 5.97/6.00 tff(18945,plain,
% 5.97/6.00 (succ(Y3!54) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[18944, 33])).
% 5.97/6.00 tff(18946,plain,
% 5.97/6.00 (succ(succ(Y3!54)) = succ(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18945])).
% 5.97/6.00 tff(18947,plain,
% 5.97/6.00 (succ(succ(Y3!54)) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[18946, 30])).
% 5.97/6.00 tff(18948,plain,
% 5.97/6.00 (succ(succ(succ(Y3!54))) = succ(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18947])).
% 5.97/6.00 tff(18949,plain,
% 5.97/6.00 (succ(succ(succ(Y3!54))) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[18948, 39])).
% 5.97/6.00 tff(18950,plain,
% 5.97/6.00 (succ(succ(succ(succ(Y3!54)))) = succ(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18949])).
% 5.97/6.00 tff(18951,plain,
% 5.97/6.00 (succ(succ(succ(succ(Y3!54)))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[18950, 53])).
% 5.97/6.00 tff(18952,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18951])).
% 5.97/6.00 tff(18953,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(Y3!54))))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[18952, 45])).
% 5.97/6.00 tff(18954,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18953])).
% 5.97/6.00 tff(18955,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[18954, 28])).
% 5.97/6.00 tff(18956,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18955])).
% 5.97/6.00 tff(18957,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[18956, 42])).
% 5.97/6.00 tff(18958,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18957])).
% 5.97/6.00 tff(18959,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[18958, 58])).
% 5.97/6.00 tff(18960,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18959])).
% 5.97/6.00 tff(18961,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[18960, 36])).
% 5.97/6.00 tff(18962,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18961])).
% 5.97/6.00 tff(18963,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[18962, 48])).
% 5.97/6.00 tff(18964,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18963])).
% 5.97/6.00 tff(18965,plain,
% 5.97/6.00 (NSY3!24 = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[485, 18964, 14])).
% 5.97/6.00 tff(18966,plain,
% 5.97/6.00 (pred(NSY3!24) = pred(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18965])).
% 5.97/6.00 tff(18967,plain,
% 5.97/6.00 (pred(NSY3!24) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[18966, 15])).
% 5.97/6.00 tff(18968,plain,
% 5.97/6.00 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n3, n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18967, 18943])).
% 5.97/6.00 tff(18969,plain,
% 5.97/6.00 (sum(pred(NSY3!24), succ(NPY3!26)) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[18968, 32])).
% 5.97/6.00 tff(18970,plain,
% 5.97/6.00 (sum(pred(Y2!56), succ(X2!57)) = sum(n0, n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18813, 18895])).
% 5.97/6.00 tff(18971,plain,
% 5.97/6.00 (sum(pred(Y2!56), succ(X2!57)) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[18970, 35])).
% 5.97/6.00 tff(18972,plain,
% 5.97/6.00 (sum(pred(X2!57), succ(Y2!56)) = sum(n0, n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18869, 18837])).
% 5.97/6.00 tff(18973,plain,
% 5.97/6.00 (sum(pred(X2!57), succ(Y2!56)) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[18972, 35])).
% 5.97/6.00 tff(18974,plain,
% 5.97/6.00 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n2, n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18973, 18971])).
% 5.97/6.00 tff(18975,plain,
% 5.97/6.00 (X3!55 = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[323, 18974, 34])).
% 5.97/6.00 tff(18976,plain,
% 5.97/6.00 (pred(X3!55) = pred(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18975])).
% 5.97/6.00 tff(18977,plain,
% 5.97/6.00 (pred(X3!55) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[18976, 15])).
% 5.97/6.00 tff(18978,plain,
% 5.97/6.00 (pred(pred(X3!55)) = pred(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18977])).
% 5.97/6.00 tff(18979,plain,
% 5.97/6.00 (pred(pred(X3!55)) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[18978, 25])).
% 5.97/6.00 tff(18980,plain,
% 5.97/6.00 (pred(pred(pred(X3!55))) = pred(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18979])).
% 5.97/6.00 tff(18981,plain,
% 5.97/6.00 (pred(pred(pred(X3!55))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[18980, 24])).
% 5.97/6.00 tff(18982,plain,
% 5.97/6.00 (pred(pred(pred(pred(X3!55)))) = pred(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18981])).
% 5.97/6.00 tff(18983,plain,
% 5.97/6.00 (pred(pred(pred(pred(X3!55)))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[18982, 23])).
% 5.97/6.00 tff(18984,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(X3!55))))) = pred(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18983])).
% 5.97/6.00 tff(18985,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(X3!55))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[18984, 22])).
% 5.97/6.00 tff(18986,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18985])).
% 5.97/6.00 tff(18987,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[18986, 21])).
% 5.97/6.00 tff(18988,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18987])).
% 5.97/6.00 tff(18989,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[18988, 20])).
% 5.97/6.00 tff(18990,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18989])).
% 5.97/6.00 tff(18991,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[18990, 19])).
% 5.97/6.00 tff(18992,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18991])).
% 5.97/6.00 tff(18993,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[18992, 18])).
% 5.97/6.00 tff(18994,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18993])).
% 5.97/6.00 tff(18995,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[18994, 17])).
% 5.97/6.00 tff(18996,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18995])).
% 5.97/6.00 tff(18997,plain,
% 5.97/6.00 (NPX3!27 = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[510, 18996, 16])).
% 5.97/6.00 tff(18998,plain,
% 5.97/6.00 (succ(NPX3!27) = succ(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18997])).
% 5.97/6.00 tff(18999,plain,
% 5.97/6.00 (succ(NPX3!27) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[18998, 33])).
% 5.97/6.00 tff(19000,plain,
% 5.97/6.00 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n5, n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18999, 18969])).
% 5.97/6.00 tff(19001,plain,
% 5.97/6.00 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19000, 558])).
% 5.97/6.00 tff(19002,plain,
% 5.97/6.00 (succ(X3!55) = succ(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18975])).
% 5.97/6.00 tff(19003,plain,
% 5.97/6.00 (succ(X3!55) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[19002, 33])).
% 5.97/6.00 tff(19004,plain,
% 5.97/6.00 (succ(succ(X3!55)) = succ(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19003])).
% 5.97/6.00 tff(19005,plain,
% 5.97/6.00 (succ(succ(X3!55)) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19004, 30])).
% 5.97/6.00 tff(19006,plain,
% 5.97/6.00 (succ(succ(succ(X3!55))) = succ(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19005])).
% 5.97/6.00 tff(19007,plain,
% 5.97/6.00 (succ(succ(succ(X3!55))) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[19006, 39])).
% 5.97/6.00 tff(19008,plain,
% 5.97/6.00 (succ(succ(succ(succ(X3!55)))) = succ(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19007])).
% 5.97/6.00 tff(19009,plain,
% 5.97/6.00 (succ(succ(succ(succ(X3!55)))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19008, 53])).
% 5.97/6.00 tff(19010,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(X3!55))))) = succ(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19009])).
% 5.97/6.00 tff(19011,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(X3!55))))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[19010, 45])).
% 5.97/6.00 tff(19012,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19011])).
% 5.97/6.00 tff(19013,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19012, 28])).
% 5.97/6.00 tff(19014,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19013])).
% 5.97/6.00 tff(19015,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[19014, 42])).
% 5.97/6.00 tff(19016,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19015])).
% 5.97/6.00 tff(19017,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[19016, 58])).
% 5.97/6.00 tff(19018,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19017])).
% 5.97/6.00 tff(19019,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19018, 36])).
% 5.97/6.00 tff(19020,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19019])).
% 5.97/6.00 tff(19021,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19020, 48])).
% 5.97/6.00 tff(19022,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19021])).
% 5.97/6.00 tff(19023,plain,
% 5.97/6.00 (NSX3!25 = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[535, 19022, 14])).
% 5.97/6.00 tff(19024,plain,
% 5.97/6.00 (pred(NSX3!25) = pred(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19023])).
% 5.97/6.00 tff(19025,plain,
% 5.97/6.00 (pred(NSX3!25) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19024, 15])).
% 5.97/6.00 tff(19026,plain,
% 5.97/6.00 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n3, n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19025, 19001])).
% 5.97/6.00 tff(19027,plain,
% 5.97/6.00 (Y4!52 = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[540, 19026, 557])).
% 5.97/6.00 tff(19028,plain,
% 5.97/6.00 (pred(Y4!52) = pred(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19027])).
% 5.97/6.00 tff(19029,plain,
% 5.97/6.00 (pred(Y4!52) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19028, 16])).
% 5.97/6.00 tff(19030,plain,
% 5.97/6.00 (pred(pred(Y4!52)) = pred(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19029])).
% 5.97/6.00 tff(19031,plain,
% 5.97/6.00 (pred(pred(Y4!52)) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19030, 15])).
% 5.97/6.00 tff(19032,plain,
% 5.97/6.00 (pred(pred(pred(Y4!52))) = pred(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19031])).
% 5.97/6.00 tff(19033,plain,
% 5.97/6.00 (pred(pred(pred(Y4!52))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19032, 25])).
% 5.97/6.00 tff(19034,plain,
% 5.97/6.00 (pred(pred(pred(pred(Y4!52)))) = pred(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19033])).
% 5.97/6.00 tff(19035,plain,
% 5.97/6.00 (pred(pred(pred(pred(Y4!52)))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[19034, 24])).
% 5.97/6.00 tff(19036,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19035])).
% 5.97/6.00 tff(19037,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(Y4!52))))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[19036, 23])).
% 5.97/6.00 tff(19038,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19037])).
% 5.97/6.00 tff(19039,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19038, 22])).
% 5.97/6.00 tff(19040,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19039])).
% 5.97/6.00 tff(19041,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[19040, 21])).
% 5.97/6.00 tff(19042,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19041])).
% 5.97/6.00 tff(19043,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19042, 20])).
% 5.97/6.00 tff(19044,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19043])).
% 5.97/6.00 tff(19045,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[19044, 19])).
% 5.97/6.00 tff(19046,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19045])).
% 5.97/6.00 tff(19047,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19046, 18])).
% 5.97/6.00 tff(19048,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19047])).
% 5.97/6.00 tff(19049,plain,
% 5.97/6.00 (NPY4!22 = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[578, 19048, 17])).
% 5.97/6.00 tff(19050,plain,
% 5.97/6.00 (succ(NPY4!22) = succ(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19049])).
% 5.97/6.00 tff(19051,plain,
% 5.97/6.00 (succ(NPY4!22) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19050, 30])).
% 5.97/6.00 tff(19052,plain,
% 5.97/6.00 (succ(Y4!52) = succ(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19027])).
% 5.97/6.00 tff(19053,plain,
% 5.97/6.00 (succ(Y4!52) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19052, 30])).
% 5.97/6.00 tff(19054,plain,
% 5.97/6.00 (succ(succ(Y4!52)) = succ(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19053])).
% 5.97/6.00 tff(19055,plain,
% 5.97/6.00 (succ(succ(Y4!52)) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[19054, 39])).
% 5.97/6.00 tff(19056,plain,
% 5.97/6.00 (succ(succ(succ(Y4!52))) = succ(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19055])).
% 5.97/6.00 tff(19057,plain,
% 5.97/6.00 (succ(succ(succ(Y4!52))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19056, 53])).
% 5.97/6.00 tff(19058,plain,
% 5.97/6.00 (succ(succ(succ(succ(Y4!52)))) = succ(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19057])).
% 5.97/6.00 tff(19059,plain,
% 5.97/6.00 (succ(succ(succ(succ(Y4!52)))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[19058, 45])).
% 5.97/6.00 tff(19060,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19059])).
% 5.97/6.00 tff(19061,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(Y4!52))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19060, 28])).
% 5.97/6.00 tff(19062,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19061])).
% 5.97/6.00 tff(19063,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[19062, 42])).
% 5.97/6.00 tff(19064,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19063])).
% 5.97/6.00 tff(19065,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[19064, 58])).
% 5.97/6.00 tff(19066,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19065])).
% 5.97/6.00 tff(19067,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19066, 36])).
% 5.97/6.00 tff(19068,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19067])).
% 5.97/6.00 tff(19069,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19068, 48])).
% 5.97/6.00 tff(19070,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19069])).
% 5.97/6.00 tff(19071,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19070, 14])).
% 5.97/6.00 tff(19072,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19071])).
% 5.97/6.00 tff(19073,plain,
% 5.97/6.00 (NSY4!20 = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[601, 19072, 33])).
% 5.97/6.00 tff(19074,plain,
% 5.97/6.00 (pred(NSY4!20) = pred(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19073])).
% 5.97/6.00 tff(19075,plain,
% 5.97/6.00 (pred(NSY4!20) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19074, 16])).
% 5.97/6.00 tff(19076,plain,
% 5.97/6.00 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n4, n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19075, 19051])).
% 5.97/6.00 tff(19077,plain,
% 5.97/6.00 (sum(pred(NSY4!20), succ(NPY4!22)) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19076, 12])).
% 5.97/6.00 tff(19078,plain,
% 5.97/6.00 (sum(pred(Y3!54), succ(X3!55)) = sum(n3, n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18921, 19003])).
% 5.97/6.00 tff(19079,plain,
% 5.97/6.00 (sum(pred(Y3!54), succ(X3!55)) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19078, 32])).
% 5.97/6.00 tff(19080,plain,
% 5.97/6.00 (sum(pred(X3!55), succ(Y3!54)) = sum(n3, n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[18977, 18945])).
% 5.97/6.00 tff(19081,plain,
% 5.97/6.00 (sum(pred(X3!55), succ(Y3!54)) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19080, 32])).
% 5.97/6.00 tff(19082,plain,
% 5.97/6.00 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n8, n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19081, 19079])).
% 5.97/6.00 tff(19083,plain,
% 5.97/6.00 (X4!53 = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[438, 19082, 31])).
% 5.97/6.00 tff(19084,plain,
% 5.97/6.00 (pred(X4!53) = pred(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19083])).
% 5.97/6.00 tff(19085,plain,
% 5.97/6.00 (pred(X4!53) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19084, 16])).
% 5.97/6.00 tff(19086,plain,
% 5.97/6.00 (pred(pred(X4!53)) = pred(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19085])).
% 5.97/6.00 tff(19087,plain,
% 5.97/6.00 (pred(pred(X4!53)) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19086, 15])).
% 5.97/6.00 tff(19088,plain,
% 5.97/6.00 (pred(pred(pred(X4!53))) = pred(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19087])).
% 5.97/6.00 tff(19089,plain,
% 5.97/6.00 (pred(pred(pred(X4!53))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19088, 25])).
% 5.97/6.00 tff(19090,plain,
% 5.97/6.00 (pred(pred(pred(pred(X4!53)))) = pred(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19089])).
% 5.97/6.00 tff(19091,plain,
% 5.97/6.00 (pred(pred(pred(pred(X4!53)))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[19090, 24])).
% 5.97/6.00 tff(19092,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(X4!53))))) = pred(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19091])).
% 5.97/6.00 tff(19093,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(X4!53))))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[19092, 23])).
% 5.97/6.00 tff(19094,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19093])).
% 5.97/6.00 tff(19095,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19094, 22])).
% 5.97/6.00 tff(19096,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19095])).
% 5.97/6.00 tff(19097,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[19096, 21])).
% 5.97/6.00 tff(19098,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19097])).
% 5.97/6.00 tff(19099,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19098, 20])).
% 5.97/6.00 tff(19100,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19099])).
% 5.97/6.00 tff(19101,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[19100, 19])).
% 5.97/6.00 tff(19102,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19101])).
% 5.97/6.00 tff(19103,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19102, 18])).
% 5.97/6.00 tff(19104,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19103])).
% 5.97/6.00 tff(19105,plain,
% 5.97/6.00 (NPX4!23 = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[626, 19104, 17])).
% 5.97/6.00 tff(19106,plain,
% 5.97/6.00 (succ(NPX4!23) = succ(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19105])).
% 5.97/6.00 tff(19107,plain,
% 5.97/6.00 (succ(NPX4!23) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19106, 30])).
% 5.97/6.00 tff(19108,plain,
% 5.97/6.00 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n6, n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19107, 19077])).
% 5.97/6.00 tff(19109,plain,
% 5.97/6.00 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[19108, 674])).
% 5.97/6.00 tff(19110,plain,
% 5.97/6.00 (succ(X4!53) = succ(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19083])).
% 5.97/6.00 tff(19111,plain,
% 5.97/6.00 (succ(X4!53) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19110, 30])).
% 5.97/6.00 tff(19112,plain,
% 5.97/6.00 (succ(succ(X4!53)) = succ(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19111])).
% 5.97/6.00 tff(19113,plain,
% 5.97/6.00 (succ(succ(X4!53)) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[19112, 39])).
% 5.97/6.00 tff(19114,plain,
% 5.97/6.00 (succ(succ(succ(X4!53))) = succ(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19113])).
% 5.97/6.00 tff(19115,plain,
% 5.97/6.00 (succ(succ(succ(X4!53))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19114, 53])).
% 5.97/6.00 tff(19116,plain,
% 5.97/6.00 (succ(succ(succ(succ(X4!53)))) = succ(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19115])).
% 5.97/6.00 tff(19117,plain,
% 5.97/6.00 (succ(succ(succ(succ(X4!53)))) = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[19116, 45])).
% 5.97/6.00 tff(19118,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(X4!53))))) = succ(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19117])).
% 5.97/6.00 tff(19119,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(X4!53))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19118, 28])).
% 5.97/6.00 tff(19120,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19119])).
% 5.97/6.00 tff(19121,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[19120, 42])).
% 5.97/6.00 tff(19122,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19121])).
% 5.97/6.00 tff(19123,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[19122, 58])).
% 5.97/6.00 tff(19124,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19123])).
% 5.97/6.00 tff(19125,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19124, 36])).
% 5.97/6.00 tff(19126,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19125])).
% 5.97/6.00 tff(19127,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19126, 48])).
% 5.97/6.00 tff(19128,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19127])).
% 5.97/6.00 tff(19129,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19128, 14])).
% 5.97/6.00 tff(19130,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19129])).
% 5.97/6.00 tff(19131,plain,
% 5.97/6.00 (NSX4!21 = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[651, 19130, 33])).
% 5.97/6.00 tff(19132,plain,
% 5.97/6.00 (pred(NSX4!21) = pred(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19131])).
% 5.97/6.00 tff(19133,plain,
% 5.97/6.00 (pred(NSX4!21) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19132, 16])).
% 5.97/6.00 tff(19134,plain,
% 5.97/6.00 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n4, n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19133, 19109])).
% 5.97/6.00 tff(19135,plain,
% 5.97/6.00 (Y5!50 = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[656, 19134, 673])).
% 5.97/6.00 tff(19136,plain,
% 5.97/6.00 (pred(Y5!50) = pred(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19135])).
% 5.97/6.00 tff(19137,plain,
% 5.97/6.00 (pred(Y5!50) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19136, 20])).
% 5.97/6.00 tff(19138,plain,
% 5.97/6.00 (pred(pred(Y5!50)) = pred(n8)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19137])).
% 5.97/6.00 tff(19139,plain,
% 5.97/6.00 (pred(pred(Y5!50)) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[19138, 19])).
% 5.97/6.00 tff(19140,plain,
% 5.97/6.00 (pred(pred(pred(Y5!50))) = pred(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19139])).
% 5.97/6.00 tff(19141,plain,
% 5.97/6.00 (pred(pred(pred(Y5!50))) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19140, 18])).
% 5.97/6.00 tff(19142,plain,
% 5.97/6.00 (pred(pred(pred(pred(Y5!50)))) = pred(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19141])).
% 5.97/6.00 tff(19143,plain,
% 5.97/6.00 (pred(pred(pred(pred(Y5!50)))) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[19142, 17])).
% 5.97/6.00 tff(19144,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19143])).
% 5.97/6.00 tff(19145,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(Y5!50))))) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19144, 16])).
% 5.97/6.00 tff(19146,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19145])).
% 5.97/6.00 tff(19147,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19146, 15])).
% 5.97/6.00 tff(19148,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19147])).
% 5.97/6.00 tff(19149,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19148, 25])).
% 5.97/6.00 tff(19150,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19149])).
% 5.97/6.00 tff(19151,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[19150, 24])).
% 5.97/6.00 tff(19152,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19151])).
% 5.97/6.00 tff(19153,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[19152, 23])).
% 5.97/6.00 tff(19154,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19153])).
% 5.97/6.00 tff(19155,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19154, 22])).
% 5.97/6.00 tff(19156,plain,
% 5.97/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19155])).
% 5.97/6.00 tff(19157,plain,
% 5.97/6.00 (NPY5!18 = n9),
% 5.97/6.00 inference(transitivity,[status(thm)],[694, 19156, 21])).
% 5.97/6.00 tff(19158,plain,
% 5.97/6.00 (succ(NPY5!18) = succ(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19157])).
% 5.97/6.00 tff(19159,plain,
% 5.97/6.00 (succ(NPY5!18) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19158, 28])).
% 5.97/6.00 tff(19160,plain,
% 5.97/6.00 (succ(Y5!50) = succ(n9)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19135])).
% 5.97/6.00 tff(19161,plain,
% 5.97/6.00 (succ(Y5!50) = n10),
% 5.97/6.00 inference(transitivity,[status(thm)],[19160, 28])).
% 5.97/6.00 tff(19162,plain,
% 5.97/6.00 (succ(succ(Y5!50)) = succ(n10)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19161])).
% 5.97/6.00 tff(19163,plain,
% 5.97/6.00 (succ(succ(Y5!50)) = n0),
% 5.97/6.00 inference(transitivity,[status(thm)],[19162, 42])).
% 5.97/6.00 tff(19164,plain,
% 5.97/6.00 (succ(succ(succ(Y5!50))) = succ(n0)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19163])).
% 5.97/6.00 tff(19165,plain,
% 5.97/6.00 (succ(succ(succ(Y5!50))) = n1),
% 5.97/6.00 inference(transitivity,[status(thm)],[19164, 58])).
% 5.97/6.00 tff(19166,plain,
% 5.97/6.00 (succ(succ(succ(succ(Y5!50)))) = succ(n1)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19165])).
% 5.97/6.00 tff(19167,plain,
% 5.97/6.00 (succ(succ(succ(succ(Y5!50)))) = n2),
% 5.97/6.00 inference(transitivity,[status(thm)],[19166, 36])).
% 5.97/6.00 tff(19168,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n2)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19167])).
% 5.97/6.00 tff(19169,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(Y5!50))))) = n3),
% 5.97/6.00 inference(transitivity,[status(thm)],[19168, 48])).
% 5.97/6.00 tff(19170,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n3)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19169])).
% 5.97/6.00 tff(19171,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n4),
% 5.97/6.00 inference(transitivity,[status(thm)],[19170, 14])).
% 5.97/6.00 tff(19172,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n4)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19171])).
% 5.97/6.00 tff(19173,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n5),
% 5.97/6.00 inference(transitivity,[status(thm)],[19172, 33])).
% 5.97/6.00 tff(19174,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n5)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19173])).
% 5.97/6.00 tff(19175,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n6),
% 5.97/6.00 inference(transitivity,[status(thm)],[19174, 30])).
% 5.97/6.00 tff(19176,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n6)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19175])).
% 5.97/6.00 tff(19177,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n7),
% 5.97/6.00 inference(transitivity,[status(thm)],[19176, 39])).
% 5.97/6.00 tff(19178,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n7)),
% 5.97/6.00 inference(monotonicity,[status(thm)],[19177])).
% 5.97/6.00 tff(19179,plain,
% 5.97/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n8),
% 5.97/6.00 inference(transitivity,[status(thm)],[19178, 53])).
% 5.97/6.00 tff(19180,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n8)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19179])).
% 6.07/6.00 tff(19181,plain,
% 6.07/6.00 (NSY5!16 = n9),
% 6.07/6.00 inference(transitivity,[status(thm)],[717, 19180, 45])).
% 6.07/6.00 tff(19182,plain,
% 6.07/6.00 (pred(NSY5!16) = pred(n9)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19181])).
% 6.07/6.00 tff(19183,plain,
% 6.07/6.00 (pred(NSY5!16) = n8),
% 6.07/6.00 inference(transitivity,[status(thm)],[19182, 20])).
% 6.07/6.00 tff(19184,plain,
% 6.07/6.00 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n8, n10)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19183, 19159])).
% 6.07/6.00 tff(19185,plain,
% 6.07/6.00 (sum(pred(NSY5!16), succ(NPY5!18)) = n7),
% 6.07/6.00 inference(transitivity,[status(thm)],[19184, 27])).
% 6.07/6.00 tff(19186,plain,
% 6.07/6.00 (sum(pred(Y4!52), succ(X4!53)) = sum(n4, n6)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19029, 19111])).
% 6.07/6.00 tff(19187,plain,
% 6.07/6.00 (sum(pred(Y4!52), succ(X4!53)) = n10),
% 6.07/6.00 inference(transitivity,[status(thm)],[19186, 12])).
% 6.07/6.00 tff(19188,plain,
% 6.07/6.00 (sum(pred(X4!53), succ(Y4!52)) = sum(n4, n6)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19085, 19053])).
% 6.07/6.00 tff(19189,plain,
% 6.07/6.00 (sum(pred(X4!53), succ(Y4!52)) = n10),
% 6.07/6.00 inference(transitivity,[status(thm)],[19188, 12])).
% 6.07/6.00 tff(19190,plain,
% 6.07/6.00 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n10, n10)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19189, 19187])).
% 6.07/6.00 tff(19191,plain,
% 6.07/6.00 (X5!51 = n9),
% 6.07/6.00 inference(transitivity,[status(thm)],[553, 19190, 29])).
% 6.07/6.00 tff(19192,plain,
% 6.07/6.00 (pred(X5!51) = pred(n9)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19191])).
% 6.07/6.00 tff(19193,plain,
% 6.07/6.00 (pred(X5!51) = n8),
% 6.07/6.00 inference(transitivity,[status(thm)],[19192, 20])).
% 6.07/6.00 tff(19194,plain,
% 6.07/6.00 (pred(pred(X5!51)) = pred(n8)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19193])).
% 6.07/6.00 tff(19195,plain,
% 6.07/6.00 (pred(pred(X5!51)) = n7),
% 6.07/6.00 inference(transitivity,[status(thm)],[19194, 19])).
% 6.07/6.00 tff(19196,plain,
% 6.07/6.00 (pred(pred(pred(X5!51))) = pred(n7)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19195])).
% 6.07/6.00 tff(19197,plain,
% 6.07/6.00 (pred(pred(pred(X5!51))) = n6),
% 6.07/6.00 inference(transitivity,[status(thm)],[19196, 18])).
% 6.07/6.00 tff(19198,plain,
% 6.07/6.00 (pred(pred(pred(pred(X5!51)))) = pred(n6)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19197])).
% 6.07/6.00 tff(19199,plain,
% 6.07/6.00 (pred(pred(pred(pred(X5!51)))) = n5),
% 6.07/6.00 inference(transitivity,[status(thm)],[19198, 17])).
% 6.07/6.00 tff(19200,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(X5!51))))) = pred(n5)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19199])).
% 6.07/6.00 tff(19201,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(X5!51))))) = n4),
% 6.07/6.00 inference(transitivity,[status(thm)],[19200, 16])).
% 6.07/6.00 tff(19202,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n4)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19201])).
% 6.07/6.00 tff(19203,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n3),
% 6.07/6.00 inference(transitivity,[status(thm)],[19202, 15])).
% 6.07/6.00 tff(19204,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n3)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19203])).
% 6.07/6.00 tff(19205,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n2),
% 6.07/6.00 inference(transitivity,[status(thm)],[19204, 25])).
% 6.07/6.00 tff(19206,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n2)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19205])).
% 6.07/6.00 tff(19207,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n1),
% 6.07/6.00 inference(transitivity,[status(thm)],[19206, 24])).
% 6.07/6.00 tff(19208,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n1)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19207])).
% 6.07/6.00 tff(19209,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n0),
% 6.07/6.00 inference(transitivity,[status(thm)],[19208, 23])).
% 6.07/6.00 tff(19210,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n0)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19209])).
% 6.07/6.00 tff(19211,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n10),
% 6.07/6.00 inference(transitivity,[status(thm)],[19210, 22])).
% 6.07/6.00 tff(19212,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n10)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19211])).
% 6.07/6.00 tff(19213,plain,
% 6.07/6.00 (NPX5!19 = n9),
% 6.07/6.00 inference(transitivity,[status(thm)],[742, 19212, 21])).
% 6.07/6.00 tff(19214,plain,
% 6.07/6.00 (succ(NPX5!19) = succ(n9)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19213])).
% 6.07/6.00 tff(19215,plain,
% 6.07/6.00 (succ(NPX5!19) = n10),
% 6.07/6.00 inference(transitivity,[status(thm)],[19214, 28])).
% 6.07/6.00 tff(19216,plain,
% 6.07/6.00 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n10, n7)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19215, 19185])).
% 6.07/6.00 tff(19217,plain,
% 6.07/6.00 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n6),
% 6.07/6.00 inference(transitivity,[status(thm)],[19216, 69])).
% 6.07/6.00 tff(19218,plain,
% 6.07/6.00 (succ(X5!51) = succ(n9)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19191])).
% 6.07/6.00 tff(19219,plain,
% 6.07/6.00 (succ(X5!51) = n10),
% 6.07/6.00 inference(transitivity,[status(thm)],[19218, 28])).
% 6.07/6.00 tff(19220,plain,
% 6.07/6.00 (succ(succ(X5!51)) = succ(n10)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19219])).
% 6.07/6.00 tff(19221,plain,
% 6.07/6.00 (succ(succ(X5!51)) = n0),
% 6.07/6.00 inference(transitivity,[status(thm)],[19220, 42])).
% 6.07/6.00 tff(19222,plain,
% 6.07/6.00 (succ(succ(succ(X5!51))) = succ(n0)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19221])).
% 6.07/6.00 tff(19223,plain,
% 6.07/6.00 (succ(succ(succ(X5!51))) = n1),
% 6.07/6.00 inference(transitivity,[status(thm)],[19222, 58])).
% 6.07/6.00 tff(19224,plain,
% 6.07/6.00 (succ(succ(succ(succ(X5!51)))) = succ(n1)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19223])).
% 6.07/6.00 tff(19225,plain,
% 6.07/6.00 (succ(succ(succ(succ(X5!51)))) = n2),
% 6.07/6.00 inference(transitivity,[status(thm)],[19224, 36])).
% 6.07/6.00 tff(19226,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(X5!51))))) = succ(n2)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19225])).
% 6.07/6.00 tff(19227,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(X5!51))))) = n3),
% 6.07/6.00 inference(transitivity,[status(thm)],[19226, 48])).
% 6.07/6.00 tff(19228,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n3)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19227])).
% 6.07/6.00 tff(19229,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n4),
% 6.07/6.00 inference(transitivity,[status(thm)],[19228, 14])).
% 6.07/6.00 tff(19230,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n4)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19229])).
% 6.07/6.00 tff(19231,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n5),
% 6.07/6.00 inference(transitivity,[status(thm)],[19230, 33])).
% 6.07/6.00 tff(19232,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n5)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19231])).
% 6.07/6.00 tff(19233,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n6),
% 6.07/6.00 inference(transitivity,[status(thm)],[19232, 30])).
% 6.07/6.00 tff(19234,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n6)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19233])).
% 6.07/6.00 tff(19235,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n7),
% 6.07/6.00 inference(transitivity,[status(thm)],[19234, 39])).
% 6.07/6.00 tff(19236,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n7)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19235])).
% 6.07/6.00 tff(19237,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n8),
% 6.07/6.00 inference(transitivity,[status(thm)],[19236, 53])).
% 6.07/6.00 tff(19238,plain,
% 6.07/6.00 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n8)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19237])).
% 6.07/6.00 tff(19239,plain,
% 6.07/6.00 (NSX5!17 = n9),
% 6.07/6.00 inference(transitivity,[status(thm)],[767, 19238, 45])).
% 6.07/6.00 tff(19240,plain,
% 6.07/6.00 (pred(NSX5!17) = pred(n9)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19239])).
% 6.07/6.00 tff(19241,plain,
% 6.07/6.00 (pred(NSX5!17) = n8),
% 6.07/6.00 inference(transitivity,[status(thm)],[19240, 20])).
% 6.07/6.00 tff(19242,plain,
% 6.07/6.00 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n8, n6)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19241, 19217])).
% 6.07/6.00 tff(19243,plain,
% 6.07/6.00 (Y6!48 = n3),
% 6.07/6.00 inference(transitivity,[status(thm)],[772, 19242, 98])).
% 6.07/6.00 tff(19244,plain,
% 6.07/6.00 (pred(Y6!48) = pred(n3)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19243])).
% 6.07/6.00 tff(19245,plain,
% 6.07/6.00 (pred(Y6!48) = n2),
% 6.07/6.00 inference(transitivity,[status(thm)],[19244, 25])).
% 6.07/6.00 tff(19246,plain,
% 6.07/6.00 (pred(pred(Y6!48)) = pred(n2)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19245])).
% 6.07/6.00 tff(19247,plain,
% 6.07/6.00 (pred(pred(Y6!48)) = n1),
% 6.07/6.00 inference(transitivity,[status(thm)],[19246, 24])).
% 6.07/6.00 tff(19248,plain,
% 6.07/6.00 (pred(pred(pred(Y6!48))) = pred(n1)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19247])).
% 6.07/6.00 tff(19249,plain,
% 6.07/6.00 (pred(pred(pred(Y6!48))) = n0),
% 6.07/6.00 inference(transitivity,[status(thm)],[19248, 23])).
% 6.07/6.00 tff(19250,plain,
% 6.07/6.00 (pred(pred(pred(pred(Y6!48)))) = pred(n0)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19249])).
% 6.07/6.00 tff(19251,plain,
% 6.07/6.00 (pred(pred(pred(pred(Y6!48)))) = n10),
% 6.07/6.00 inference(transitivity,[status(thm)],[19250, 22])).
% 6.07/6.00 tff(19252,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n10)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19251])).
% 6.07/6.00 tff(19253,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(Y6!48))))) = n9),
% 6.07/6.00 inference(transitivity,[status(thm)],[19252, 21])).
% 6.07/6.00 tff(19254,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n9)),
% 6.07/6.00 inference(monotonicity,[status(thm)],[19253])).
% 6.07/6.00 tff(19255,plain,
% 6.07/6.00 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19254, 20])).
% 6.07/6.01 tff(19256,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19255])).
% 6.07/6.01 tff(19257,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19256, 19])).
% 6.07/6.01 tff(19258,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19257])).
% 6.07/6.01 tff(19259,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19258, 18])).
% 6.07/6.01 tff(19260,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19259])).
% 6.07/6.01 tff(19261,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19260, 17])).
% 6.07/6.01 tff(19262,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19261])).
% 6.07/6.01 tff(19263,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19262, 16])).
% 6.07/6.01 tff(19264,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19263])).
% 6.07/6.01 tff(19265,plain,
% 6.07/6.01 (NPY6!14 = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[1465, 19264, 15])).
% 6.07/6.01 tff(19266,plain,
% 6.07/6.01 (succ(NPY6!14) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19265])).
% 6.07/6.01 tff(19267,plain,
% 6.07/6.01 (succ(NPY6!14) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19266, 14])).
% 6.07/6.01 tff(19268,plain,
% 6.07/6.01 (succ(Y6!48) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19243])).
% 6.07/6.01 tff(19269,plain,
% 6.07/6.01 (succ(Y6!48) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19268, 14])).
% 6.07/6.01 tff(19270,plain,
% 6.07/6.01 (succ(succ(Y6!48)) = succ(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19269])).
% 6.07/6.01 tff(19271,plain,
% 6.07/6.01 (succ(succ(Y6!48)) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19270, 33])).
% 6.07/6.01 tff(19272,plain,
% 6.07/6.01 (succ(succ(succ(Y6!48))) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19271])).
% 6.07/6.01 tff(19273,plain,
% 6.07/6.01 (succ(succ(succ(Y6!48))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19272, 30])).
% 6.07/6.01 tff(19274,plain,
% 6.07/6.01 (succ(succ(succ(succ(Y6!48)))) = succ(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19273])).
% 6.07/6.01 tff(19275,plain,
% 6.07/6.01 (succ(succ(succ(succ(Y6!48)))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19274, 39])).
% 6.07/6.01 tff(19276,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19275])).
% 6.07/6.01 tff(19277,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(Y6!48))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19276, 53])).
% 6.07/6.01 tff(19278,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19277])).
% 6.07/6.01 tff(19279,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[19278, 45])).
% 6.07/6.01 tff(19280,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19279])).
% 6.07/6.01 tff(19281,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19280, 28])).
% 6.07/6.01 tff(19282,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19281])).
% 6.07/6.01 tff(19283,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19282, 42])).
% 6.07/6.01 tff(19284,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19283])).
% 6.07/6.01 tff(19285,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19284, 58])).
% 6.07/6.01 tff(19286,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19285])).
% 6.07/6.01 tff(19287,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19286, 36])).
% 6.07/6.01 tff(19288,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19287])).
% 6.07/6.01 tff(19289,plain,
% 6.07/6.01 (NSY6!12 = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[1490, 19288, 48])).
% 6.07/6.01 tff(19290,plain,
% 6.07/6.01 (pred(NSY6!12) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19289])).
% 6.07/6.01 tff(19291,plain,
% 6.07/6.01 (pred(NSY6!12) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19290, 25])).
% 6.07/6.01 tff(19292,plain,
% 6.07/6.01 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n2, n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19291, 19267])).
% 6.07/6.01 tff(19293,plain,
% 6.07/6.01 (sum(pred(NSY6!12), succ(NPY6!14)) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19292, 13])).
% 6.07/6.01 tff(19294,plain,
% 6.07/6.01 (sum(pred(Y5!50), succ(X5!51)) = sum(n8, n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19137, 19219])).
% 6.07/6.01 tff(19295,plain,
% 6.07/6.01 (sum(pred(Y5!50), succ(X5!51)) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19294, 27])).
% 6.07/6.01 tff(19296,plain,
% 6.07/6.01 (sum(pred(X5!51), succ(Y5!50)) = sum(n8, n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19193, 19161])).
% 6.07/6.01 tff(19297,plain,
% 6.07/6.01 (sum(pred(X5!51), succ(Y5!50)) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19296, 27])).
% 6.07/6.01 tff(19298,plain,
% 6.07/6.01 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n7, n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19297, 19295])).
% 6.07/6.01 tff(19299,plain,
% 6.07/6.01 (X6!49 = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[669, 19298, 26])).
% 6.07/6.01 tff(19300,plain,
% 6.07/6.01 (pred(X6!49) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19299])).
% 6.07/6.01 tff(19301,plain,
% 6.07/6.01 (pred(X6!49) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19300, 25])).
% 6.07/6.01 tff(19302,plain,
% 6.07/6.01 (pred(pred(X6!49)) = pred(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19301])).
% 6.07/6.01 tff(19303,plain,
% 6.07/6.01 (pred(pred(X6!49)) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19302, 24])).
% 6.07/6.01 tff(19304,plain,
% 6.07/6.01 (pred(pred(pred(X6!49))) = pred(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19303])).
% 6.07/6.01 tff(19305,plain,
% 6.07/6.01 (pred(pred(pred(X6!49))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19304, 23])).
% 6.07/6.01 tff(19306,plain,
% 6.07/6.01 (pred(pred(pred(pred(X6!49)))) = pred(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19305])).
% 6.07/6.01 tff(19307,plain,
% 6.07/6.01 (pred(pred(pred(pred(X6!49)))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19306, 22])).
% 6.07/6.01 tff(19308,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(X6!49))))) = pred(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19307])).
% 6.07/6.01 tff(19309,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(X6!49))))) = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[19308, 21])).
% 6.07/6.01 tff(19310,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19309])).
% 6.07/6.01 tff(19311,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19310, 20])).
% 6.07/6.01 tff(19312,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19311])).
% 6.07/6.01 tff(19313,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19312, 19])).
% 6.07/6.01 tff(19314,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19313])).
% 6.07/6.01 tff(19315,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19314, 18])).
% 6.07/6.01 tff(19316,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19315])).
% 6.07/6.01 tff(19317,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19316, 17])).
% 6.07/6.01 tff(19318,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19317])).
% 6.07/6.01 tff(19319,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19318, 16])).
% 6.07/6.01 tff(19320,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19319])).
% 6.07/6.01 tff(19321,plain,
% 6.07/6.01 (NPX6!15 = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[1523, 19320, 15])).
% 6.07/6.01 tff(19322,plain,
% 6.07/6.01 (succ(NPX6!15) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19321])).
% 6.07/6.01 tff(19323,plain,
% 6.07/6.01 (succ(NPX6!15) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19322, 14])).
% 6.07/6.01 tff(19324,plain,
% 6.07/6.01 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n4, n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19323, 19293])).
% 6.07/6.01 tff(19325,plain,
% 6.07/6.01 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19324, 12])).
% 6.07/6.01 tff(19326,plain,
% 6.07/6.01 (succ(X6!49) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19299])).
% 6.07/6.01 tff(19327,plain,
% 6.07/6.01 (succ(X6!49) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19326, 14])).
% 6.07/6.01 tff(19328,plain,
% 6.07/6.01 (succ(succ(X6!49)) = succ(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19327])).
% 6.07/6.01 tff(19329,plain,
% 6.07/6.01 (succ(succ(X6!49)) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19328, 33])).
% 6.07/6.01 tff(19330,plain,
% 6.07/6.01 (succ(succ(succ(X6!49))) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19329])).
% 6.07/6.01 tff(19331,plain,
% 6.07/6.01 (succ(succ(succ(X6!49))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19330, 30])).
% 6.07/6.01 tff(19332,plain,
% 6.07/6.01 (succ(succ(succ(succ(X6!49)))) = succ(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19331])).
% 6.07/6.01 tff(19333,plain,
% 6.07/6.01 (succ(succ(succ(succ(X6!49)))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19332, 39])).
% 6.07/6.01 tff(19334,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(X6!49))))) = succ(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19333])).
% 6.07/6.01 tff(19335,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(X6!49))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19334, 53])).
% 6.07/6.01 tff(19336,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19335])).
% 6.07/6.01 tff(19337,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[19336, 45])).
% 6.07/6.01 tff(19338,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19337])).
% 6.07/6.01 tff(19339,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19338, 28])).
% 6.07/6.01 tff(19340,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19339])).
% 6.07/6.01 tff(19341,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19340, 42])).
% 6.07/6.01 tff(19342,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19341])).
% 6.07/6.01 tff(19343,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19342, 58])).
% 6.07/6.01 tff(19344,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19343])).
% 6.07/6.01 tff(19345,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19344, 36])).
% 6.07/6.01 tff(19346,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19345])).
% 6.07/6.01 tff(19347,plain,
% 6.07/6.01 (NSX6!13 = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[1550, 19346, 48])).
% 6.07/6.01 tff(19348,plain,
% 6.07/6.01 (pred(NSX6!13) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19347])).
% 6.07/6.01 tff(19349,plain,
% 6.07/6.01 (pred(NSX6!13) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19348, 25])).
% 6.07/6.01 tff(19350,plain,
% 6.07/6.01 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n2, n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19349, 19325])).
% 6.07/6.01 tff(19351,plain,
% 6.07/6.01 (sum(n2, n10) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 6.07/6.01 inference(symmetry,[status(thm)],[19350])).
% 6.07/6.01 tff(19352,plain,
% 6.07/6.01 (sum(pred(Y6!48), succ(X6!49)) = sum(n2, n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19245, 19327])).
% 6.07/6.01 tff(19353,plain,
% 6.07/6.01 (sum(pred(Y6!48), succ(X6!49)) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19352, 13])).
% 6.07/6.01 tff(19354,plain,
% 6.07/6.01 (sum(pred(X6!49), succ(Y6!48)) = sum(n2, n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19301, 19269])).
% 6.07/6.01 tff(19355,plain,
% 6.07/6.01 (sum(pred(X6!49), succ(Y6!48)) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19354, 13])).
% 6.07/6.01 tff(19356,plain,
% 6.07/6.01 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n6, n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19355, 19353])).
% 6.07/6.01 tff(19357,plain,
% 6.07/6.01 (X7!47 = Y7!46),
% 6.07/6.01 inference(transitivity,[status(thm)],[785, 19356, 37, 9930, 19351, 794])).
% 6.07/6.01 tff(19358,plain,
% 6.07/6.01 ($false),
% 6.07/6.01 inference(unit_resolution,[status(thm)],[792, 19357])).
% 6.07/6.01 tff(19359,plain,((~(Y0!60 = n4)) | (X7!47 = Y7!46) | (~(X0!61 = n3))), inference(lemma,lemma(discharge,[]))).
% 6.07/6.01 tff(19360,plain,
% 6.07/6.01 (~(Y0!60 = n4)),
% 6.07/6.01 inference(unit_resolution,[status(thm)],[19359, 17987, 792])).
% 6.07/6.01 tff(19361,plain,
% 6.07/6.01 (sum(n2, n3) = n5),
% 6.07/6.01 inference(and_elim,[status(thm)],[9])).
% 6.07/6.01 tff(19362,plain,
% 6.07/6.01 (sum(n4, n10) = n3),
% 6.07/6.01 inference(and_elim,[status(thm)],[9])).
% 6.07/6.01 tff(19363,plain,
% 6.07/6.01 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n4, n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[18011, 3768])).
% 6.07/6.01 tff(19364,plain,
% 6.07/6.01 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19363, 19362])).
% 6.07/6.01 tff(19365,plain,
% 6.07/6.01 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n2, n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[18037, 19364])).
% 6.07/6.01 tff(19366,plain,
% 6.07/6.01 (Y1!58 = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[196, 19365, 19361])).
% 6.07/6.01 tff(19367,plain,
% 6.07/6.01 (pred(Y1!58) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19366])).
% 6.07/6.01 tff(19368,plain,
% 6.07/6.01 (pred(Y1!58) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19367, 16])).
% 6.07/6.01 tff(19369,plain,
% 6.07/6.01 (pred(pred(Y1!58)) = pred(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19368])).
% 6.07/6.01 tff(19370,plain,
% 6.07/6.01 (pred(pred(Y1!58)) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19369, 15])).
% 6.07/6.01 tff(19371,plain,
% 6.07/6.01 (pred(pred(pred(Y1!58))) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19370])).
% 6.07/6.01 tff(19372,plain,
% 6.07/6.01 (pred(pred(pred(Y1!58))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19371, 25])).
% 6.07/6.01 tff(19373,plain,
% 6.07/6.01 (pred(pred(pred(pred(Y1!58)))) = pred(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19372])).
% 6.07/6.01 tff(19374,plain,
% 6.07/6.01 (pred(pred(pred(pred(Y1!58)))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19373, 24])).
% 6.07/6.01 tff(19375,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19374])).
% 6.07/6.01 tff(19376,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(Y1!58))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19375, 23])).
% 6.07/6.01 tff(19377,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19376])).
% 6.07/6.01 tff(19378,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19377, 22])).
% 6.07/6.01 tff(19379,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19378])).
% 6.07/6.01 tff(19380,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[19379, 21])).
% 6.07/6.01 tff(19381,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19380])).
% 6.07/6.01 tff(19382,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19381, 20])).
% 6.07/6.01 tff(19383,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19382])).
% 6.07/6.01 tff(19384,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19383, 19])).
% 6.07/6.01 tff(19385,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19384])).
% 6.07/6.01 tff(19386,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19385, 18])).
% 6.07/6.01 tff(19387,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19386])).
% 6.07/6.01 tff(19388,plain,
% 6.07/6.01 (NPY1!34 = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[232, 19387, 17])).
% 6.07/6.01 tff(19389,plain,
% 6.07/6.01 (succ(NPY1!34) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19388])).
% 6.07/6.01 tff(19390,plain,
% 6.07/6.01 (succ(NPY1!34) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19389, 30])).
% 6.07/6.01 tff(19391,plain,
% 6.07/6.01 (succ(Y1!58) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19366])).
% 6.07/6.01 tff(19392,plain,
% 6.07/6.01 (succ(Y1!58) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19391, 30])).
% 6.07/6.01 tff(19393,plain,
% 6.07/6.01 (succ(succ(Y1!58)) = succ(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19392])).
% 6.07/6.01 tff(19394,plain,
% 6.07/6.01 (succ(succ(Y1!58)) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19393, 39])).
% 6.07/6.01 tff(19395,plain,
% 6.07/6.01 (succ(succ(succ(Y1!58))) = succ(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19394])).
% 6.07/6.01 tff(19396,plain,
% 6.07/6.01 (succ(succ(succ(Y1!58))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19395, 53])).
% 6.07/6.01 tff(19397,plain,
% 6.07/6.01 (succ(succ(succ(succ(Y1!58)))) = succ(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19396])).
% 6.07/6.01 tff(19398,plain,
% 6.07/6.01 (succ(succ(succ(succ(Y1!58)))) = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[19397, 45])).
% 6.07/6.01 tff(19399,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19398])).
% 6.07/6.01 tff(19400,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(Y1!58))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19399, 28])).
% 6.07/6.01 tff(19401,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19400])).
% 6.07/6.01 tff(19402,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19401, 42])).
% 6.07/6.01 tff(19403,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19402])).
% 6.07/6.01 tff(19404,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19403, 58])).
% 6.07/6.01 tff(19405,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19404])).
% 6.07/6.01 tff(19406,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19405, 36])).
% 6.07/6.01 tff(19407,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19406])).
% 6.07/6.01 tff(19408,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19407, 48])).
% 6.07/6.01 tff(19409,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19408])).
% 6.07/6.01 tff(19410,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19409, 14])).
% 6.07/6.01 tff(19411,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19410])).
% 6.07/6.01 tff(19412,plain,
% 6.07/6.01 (NSY1!32 = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[255, 19411, 33])).
% 6.07/6.01 tff(19413,plain,
% 6.07/6.01 (pred(NSY1!32) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19412])).
% 6.07/6.01 tff(19414,plain,
% 6.07/6.01 (pred(NSY1!32) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19413, 16])).
% 6.07/6.01 tff(19415,plain,
% 6.07/6.01 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n4, n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19414, 19390])).
% 6.07/6.01 tff(19416,plain,
% 6.07/6.01 (sum(pred(NSY1!32), succ(NPY1!34)) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19415, 12])).
% 6.07/6.01 tff(19417,plain,
% 6.07/6.01 (sum(pred(Y0!60), succ(X0!61)) = sum(n4, n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[3720, 18015])).
% 6.07/6.01 tff(19418,plain,
% 6.07/6.01 (sum(pred(Y0!60), succ(X0!61)) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19417, 46])).
% 6.07/6.01 tff(19419,plain,
% 6.07/6.01 (sum(n2, n6) = n8),
% 6.07/6.01 inference(and_elim,[status(thm)],[9])).
% 6.07/6.01 tff(19420,plain,
% 6.07/6.01 (sum(pred(X0!61), succ(Y0!60)) = sum(n2, n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[17989, 3744])).
% 6.07/6.01 tff(19421,plain,
% 6.07/6.01 (sum(pred(X0!61), succ(Y0!60)) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19420, 19419])).
% 6.07/6.01 tff(19422,plain,
% 6.07/6.01 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n8, n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19421, 19418])).
% 6.07/6.01 tff(19423,plain,
% 6.07/6.01 (X1!59 = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[93, 19422, 31])).
% 6.07/6.01 tff(19424,plain,
% 6.07/6.01 (pred(X1!59) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19423])).
% 6.07/6.01 tff(19425,plain,
% 6.07/6.01 (pred(X1!59) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19424, 16])).
% 6.07/6.01 tff(19426,plain,
% 6.07/6.01 (pred(pred(X1!59)) = pred(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19425])).
% 6.07/6.01 tff(19427,plain,
% 6.07/6.01 (pred(pred(X1!59)) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19426, 15])).
% 6.07/6.01 tff(19428,plain,
% 6.07/6.01 (pred(pred(pred(X1!59))) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19427])).
% 6.07/6.01 tff(19429,plain,
% 6.07/6.01 (pred(pred(pred(X1!59))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19428, 25])).
% 6.07/6.01 tff(19430,plain,
% 6.07/6.01 (pred(pred(pred(pred(X1!59)))) = pred(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19429])).
% 6.07/6.01 tff(19431,plain,
% 6.07/6.01 (pred(pred(pred(pred(X1!59)))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19430, 24])).
% 6.07/6.01 tff(19432,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(X1!59))))) = pred(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19431])).
% 6.07/6.01 tff(19433,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(X1!59))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19432, 23])).
% 6.07/6.01 tff(19434,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19433])).
% 6.07/6.01 tff(19435,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19434, 22])).
% 6.07/6.01 tff(19436,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19435])).
% 6.07/6.01 tff(19437,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[19436, 21])).
% 6.07/6.01 tff(19438,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19437])).
% 6.07/6.01 tff(19439,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19438, 20])).
% 6.07/6.01 tff(19440,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19439])).
% 6.07/6.01 tff(19441,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19440, 19])).
% 6.07/6.01 tff(19442,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19441])).
% 6.07/6.01 tff(19443,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19442, 18])).
% 6.07/6.01 tff(19444,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19443])).
% 6.07/6.01 tff(19445,plain,
% 6.07/6.01 (NPX1!35 = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[280, 19444, 17])).
% 6.07/6.01 tff(19446,plain,
% 6.07/6.01 (succ(NPX1!35) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19445])).
% 6.07/6.01 tff(19447,plain,
% 6.07/6.01 (succ(NPX1!35) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19446, 30])).
% 6.07/6.01 tff(19448,plain,
% 6.07/6.01 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n6, n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19447, 19416])).
% 6.07/6.01 tff(19449,plain,
% 6.07/6.01 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19448, 674])).
% 6.07/6.01 tff(19450,plain,
% 6.07/6.01 (succ(X1!59) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19423])).
% 6.07/6.01 tff(19451,plain,
% 6.07/6.01 (succ(X1!59) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19450, 30])).
% 6.07/6.01 tff(19452,plain,
% 6.07/6.01 (succ(succ(X1!59)) = succ(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19451])).
% 6.07/6.01 tff(19453,plain,
% 6.07/6.01 (succ(succ(X1!59)) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19452, 39])).
% 6.07/6.01 tff(19454,plain,
% 6.07/6.01 (succ(succ(succ(X1!59))) = succ(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19453])).
% 6.07/6.01 tff(19455,plain,
% 6.07/6.01 (succ(succ(succ(X1!59))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19454, 53])).
% 6.07/6.01 tff(19456,plain,
% 6.07/6.01 (succ(succ(succ(succ(X1!59)))) = succ(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19455])).
% 6.07/6.01 tff(19457,plain,
% 6.07/6.01 (succ(succ(succ(succ(X1!59)))) = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[19456, 45])).
% 6.07/6.01 tff(19458,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(X1!59))))) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19457])).
% 6.07/6.01 tff(19459,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(X1!59))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19458, 28])).
% 6.07/6.01 tff(19460,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19459])).
% 6.07/6.01 tff(19461,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19460, 42])).
% 6.07/6.01 tff(19462,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19461])).
% 6.07/6.01 tff(19463,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19462, 58])).
% 6.07/6.01 tff(19464,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19463])).
% 6.07/6.01 tff(19465,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19464, 36])).
% 6.07/6.01 tff(19466,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19465])).
% 6.07/6.01 tff(19467,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19466, 48])).
% 6.07/6.01 tff(19468,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19467])).
% 6.07/6.01 tff(19469,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19468, 14])).
% 6.07/6.01 tff(19470,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19469])).
% 6.07/6.01 tff(19471,plain,
% 6.07/6.01 (NSX1!33 = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[305, 19470, 33])).
% 6.07/6.01 tff(19472,plain,
% 6.07/6.01 (pred(NSX1!33) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19471])).
% 6.07/6.01 tff(19473,plain,
% 6.07/6.01 (pred(NSX1!33) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19472, 16])).
% 6.07/6.01 tff(19474,plain,
% 6.07/6.01 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n4, n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19473, 19449])).
% 6.07/6.01 tff(19475,plain,
% 6.07/6.01 (Y2!56 = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[310, 19474, 673])).
% 6.07/6.01 tff(19476,plain,
% 6.07/6.01 (pred(Y2!56) = pred(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19475])).
% 6.07/6.01 tff(19477,plain,
% 6.07/6.01 (pred(Y2!56) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19476, 20])).
% 6.07/6.01 tff(19478,plain,
% 6.07/6.01 (pred(pred(Y2!56)) = pred(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19477])).
% 6.07/6.01 tff(19479,plain,
% 6.07/6.01 (pred(pred(Y2!56)) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19478, 19])).
% 6.07/6.01 tff(19480,plain,
% 6.07/6.01 (pred(pred(pred(Y2!56))) = pred(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19479])).
% 6.07/6.01 tff(19481,plain,
% 6.07/6.01 (pred(pred(pred(Y2!56))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19480, 18])).
% 6.07/6.01 tff(19482,plain,
% 6.07/6.01 (pred(pred(pred(pred(Y2!56)))) = pred(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19481])).
% 6.07/6.01 tff(19483,plain,
% 6.07/6.01 (pred(pred(pred(pred(Y2!56)))) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19482, 17])).
% 6.07/6.01 tff(19484,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19483])).
% 6.07/6.01 tff(19485,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(Y2!56))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19484, 16])).
% 6.07/6.01 tff(19486,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19485])).
% 6.07/6.01 tff(19487,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19486, 15])).
% 6.07/6.01 tff(19488,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19487])).
% 6.07/6.01 tff(19489,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19488, 25])).
% 6.07/6.01 tff(19490,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19489])).
% 6.07/6.01 tff(19491,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19490, 24])).
% 6.07/6.01 tff(19492,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19491])).
% 6.07/6.01 tff(19493,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19492, 23])).
% 6.07/6.01 tff(19494,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19493])).
% 6.07/6.01 tff(19495,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19494, 22])).
% 6.07/6.01 tff(19496,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19495])).
% 6.07/6.01 tff(19497,plain,
% 6.07/6.01 (NPY2!30 = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[347, 19496, 21])).
% 6.07/6.01 tff(19498,plain,
% 6.07/6.01 (succ(NPY2!30) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19497])).
% 6.07/6.01 tff(19499,plain,
% 6.07/6.01 (succ(NPY2!30) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19498, 28])).
% 6.07/6.01 tff(19500,plain,
% 6.07/6.01 (succ(Y2!56) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19475])).
% 6.07/6.01 tff(19501,plain,
% 6.07/6.01 (succ(Y2!56) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19500, 28])).
% 6.07/6.01 tff(19502,plain,
% 6.07/6.01 (succ(succ(Y2!56)) = succ(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19501])).
% 6.07/6.01 tff(19503,plain,
% 6.07/6.01 (succ(succ(Y2!56)) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19502, 42])).
% 6.07/6.01 tff(19504,plain,
% 6.07/6.01 (succ(succ(succ(Y2!56))) = succ(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19503])).
% 6.07/6.01 tff(19505,plain,
% 6.07/6.01 (succ(succ(succ(Y2!56))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19504, 58])).
% 6.07/6.01 tff(19506,plain,
% 6.07/6.01 (succ(succ(succ(succ(Y2!56)))) = succ(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19505])).
% 6.07/6.01 tff(19507,plain,
% 6.07/6.01 (succ(succ(succ(succ(Y2!56)))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19506, 36])).
% 6.07/6.01 tff(19508,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19507])).
% 6.07/6.01 tff(19509,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(Y2!56))))) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19508, 48])).
% 6.07/6.01 tff(19510,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19509])).
% 6.07/6.01 tff(19511,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19510, 14])).
% 6.07/6.01 tff(19512,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19511])).
% 6.07/6.01 tff(19513,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19512, 33])).
% 6.07/6.01 tff(19514,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19513])).
% 6.07/6.01 tff(19515,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19514, 30])).
% 6.07/6.01 tff(19516,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19515])).
% 6.07/6.01 tff(19517,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19516, 39])).
% 6.07/6.01 tff(19518,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19517])).
% 6.07/6.01 tff(19519,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19518, 53])).
% 6.07/6.01 tff(19520,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19519])).
% 6.07/6.01 tff(19521,plain,
% 6.07/6.01 (NSY2!28 = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[370, 19520, 45])).
% 6.07/6.01 tff(19522,plain,
% 6.07/6.01 (pred(NSY2!28) = pred(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19521])).
% 6.07/6.01 tff(19523,plain,
% 6.07/6.01 (pred(NSY2!28) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19522, 20])).
% 6.07/6.01 tff(19524,plain,
% 6.07/6.01 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n8, n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19523, 19499])).
% 6.07/6.01 tff(19525,plain,
% 6.07/6.01 (sum(pred(NSY2!28), succ(NPY2!30)) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19524, 27])).
% 6.07/6.01 tff(19526,plain,
% 6.07/6.01 (sum(pred(Y1!58), succ(X1!59)) = sum(n4, n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19368, 19451])).
% 6.07/6.01 tff(19527,plain,
% 6.07/6.01 (sum(pred(Y1!58), succ(X1!59)) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19526, 12])).
% 6.07/6.01 tff(19528,plain,
% 6.07/6.01 (sum(pred(X1!59), succ(Y1!58)) = sum(n4, n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19425, 19392])).
% 6.07/6.01 tff(19529,plain,
% 6.07/6.01 (sum(pred(X1!59), succ(Y1!58)) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19528, 12])).
% 6.07/6.01 tff(19530,plain,
% 6.07/6.01 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n10, n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19529, 19527])).
% 6.07/6.01 tff(19531,plain,
% 6.07/6.01 (X2!57 = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[209, 19530, 29])).
% 6.07/6.01 tff(19532,plain,
% 6.07/6.01 (pred(X2!57) = pred(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19531])).
% 6.07/6.01 tff(19533,plain,
% 6.07/6.01 (pred(X2!57) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19532, 20])).
% 6.07/6.01 tff(19534,plain,
% 6.07/6.01 (pred(pred(X2!57)) = pred(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19533])).
% 6.07/6.01 tff(19535,plain,
% 6.07/6.01 (pred(pred(X2!57)) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19534, 19])).
% 6.07/6.01 tff(19536,plain,
% 6.07/6.01 (pred(pred(pred(X2!57))) = pred(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19535])).
% 6.07/6.01 tff(19537,plain,
% 6.07/6.01 (pred(pred(pred(X2!57))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19536, 18])).
% 6.07/6.01 tff(19538,plain,
% 6.07/6.01 (pred(pred(pred(pred(X2!57)))) = pred(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19537])).
% 6.07/6.01 tff(19539,plain,
% 6.07/6.01 (pred(pred(pred(pred(X2!57)))) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19538, 17])).
% 6.07/6.01 tff(19540,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(X2!57))))) = pred(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19539])).
% 6.07/6.01 tff(19541,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(X2!57))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19540, 16])).
% 6.07/6.01 tff(19542,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19541])).
% 6.07/6.01 tff(19543,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19542, 15])).
% 6.07/6.01 tff(19544,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19543])).
% 6.07/6.01 tff(19545,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19544, 25])).
% 6.07/6.01 tff(19546,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19545])).
% 6.07/6.01 tff(19547,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19546, 24])).
% 6.07/6.01 tff(19548,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19547])).
% 6.07/6.01 tff(19549,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19548, 23])).
% 6.07/6.01 tff(19550,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19549])).
% 6.07/6.01 tff(19551,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19550, 22])).
% 6.07/6.01 tff(19552,plain,
% 6.07/6.01 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19551])).
% 6.07/6.01 tff(19553,plain,
% 6.07/6.01 (NPX2!31 = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[395, 19552, 21])).
% 6.07/6.01 tff(19554,plain,
% 6.07/6.01 (succ(NPX2!31) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19553])).
% 6.07/6.01 tff(19555,plain,
% 6.07/6.01 (succ(NPX2!31) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19554, 28])).
% 6.07/6.01 tff(19556,plain,
% 6.07/6.01 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n10, n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19555, 19525])).
% 6.07/6.01 tff(19557,plain,
% 6.07/6.01 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19556, 69])).
% 6.07/6.01 tff(19558,plain,
% 6.07/6.01 (succ(X2!57) = succ(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19531])).
% 6.07/6.01 tff(19559,plain,
% 6.07/6.01 (succ(X2!57) = n10),
% 6.07/6.01 inference(transitivity,[status(thm)],[19558, 28])).
% 6.07/6.01 tff(19560,plain,
% 6.07/6.01 (succ(succ(X2!57)) = succ(n10)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19559])).
% 6.07/6.01 tff(19561,plain,
% 6.07/6.01 (succ(succ(X2!57)) = n0),
% 6.07/6.01 inference(transitivity,[status(thm)],[19560, 42])).
% 6.07/6.01 tff(19562,plain,
% 6.07/6.01 (succ(succ(succ(X2!57))) = succ(n0)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19561])).
% 6.07/6.01 tff(19563,plain,
% 6.07/6.01 (succ(succ(succ(X2!57))) = n1),
% 6.07/6.01 inference(transitivity,[status(thm)],[19562, 58])).
% 6.07/6.01 tff(19564,plain,
% 6.07/6.01 (succ(succ(succ(succ(X2!57)))) = succ(n1)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19563])).
% 6.07/6.01 tff(19565,plain,
% 6.07/6.01 (succ(succ(succ(succ(X2!57)))) = n2),
% 6.07/6.01 inference(transitivity,[status(thm)],[19564, 36])).
% 6.07/6.01 tff(19566,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(X2!57))))) = succ(n2)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19565])).
% 6.07/6.01 tff(19567,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(X2!57))))) = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[19566, 48])).
% 6.07/6.01 tff(19568,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19567])).
% 6.07/6.01 tff(19569,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n4),
% 6.07/6.01 inference(transitivity,[status(thm)],[19568, 14])).
% 6.07/6.01 tff(19570,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n4)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19569])).
% 6.07/6.01 tff(19571,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n5),
% 6.07/6.01 inference(transitivity,[status(thm)],[19570, 33])).
% 6.07/6.01 tff(19572,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n5)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19571])).
% 6.07/6.01 tff(19573,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n6),
% 6.07/6.01 inference(transitivity,[status(thm)],[19572, 30])).
% 6.07/6.01 tff(19574,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19573])).
% 6.07/6.01 tff(19575,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n7),
% 6.07/6.01 inference(transitivity,[status(thm)],[19574, 39])).
% 6.07/6.01 tff(19576,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n7)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19575])).
% 6.07/6.01 tff(19577,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19576, 53])).
% 6.07/6.01 tff(19578,plain,
% 6.07/6.01 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n8)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19577])).
% 6.07/6.01 tff(19579,plain,
% 6.07/6.01 (NSX2!29 = n9),
% 6.07/6.01 inference(transitivity,[status(thm)],[420, 19578, 45])).
% 6.07/6.01 tff(19580,plain,
% 6.07/6.01 (pred(NSX2!29) = pred(n9)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19579])).
% 6.07/6.01 tff(19581,plain,
% 6.07/6.01 (pred(NSX2!29) = n8),
% 6.07/6.01 inference(transitivity,[status(thm)],[19580, 20])).
% 6.07/6.01 tff(19582,plain,
% 6.07/6.01 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n8, n6)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19581, 19557])).
% 6.07/6.01 tff(19583,plain,
% 6.07/6.01 (Y3!54 = n3),
% 6.07/6.01 inference(transitivity,[status(thm)],[425, 19582, 98])).
% 6.07/6.01 tff(19584,plain,
% 6.07/6.01 (pred(Y3!54) = pred(n3)),
% 6.07/6.01 inference(monotonicity,[status(thm)],[19583])).
% 6.07/6.01 tff(19585,plain,
% 6.07/6.01 (pred(Y3!54) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19584, 25])).
% 6.07/6.02 tff(19586,plain,
% 6.07/6.02 (pred(pred(Y3!54)) = pred(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19585])).
% 6.07/6.02 tff(19587,plain,
% 6.07/6.02 (pred(pred(Y3!54)) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19586, 24])).
% 6.07/6.02 tff(19588,plain,
% 6.07/6.02 (pred(pred(pred(Y3!54))) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19587])).
% 6.07/6.02 tff(19589,plain,
% 6.07/6.02 (pred(pred(pred(Y3!54))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19588, 23])).
% 6.07/6.02 tff(19590,plain,
% 6.07/6.02 (pred(pred(pred(pred(Y3!54)))) = pred(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19589])).
% 6.07/6.02 tff(19591,plain,
% 6.07/6.02 (pred(pred(pred(pred(Y3!54)))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19590, 22])).
% 6.07/6.02 tff(19592,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19591])).
% 6.07/6.02 tff(19593,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(Y3!54))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19592, 21])).
% 6.07/6.02 tff(19594,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19593])).
% 6.07/6.02 tff(19595,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19594, 20])).
% 6.07/6.02 tff(19596,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19595])).
% 6.07/6.02 tff(19597,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19596, 19])).
% 6.07/6.02 tff(19598,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19597])).
% 6.07/6.02 tff(19599,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19598, 18])).
% 6.07/6.02 tff(19600,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19599])).
% 6.07/6.02 tff(19601,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19600, 17])).
% 6.07/6.02 tff(19602,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19601])).
% 6.07/6.02 tff(19603,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19602, 16])).
% 6.07/6.02 tff(19604,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19603])).
% 6.07/6.02 tff(19605,plain,
% 6.07/6.02 (NPY3!26 = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[462, 19604, 15])).
% 6.07/6.02 tff(19606,plain,
% 6.07/6.02 (succ(NPY3!26) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19605])).
% 6.07/6.02 tff(19607,plain,
% 6.07/6.02 (succ(NPY3!26) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19606, 14])).
% 6.07/6.02 tff(19608,plain,
% 6.07/6.02 (succ(Y3!54) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19583])).
% 6.07/6.02 tff(19609,plain,
% 6.07/6.02 (succ(Y3!54) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19608, 14])).
% 6.07/6.02 tff(19610,plain,
% 6.07/6.02 (succ(succ(Y3!54)) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19609])).
% 6.07/6.02 tff(19611,plain,
% 6.07/6.02 (succ(succ(Y3!54)) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19610, 33])).
% 6.07/6.02 tff(19612,plain,
% 6.07/6.02 (succ(succ(succ(Y3!54))) = succ(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19611])).
% 6.07/6.02 tff(19613,plain,
% 6.07/6.02 (succ(succ(succ(Y3!54))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19612, 30])).
% 6.07/6.02 tff(19614,plain,
% 6.07/6.02 (succ(succ(succ(succ(Y3!54)))) = succ(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19613])).
% 6.07/6.02 tff(19615,plain,
% 6.07/6.02 (succ(succ(succ(succ(Y3!54)))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19614, 39])).
% 6.07/6.02 tff(19616,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19615])).
% 6.07/6.02 tff(19617,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(Y3!54))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19616, 53])).
% 6.07/6.02 tff(19618,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19617])).
% 6.07/6.02 tff(19619,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19618, 45])).
% 6.07/6.02 tff(19620,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19619])).
% 6.07/6.02 tff(19621,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19620, 28])).
% 6.07/6.02 tff(19622,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19621])).
% 6.07/6.02 tff(19623,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19622, 42])).
% 6.07/6.02 tff(19624,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19623])).
% 6.07/6.02 tff(19625,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19624, 58])).
% 6.07/6.02 tff(19626,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19625])).
% 6.07/6.02 tff(19627,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19626, 36])).
% 6.07/6.02 tff(19628,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19627])).
% 6.07/6.02 tff(19629,plain,
% 6.07/6.02 (NSY3!24 = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[485, 19628, 48])).
% 6.07/6.02 tff(19630,plain,
% 6.07/6.02 (pred(NSY3!24) = pred(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19629])).
% 6.07/6.02 tff(19631,plain,
% 6.07/6.02 (pred(NSY3!24) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19630, 25])).
% 6.07/6.02 tff(19632,plain,
% 6.07/6.02 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n2, n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19631, 19607])).
% 6.07/6.02 tff(19633,plain,
% 6.07/6.02 (sum(pred(NSY3!24), succ(NPY3!26)) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19632, 13])).
% 6.07/6.02 tff(19634,plain,
% 6.07/6.02 (sum(pred(Y2!56), succ(X2!57)) = sum(n8, n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19477, 19559])).
% 6.07/6.02 tff(19635,plain,
% 6.07/6.02 (sum(pred(Y2!56), succ(X2!57)) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19634, 27])).
% 6.07/6.02 tff(19636,plain,
% 6.07/6.02 (sum(pred(X2!57), succ(Y2!56)) = sum(n8, n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19533, 19501])).
% 6.07/6.02 tff(19637,plain,
% 6.07/6.02 (sum(pred(X2!57), succ(Y2!56)) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19636, 27])).
% 6.07/6.02 tff(19638,plain,
% 6.07/6.02 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n7, n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19637, 19635])).
% 6.07/6.02 tff(19639,plain,
% 6.07/6.02 (X3!55 = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[323, 19638, 26])).
% 6.07/6.02 tff(19640,plain,
% 6.07/6.02 (pred(X3!55) = pred(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19639])).
% 6.07/6.02 tff(19641,plain,
% 6.07/6.02 (pred(X3!55) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19640, 25])).
% 6.07/6.02 tff(19642,plain,
% 6.07/6.02 (pred(pred(X3!55)) = pred(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19641])).
% 6.07/6.02 tff(19643,plain,
% 6.07/6.02 (pred(pred(X3!55)) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19642, 24])).
% 6.07/6.02 tff(19644,plain,
% 6.07/6.02 (pred(pred(pred(X3!55))) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19643])).
% 6.07/6.02 tff(19645,plain,
% 6.07/6.02 (pred(pred(pred(X3!55))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19644, 23])).
% 6.07/6.02 tff(19646,plain,
% 6.07/6.02 (pred(pred(pred(pred(X3!55)))) = pred(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19645])).
% 6.07/6.02 tff(19647,plain,
% 6.07/6.02 (pred(pred(pred(pred(X3!55)))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19646, 22])).
% 6.07/6.02 tff(19648,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(X3!55))))) = pred(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19647])).
% 6.07/6.02 tff(19649,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(X3!55))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19648, 21])).
% 6.07/6.02 tff(19650,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19649])).
% 6.07/6.02 tff(19651,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19650, 20])).
% 6.07/6.02 tff(19652,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19651])).
% 6.07/6.02 tff(19653,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19652, 19])).
% 6.07/6.02 tff(19654,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19653])).
% 6.07/6.02 tff(19655,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19654, 18])).
% 6.07/6.02 tff(19656,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19655])).
% 6.07/6.02 tff(19657,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19656, 17])).
% 6.07/6.02 tff(19658,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19657])).
% 6.07/6.02 tff(19659,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19658, 16])).
% 6.07/6.02 tff(19660,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19659])).
% 6.07/6.02 tff(19661,plain,
% 6.07/6.02 (NPX3!27 = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[510, 19660, 15])).
% 6.07/6.02 tff(19662,plain,
% 6.07/6.02 (succ(NPX3!27) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19661])).
% 6.07/6.02 tff(19663,plain,
% 6.07/6.02 (succ(NPX3!27) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19662, 14])).
% 6.07/6.02 tff(19664,plain,
% 6.07/6.02 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n4, n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19663, 19633])).
% 6.07/6.02 tff(19665,plain,
% 6.07/6.02 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19664, 12])).
% 6.07/6.02 tff(19666,plain,
% 6.07/6.02 (succ(X3!55) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19639])).
% 6.07/6.02 tff(19667,plain,
% 6.07/6.02 (succ(X3!55) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19666, 14])).
% 6.07/6.02 tff(19668,plain,
% 6.07/6.02 (succ(succ(X3!55)) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19667])).
% 6.07/6.02 tff(19669,plain,
% 6.07/6.02 (succ(succ(X3!55)) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19668, 33])).
% 6.07/6.02 tff(19670,plain,
% 6.07/6.02 (succ(succ(succ(X3!55))) = succ(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19669])).
% 6.07/6.02 tff(19671,plain,
% 6.07/6.02 (succ(succ(succ(X3!55))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19670, 30])).
% 6.07/6.02 tff(19672,plain,
% 6.07/6.02 (succ(succ(succ(succ(X3!55)))) = succ(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19671])).
% 6.07/6.02 tff(19673,plain,
% 6.07/6.02 (succ(succ(succ(succ(X3!55)))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19672, 39])).
% 6.07/6.02 tff(19674,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(X3!55))))) = succ(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19673])).
% 6.07/6.02 tff(19675,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(X3!55))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19674, 53])).
% 6.07/6.02 tff(19676,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19675])).
% 6.07/6.02 tff(19677,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19676, 45])).
% 6.07/6.02 tff(19678,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19677])).
% 6.07/6.02 tff(19679,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19678, 28])).
% 6.07/6.02 tff(19680,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19679])).
% 6.07/6.02 tff(19681,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19680, 42])).
% 6.07/6.02 tff(19682,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19681])).
% 6.07/6.02 tff(19683,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19682, 58])).
% 6.07/6.02 tff(19684,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19683])).
% 6.07/6.02 tff(19685,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19684, 36])).
% 6.07/6.02 tff(19686,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19685])).
% 6.07/6.02 tff(19687,plain,
% 6.07/6.02 (NSX3!25 = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[535, 19686, 48])).
% 6.07/6.02 tff(19688,plain,
% 6.07/6.02 (pred(NSX3!25) = pred(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19687])).
% 6.07/6.02 tff(19689,plain,
% 6.07/6.02 (pred(NSX3!25) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19688, 25])).
% 6.07/6.02 tff(19690,plain,
% 6.07/6.02 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n2, n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19689, 19665])).
% 6.07/6.02 tff(19691,plain,
% 6.07/6.02 (Y4!52 = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[540, 19690, 327])).
% 6.07/6.02 tff(19692,plain,
% 6.07/6.02 (pred(Y4!52) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19691])).
% 6.07/6.02 tff(19693,plain,
% 6.07/6.02 (pred(Y4!52) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19692, 23])).
% 6.07/6.02 tff(19694,plain,
% 6.07/6.02 (pred(pred(Y4!52)) = pred(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19693])).
% 6.07/6.02 tff(19695,plain,
% 6.07/6.02 (pred(pred(Y4!52)) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19694, 22])).
% 6.07/6.02 tff(19696,plain,
% 6.07/6.02 (pred(pred(pred(Y4!52))) = pred(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19695])).
% 6.07/6.02 tff(19697,plain,
% 6.07/6.02 (pred(pred(pred(Y4!52))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19696, 21])).
% 6.07/6.02 tff(19698,plain,
% 6.07/6.02 (pred(pred(pred(pred(Y4!52)))) = pred(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19697])).
% 6.07/6.02 tff(19699,plain,
% 6.07/6.02 (pred(pred(pred(pred(Y4!52)))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19698, 20])).
% 6.07/6.02 tff(19700,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19699])).
% 6.07/6.02 tff(19701,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(Y4!52))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19700, 19])).
% 6.07/6.02 tff(19702,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19701])).
% 6.07/6.02 tff(19703,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19702, 18])).
% 6.07/6.02 tff(19704,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19703])).
% 6.07/6.02 tff(19705,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19704, 17])).
% 6.07/6.02 tff(19706,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19705])).
% 6.07/6.02 tff(19707,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19706, 16])).
% 6.07/6.02 tff(19708,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19707])).
% 6.07/6.02 tff(19709,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19708, 15])).
% 6.07/6.02 tff(19710,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19709])).
% 6.07/6.02 tff(19711,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19710, 25])).
% 6.07/6.02 tff(19712,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19711])).
% 6.07/6.02 tff(19713,plain,
% 6.07/6.02 (NPY4!22 = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[578, 19712, 24])).
% 6.07/6.02 tff(19714,plain,
% 6.07/6.02 (succ(NPY4!22) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19713])).
% 6.07/6.02 tff(19715,plain,
% 6.07/6.02 (succ(NPY4!22) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19714, 36])).
% 6.07/6.02 tff(19716,plain,
% 6.07/6.02 (succ(Y4!52) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19691])).
% 6.07/6.02 tff(19717,plain,
% 6.07/6.02 (succ(Y4!52) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19716, 36])).
% 6.07/6.02 tff(19718,plain,
% 6.07/6.02 (succ(succ(Y4!52)) = succ(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19717])).
% 6.07/6.02 tff(19719,plain,
% 6.07/6.02 (succ(succ(Y4!52)) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19718, 48])).
% 6.07/6.02 tff(19720,plain,
% 6.07/6.02 (succ(succ(succ(Y4!52))) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19719])).
% 6.07/6.02 tff(19721,plain,
% 6.07/6.02 (succ(succ(succ(Y4!52))) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19720, 14])).
% 6.07/6.02 tff(19722,plain,
% 6.07/6.02 (succ(succ(succ(succ(Y4!52)))) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19721])).
% 6.07/6.02 tff(19723,plain,
% 6.07/6.02 (succ(succ(succ(succ(Y4!52)))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19722, 33])).
% 6.07/6.02 tff(19724,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19723])).
% 6.07/6.02 tff(19725,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(Y4!52))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19724, 30])).
% 6.07/6.02 tff(19726,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19725])).
% 6.07/6.02 tff(19727,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19726, 39])).
% 6.07/6.02 tff(19728,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19727])).
% 6.07/6.02 tff(19729,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19728, 53])).
% 6.07/6.02 tff(19730,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19729])).
% 6.07/6.02 tff(19731,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19730, 45])).
% 6.07/6.02 tff(19732,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19731])).
% 6.07/6.02 tff(19733,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19732, 28])).
% 6.07/6.02 tff(19734,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19733])).
% 6.07/6.02 tff(19735,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19734, 42])).
% 6.07/6.02 tff(19736,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19735])).
% 6.07/6.02 tff(19737,plain,
% 6.07/6.02 (NSY4!20 = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[601, 19736, 58])).
% 6.07/6.02 tff(19738,plain,
% 6.07/6.02 (pred(NSY4!20) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19737])).
% 6.07/6.02 tff(19739,plain,
% 6.07/6.02 (pred(NSY4!20) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19738, 23])).
% 6.07/6.02 tff(19740,plain,
% 6.07/6.02 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n0, n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19739, 19715])).
% 6.07/6.02 tff(19741,plain,
% 6.07/6.02 (sum(pred(NSY4!20), succ(NPY4!22)) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19740, 35])).
% 6.07/6.02 tff(19742,plain,
% 6.07/6.02 (sum(pred(Y3!54), succ(X3!55)) = sum(n2, n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19585, 19667])).
% 6.07/6.02 tff(19743,plain,
% 6.07/6.02 (sum(pred(Y3!54), succ(X3!55)) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19742, 13])).
% 6.07/6.02 tff(19744,plain,
% 6.07/6.02 (sum(pred(X3!55), succ(Y3!54)) = sum(n2, n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19641, 19609])).
% 6.07/6.02 tff(19745,plain,
% 6.07/6.02 (sum(pred(X3!55), succ(Y3!54)) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19744, 13])).
% 6.07/6.02 tff(19746,plain,
% 6.07/6.02 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n6, n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19745, 19743])).
% 6.07/6.02 tff(19747,plain,
% 6.07/6.02 (X4!53 = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[438, 19746, 37])).
% 6.07/6.02 tff(19748,plain,
% 6.07/6.02 (pred(X4!53) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19747])).
% 6.07/6.02 tff(19749,plain,
% 6.07/6.02 (pred(X4!53) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19748, 23])).
% 6.07/6.02 tff(19750,plain,
% 6.07/6.02 (pred(pred(X4!53)) = pred(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19749])).
% 6.07/6.02 tff(19751,plain,
% 6.07/6.02 (pred(pred(X4!53)) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19750, 22])).
% 6.07/6.02 tff(19752,plain,
% 6.07/6.02 (pred(pred(pred(X4!53))) = pred(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19751])).
% 6.07/6.02 tff(19753,plain,
% 6.07/6.02 (pred(pred(pred(X4!53))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19752, 21])).
% 6.07/6.02 tff(19754,plain,
% 6.07/6.02 (pred(pred(pred(pred(X4!53)))) = pred(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19753])).
% 6.07/6.02 tff(19755,plain,
% 6.07/6.02 (pred(pred(pred(pred(X4!53)))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19754, 20])).
% 6.07/6.02 tff(19756,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(X4!53))))) = pred(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19755])).
% 6.07/6.02 tff(19757,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(X4!53))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19756, 19])).
% 6.07/6.02 tff(19758,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19757])).
% 6.07/6.02 tff(19759,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19758, 18])).
% 6.07/6.02 tff(19760,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19759])).
% 6.07/6.02 tff(19761,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19760, 17])).
% 6.07/6.02 tff(19762,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19761])).
% 6.07/6.02 tff(19763,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19762, 16])).
% 6.07/6.02 tff(19764,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19763])).
% 6.07/6.02 tff(19765,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19764, 15])).
% 6.07/6.02 tff(19766,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19765])).
% 6.07/6.02 tff(19767,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19766, 25])).
% 6.07/6.02 tff(19768,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19767])).
% 6.07/6.02 tff(19769,plain,
% 6.07/6.02 (NPX4!23 = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[626, 19768, 24])).
% 6.07/6.02 tff(19770,plain,
% 6.07/6.02 (succ(NPX4!23) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19769])).
% 6.07/6.02 tff(19771,plain,
% 6.07/6.02 (succ(NPX4!23) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19770, 36])).
% 6.07/6.02 tff(19772,plain,
% 6.07/6.02 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n2, n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19771, 19741])).
% 6.07/6.02 tff(19773,plain,
% 6.07/6.02 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19772, 34])).
% 6.07/6.02 tff(19774,plain,
% 6.07/6.02 (succ(X4!53) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19747])).
% 6.07/6.02 tff(19775,plain,
% 6.07/6.02 (succ(X4!53) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19774, 36])).
% 6.07/6.02 tff(19776,plain,
% 6.07/6.02 (succ(succ(X4!53)) = succ(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19775])).
% 6.07/6.02 tff(19777,plain,
% 6.07/6.02 (succ(succ(X4!53)) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19776, 48])).
% 6.07/6.02 tff(19778,plain,
% 6.07/6.02 (succ(succ(succ(X4!53))) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19777])).
% 6.07/6.02 tff(19779,plain,
% 6.07/6.02 (succ(succ(succ(X4!53))) = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[19778, 14])).
% 6.07/6.02 tff(19780,plain,
% 6.07/6.02 (succ(succ(succ(succ(X4!53)))) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19779])).
% 6.07/6.02 tff(19781,plain,
% 6.07/6.02 (succ(succ(succ(succ(X4!53)))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19780, 33])).
% 6.07/6.02 tff(19782,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(X4!53))))) = succ(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19781])).
% 6.07/6.02 tff(19783,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(X4!53))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19782, 30])).
% 6.07/6.02 tff(19784,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19783])).
% 6.07/6.02 tff(19785,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19784, 39])).
% 6.07/6.02 tff(19786,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19785])).
% 6.07/6.02 tff(19787,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19786, 53])).
% 6.07/6.02 tff(19788,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19787])).
% 6.07/6.02 tff(19789,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19788, 45])).
% 6.07/6.02 tff(19790,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19789])).
% 6.07/6.02 tff(19791,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19790, 28])).
% 6.07/6.02 tff(19792,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19791])).
% 6.07/6.02 tff(19793,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19792, 42])).
% 6.07/6.02 tff(19794,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19793])).
% 6.07/6.02 tff(19795,plain,
% 6.07/6.02 (NSX4!21 = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[651, 19794, 58])).
% 6.07/6.02 tff(19796,plain,
% 6.07/6.02 (pred(NSX4!21) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19795])).
% 6.07/6.02 tff(19797,plain,
% 6.07/6.02 (pred(NSX4!21) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19796, 23])).
% 6.07/6.02 tff(19798,plain,
% 6.07/6.02 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n0, n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19797, 19773])).
% 6.07/6.02 tff(19799,plain,
% 6.07/6.02 (Y5!50 = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[656, 19798, 442])).
% 6.07/6.02 tff(19800,plain,
% 6.07/6.02 (pred(Y5!50) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19799])).
% 6.07/6.02 tff(19801,plain,
% 6.07/6.02 (pred(Y5!50) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19800, 15])).
% 6.07/6.02 tff(19802,plain,
% 6.07/6.02 (pred(pred(Y5!50)) = pred(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19801])).
% 6.07/6.02 tff(19803,plain,
% 6.07/6.02 (pred(pred(Y5!50)) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19802, 25])).
% 6.07/6.02 tff(19804,plain,
% 6.07/6.02 (pred(pred(pred(Y5!50))) = pred(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19803])).
% 6.07/6.02 tff(19805,plain,
% 6.07/6.02 (pred(pred(pred(Y5!50))) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19804, 24])).
% 6.07/6.02 tff(19806,plain,
% 6.07/6.02 (pred(pred(pred(pred(Y5!50)))) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19805])).
% 6.07/6.02 tff(19807,plain,
% 6.07/6.02 (pred(pred(pred(pred(Y5!50)))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19806, 23])).
% 6.07/6.02 tff(19808,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19807])).
% 6.07/6.02 tff(19809,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(Y5!50))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19808, 22])).
% 6.07/6.02 tff(19810,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19809])).
% 6.07/6.02 tff(19811,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19810, 21])).
% 6.07/6.02 tff(19812,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19811])).
% 6.07/6.02 tff(19813,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19812, 20])).
% 6.07/6.02 tff(19814,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19813])).
% 6.07/6.02 tff(19815,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19814, 19])).
% 6.07/6.02 tff(19816,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19815])).
% 6.07/6.02 tff(19817,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19816, 18])).
% 6.07/6.02 tff(19818,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19817])).
% 6.07/6.02 tff(19819,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19818, 17])).
% 6.07/6.02 tff(19820,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19819])).
% 6.07/6.02 tff(19821,plain,
% 6.07/6.02 (NPY5!18 = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[694, 19820, 16])).
% 6.07/6.02 tff(19822,plain,
% 6.07/6.02 (succ(NPY5!18) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19821])).
% 6.07/6.02 tff(19823,plain,
% 6.07/6.02 (succ(NPY5!18) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19822, 33])).
% 6.07/6.02 tff(19824,plain,
% 6.07/6.02 (succ(Y5!50) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19799])).
% 6.07/6.02 tff(19825,plain,
% 6.07/6.02 (succ(Y5!50) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19824, 33])).
% 6.07/6.02 tff(19826,plain,
% 6.07/6.02 (succ(succ(Y5!50)) = succ(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19825])).
% 6.07/6.02 tff(19827,plain,
% 6.07/6.02 (succ(succ(Y5!50)) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19826, 30])).
% 6.07/6.02 tff(19828,plain,
% 6.07/6.02 (succ(succ(succ(Y5!50))) = succ(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19827])).
% 6.07/6.02 tff(19829,plain,
% 6.07/6.02 (succ(succ(succ(Y5!50))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19828, 39])).
% 6.07/6.02 tff(19830,plain,
% 6.07/6.02 (succ(succ(succ(succ(Y5!50)))) = succ(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19829])).
% 6.07/6.02 tff(19831,plain,
% 6.07/6.02 (succ(succ(succ(succ(Y5!50)))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19830, 53])).
% 6.07/6.02 tff(19832,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19831])).
% 6.07/6.02 tff(19833,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(Y5!50))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19832, 45])).
% 6.07/6.02 tff(19834,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19833])).
% 6.07/6.02 tff(19835,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19834, 28])).
% 6.07/6.02 tff(19836,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19835])).
% 6.07/6.02 tff(19837,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19836, 42])).
% 6.07/6.02 tff(19838,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19837])).
% 6.07/6.02 tff(19839,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19838, 58])).
% 6.07/6.02 tff(19840,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19839])).
% 6.07/6.02 tff(19841,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19840, 36])).
% 6.07/6.02 tff(19842,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19841])).
% 6.07/6.02 tff(19843,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19842, 48])).
% 6.07/6.02 tff(19844,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19843])).
% 6.07/6.02 tff(19845,plain,
% 6.07/6.02 (NSY5!16 = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[717, 19844, 14])).
% 6.07/6.02 tff(19846,plain,
% 6.07/6.02 (pred(NSY5!16) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19845])).
% 6.07/6.02 tff(19847,plain,
% 6.07/6.02 (pred(NSY5!16) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19846, 15])).
% 6.07/6.02 tff(19848,plain,
% 6.07/6.02 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n3, n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19847, 19823])).
% 6.07/6.02 tff(19849,plain,
% 6.07/6.02 (sum(pred(NSY5!16), succ(NPY5!18)) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19848, 32])).
% 6.07/6.02 tff(19850,plain,
% 6.07/6.02 (sum(pred(Y4!52), succ(X4!53)) = sum(n0, n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19693, 19775])).
% 6.07/6.02 tff(19851,plain,
% 6.07/6.02 (sum(pred(Y4!52), succ(X4!53)) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19850, 35])).
% 6.07/6.02 tff(19852,plain,
% 6.07/6.02 (sum(pred(X4!53), succ(Y4!52)) = sum(n0, n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19749, 19717])).
% 6.07/6.02 tff(19853,plain,
% 6.07/6.02 (sum(pred(X4!53), succ(Y4!52)) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19852, 35])).
% 6.07/6.02 tff(19854,plain,
% 6.07/6.02 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n2, n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19853, 19851])).
% 6.07/6.02 tff(19855,plain,
% 6.07/6.02 (X5!51 = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[553, 19854, 34])).
% 6.07/6.02 tff(19856,plain,
% 6.07/6.02 (pred(X5!51) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19855])).
% 6.07/6.02 tff(19857,plain,
% 6.07/6.02 (pred(X5!51) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19856, 15])).
% 6.07/6.02 tff(19858,plain,
% 6.07/6.02 (pred(pred(X5!51)) = pred(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19857])).
% 6.07/6.02 tff(19859,plain,
% 6.07/6.02 (pred(pred(X5!51)) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19858, 25])).
% 6.07/6.02 tff(19860,plain,
% 6.07/6.02 (pred(pred(pred(X5!51))) = pred(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19859])).
% 6.07/6.02 tff(19861,plain,
% 6.07/6.02 (pred(pred(pred(X5!51))) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19860, 24])).
% 6.07/6.02 tff(19862,plain,
% 6.07/6.02 (pred(pred(pred(pred(X5!51)))) = pred(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19861])).
% 6.07/6.02 tff(19863,plain,
% 6.07/6.02 (pred(pred(pred(pred(X5!51)))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19862, 23])).
% 6.07/6.02 tff(19864,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(X5!51))))) = pred(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19863])).
% 6.07/6.02 tff(19865,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(X5!51))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19864, 22])).
% 6.07/6.02 tff(19866,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19865])).
% 6.07/6.02 tff(19867,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19866, 21])).
% 6.07/6.02 tff(19868,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19867])).
% 6.07/6.02 tff(19869,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19868, 20])).
% 6.07/6.02 tff(19870,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19869])).
% 6.07/6.02 tff(19871,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19870, 19])).
% 6.07/6.02 tff(19872,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19871])).
% 6.07/6.02 tff(19873,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19872, 18])).
% 6.07/6.02 tff(19874,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19873])).
% 6.07/6.02 tff(19875,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19874, 17])).
% 6.07/6.02 tff(19876,plain,
% 6.07/6.02 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19875])).
% 6.07/6.02 tff(19877,plain,
% 6.07/6.02 (NPX5!19 = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[742, 19876, 16])).
% 6.07/6.02 tff(19878,plain,
% 6.07/6.02 (succ(NPX5!19) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19877])).
% 6.07/6.02 tff(19879,plain,
% 6.07/6.02 (succ(NPX5!19) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19878, 33])).
% 6.07/6.02 tff(19880,plain,
% 6.07/6.02 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n5, n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19879, 19849])).
% 6.07/6.02 tff(19881,plain,
% 6.07/6.02 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19880, 558])).
% 6.07/6.02 tff(19882,plain,
% 6.07/6.02 (succ(X5!51) = succ(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19855])).
% 6.07/6.02 tff(19883,plain,
% 6.07/6.02 (succ(X5!51) = n5),
% 6.07/6.02 inference(transitivity,[status(thm)],[19882, 33])).
% 6.07/6.02 tff(19884,plain,
% 6.07/6.02 (succ(succ(X5!51)) = succ(n5)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19883])).
% 6.07/6.02 tff(19885,plain,
% 6.07/6.02 (succ(succ(X5!51)) = n6),
% 6.07/6.02 inference(transitivity,[status(thm)],[19884, 30])).
% 6.07/6.02 tff(19886,plain,
% 6.07/6.02 (succ(succ(succ(X5!51))) = succ(n6)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19885])).
% 6.07/6.02 tff(19887,plain,
% 6.07/6.02 (succ(succ(succ(X5!51))) = n7),
% 6.07/6.02 inference(transitivity,[status(thm)],[19886, 39])).
% 6.07/6.02 tff(19888,plain,
% 6.07/6.02 (succ(succ(succ(succ(X5!51)))) = succ(n7)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19887])).
% 6.07/6.02 tff(19889,plain,
% 6.07/6.02 (succ(succ(succ(succ(X5!51)))) = n8),
% 6.07/6.02 inference(transitivity,[status(thm)],[19888, 53])).
% 6.07/6.02 tff(19890,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(X5!51))))) = succ(n8)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19889])).
% 6.07/6.02 tff(19891,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(X5!51))))) = n9),
% 6.07/6.02 inference(transitivity,[status(thm)],[19890, 45])).
% 6.07/6.02 tff(19892,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n9)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19891])).
% 6.07/6.02 tff(19893,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n10),
% 6.07/6.02 inference(transitivity,[status(thm)],[19892, 28])).
% 6.07/6.02 tff(19894,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n10)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19893])).
% 6.07/6.02 tff(19895,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n0),
% 6.07/6.02 inference(transitivity,[status(thm)],[19894, 42])).
% 6.07/6.02 tff(19896,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n0)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19895])).
% 6.07/6.02 tff(19897,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n1),
% 6.07/6.02 inference(transitivity,[status(thm)],[19896, 58])).
% 6.07/6.02 tff(19898,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n1)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19897])).
% 6.07/6.02 tff(19899,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n2),
% 6.07/6.02 inference(transitivity,[status(thm)],[19898, 36])).
% 6.07/6.02 tff(19900,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19899])).
% 6.07/6.02 tff(19901,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19900, 48])).
% 6.07/6.02 tff(19902,plain,
% 6.07/6.02 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n3)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19901])).
% 6.07/6.02 tff(19903,plain,
% 6.07/6.02 (NSX5!17 = n4),
% 6.07/6.02 inference(transitivity,[status(thm)],[767, 19902, 14])).
% 6.07/6.02 tff(19904,plain,
% 6.07/6.02 (pred(NSX5!17) = pred(n4)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19903])).
% 6.07/6.02 tff(19905,plain,
% 6.07/6.02 (pred(NSX5!17) = n3),
% 6.07/6.02 inference(transitivity,[status(thm)],[19904, 15])).
% 6.07/6.02 tff(19906,plain,
% 6.07/6.02 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n3, n2)),
% 6.07/6.02 inference(monotonicity,[status(thm)],[19905, 19881])).
% 6.07/6.03 tff(19907,plain,
% 6.07/6.03 (Y6!48 = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[772, 19906, 557])).
% 6.07/6.03 tff(19908,plain,
% 6.07/6.03 (pred(Y6!48) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19907])).
% 6.07/6.03 tff(19909,plain,
% 6.07/6.03 (pred(Y6!48) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[19908, 16])).
% 6.07/6.03 tff(19910,plain,
% 6.07/6.03 (pred(pred(Y6!48)) = pred(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19909])).
% 6.07/6.03 tff(19911,plain,
% 6.07/6.03 (pred(pred(Y6!48)) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[19910, 15])).
% 6.07/6.03 tff(19912,plain,
% 6.07/6.03 (pred(pred(pred(Y6!48))) = pred(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19911])).
% 6.07/6.03 tff(19913,plain,
% 6.07/6.03 (pred(pred(pred(Y6!48))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[19912, 25])).
% 6.07/6.03 tff(19914,plain,
% 6.07/6.03 (pred(pred(pred(pred(Y6!48)))) = pred(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19913])).
% 6.07/6.03 tff(19915,plain,
% 6.07/6.03 (pred(pred(pred(pred(Y6!48)))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[19914, 24])).
% 6.07/6.03 tff(19916,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19915])).
% 6.07/6.03 tff(19917,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(Y6!48))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[19916, 23])).
% 6.07/6.03 tff(19918,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19917])).
% 6.07/6.03 tff(19919,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[19918, 22])).
% 6.07/6.03 tff(19920,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19919])).
% 6.07/6.03 tff(19921,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[19920, 21])).
% 6.07/6.03 tff(19922,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19921])).
% 6.07/6.03 tff(19923,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[19922, 20])).
% 6.07/6.03 tff(19924,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19923])).
% 6.07/6.03 tff(19925,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[19924, 19])).
% 6.07/6.03 tff(19926,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19925])).
% 6.07/6.03 tff(19927,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[19926, 18])).
% 6.07/6.03 tff(19928,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19927])).
% 6.07/6.03 tff(19929,plain,
% 6.07/6.03 (NPY6!14 = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[1465, 19928, 17])).
% 6.07/6.03 tff(19930,plain,
% 6.07/6.03 (succ(NPY6!14) = succ(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19929])).
% 6.07/6.03 tff(19931,plain,
% 6.07/6.03 (succ(NPY6!14) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[19930, 30])).
% 6.07/6.03 tff(19932,plain,
% 6.07/6.03 (succ(Y6!48) = succ(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19907])).
% 6.07/6.03 tff(19933,plain,
% 6.07/6.03 (succ(Y6!48) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[19932, 30])).
% 6.07/6.03 tff(19934,plain,
% 6.07/6.03 (succ(succ(Y6!48)) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19933])).
% 6.07/6.03 tff(19935,plain,
% 6.07/6.03 (succ(succ(Y6!48)) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[19934, 39])).
% 6.07/6.03 tff(19936,plain,
% 6.07/6.03 (succ(succ(succ(Y6!48))) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19935])).
% 6.07/6.03 tff(19937,plain,
% 6.07/6.03 (succ(succ(succ(Y6!48))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[19936, 53])).
% 6.07/6.03 tff(19938,plain,
% 6.07/6.03 (succ(succ(succ(succ(Y6!48)))) = succ(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19937])).
% 6.07/6.03 tff(19939,plain,
% 6.07/6.03 (succ(succ(succ(succ(Y6!48)))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[19938, 45])).
% 6.07/6.03 tff(19940,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19939])).
% 6.07/6.03 tff(19941,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(Y6!48))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[19940, 28])).
% 6.07/6.03 tff(19942,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19941])).
% 6.07/6.03 tff(19943,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[19942, 42])).
% 6.07/6.03 tff(19944,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19943])).
% 6.07/6.03 tff(19945,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[19944, 58])).
% 6.07/6.03 tff(19946,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19945])).
% 6.07/6.03 tff(19947,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[19946, 36])).
% 6.07/6.03 tff(19948,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19947])).
% 6.07/6.03 tff(19949,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[19948, 48])).
% 6.07/6.03 tff(19950,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19949])).
% 6.07/6.03 tff(19951,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[19950, 14])).
% 6.07/6.03 tff(19952,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19951])).
% 6.07/6.03 tff(19953,plain,
% 6.07/6.03 (NSY6!12 = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[1490, 19952, 33])).
% 6.07/6.03 tff(19954,plain,
% 6.07/6.03 (pred(NSY6!12) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19953])).
% 6.07/6.03 tff(19955,plain,
% 6.07/6.03 (pred(NSY6!12) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[19954, 16])).
% 6.07/6.03 tff(19956,plain,
% 6.07/6.03 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n4, n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19955, 19931])).
% 6.07/6.03 tff(19957,plain,
% 6.07/6.03 (sum(pred(NSY6!12), succ(NPY6!14)) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[19956, 12])).
% 6.07/6.03 tff(19958,plain,
% 6.07/6.03 (sum(pred(Y5!50), succ(X5!51)) = sum(n3, n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19801, 19883])).
% 6.07/6.03 tff(19959,plain,
% 6.07/6.03 (sum(pred(Y5!50), succ(X5!51)) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[19958, 32])).
% 6.07/6.03 tff(19960,plain,
% 6.07/6.03 (sum(pred(X5!51), succ(Y5!50)) = sum(n3, n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19857, 19825])).
% 6.07/6.03 tff(19961,plain,
% 6.07/6.03 (sum(pred(X5!51), succ(Y5!50)) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[19960, 32])).
% 6.07/6.03 tff(19962,plain,
% 6.07/6.03 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n8, n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19961, 19959])).
% 6.07/6.03 tff(19963,plain,
% 6.07/6.03 (X6!49 = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[669, 19962, 31])).
% 6.07/6.03 tff(19964,plain,
% 6.07/6.03 (pred(X6!49) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19963])).
% 6.07/6.03 tff(19965,plain,
% 6.07/6.03 (pred(X6!49) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[19964, 16])).
% 6.07/6.03 tff(19966,plain,
% 6.07/6.03 (pred(pred(X6!49)) = pred(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19965])).
% 6.07/6.03 tff(19967,plain,
% 6.07/6.03 (pred(pred(X6!49)) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[19966, 15])).
% 6.07/6.03 tff(19968,plain,
% 6.07/6.03 (pred(pred(pred(X6!49))) = pred(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19967])).
% 6.07/6.03 tff(19969,plain,
% 6.07/6.03 (pred(pred(pred(X6!49))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[19968, 25])).
% 6.07/6.03 tff(19970,plain,
% 6.07/6.03 (pred(pred(pred(pred(X6!49)))) = pred(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19969])).
% 6.07/6.03 tff(19971,plain,
% 6.07/6.03 (pred(pred(pred(pred(X6!49)))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[19970, 24])).
% 6.07/6.03 tff(19972,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(X6!49))))) = pred(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19971])).
% 6.07/6.03 tff(19973,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(X6!49))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[19972, 23])).
% 6.07/6.03 tff(19974,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19973])).
% 6.07/6.03 tff(19975,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[19974, 22])).
% 6.07/6.03 tff(19976,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19975])).
% 6.07/6.03 tff(19977,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[19976, 21])).
% 6.07/6.03 tff(19978,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19977])).
% 6.07/6.03 tff(19979,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[19978, 20])).
% 6.07/6.03 tff(19980,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19979])).
% 6.07/6.03 tff(19981,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[19980, 19])).
% 6.07/6.03 tff(19982,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19981])).
% 6.07/6.03 tff(19983,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[19982, 18])).
% 6.07/6.03 tff(19984,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19983])).
% 6.07/6.03 tff(19985,plain,
% 6.07/6.03 (NPX6!15 = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[1523, 19984, 17])).
% 6.07/6.03 tff(19986,plain,
% 6.07/6.03 (succ(NPX6!15) = succ(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19985])).
% 6.07/6.03 tff(19987,plain,
% 6.07/6.03 (succ(NPX6!15) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[19986, 30])).
% 6.07/6.03 tff(19988,plain,
% 6.07/6.03 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n6, n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19987, 19957])).
% 6.07/6.03 tff(19989,plain,
% 6.07/6.03 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[19988, 674])).
% 6.07/6.03 tff(19990,plain,
% 6.07/6.03 (succ(X6!49) = succ(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19963])).
% 6.07/6.03 tff(19991,plain,
% 6.07/6.03 (succ(X6!49) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[19990, 30])).
% 6.07/6.03 tff(19992,plain,
% 6.07/6.03 (succ(succ(X6!49)) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19991])).
% 6.07/6.03 tff(19993,plain,
% 6.07/6.03 (succ(succ(X6!49)) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[19992, 39])).
% 6.07/6.03 tff(19994,plain,
% 6.07/6.03 (succ(succ(succ(X6!49))) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19993])).
% 6.07/6.03 tff(19995,plain,
% 6.07/6.03 (succ(succ(succ(X6!49))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[19994, 53])).
% 6.07/6.03 tff(19996,plain,
% 6.07/6.03 (succ(succ(succ(succ(X6!49)))) = succ(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19995])).
% 6.07/6.03 tff(19997,plain,
% 6.07/6.03 (succ(succ(succ(succ(X6!49)))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[19996, 45])).
% 6.07/6.03 tff(19998,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(X6!49))))) = succ(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19997])).
% 6.07/6.03 tff(19999,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(X6!49))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[19998, 28])).
% 6.07/6.03 tff(20000,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19999])).
% 6.07/6.03 tff(20001,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20000, 42])).
% 6.07/6.03 tff(20002,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20001])).
% 6.07/6.03 tff(20003,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20002, 58])).
% 6.07/6.03 tff(20004,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20003])).
% 6.07/6.03 tff(20005,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20004, 36])).
% 6.07/6.03 tff(20006,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20005])).
% 6.07/6.03 tff(20007,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20006, 48])).
% 6.07/6.03 tff(20008,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20007])).
% 6.07/6.03 tff(20009,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20008, 14])).
% 6.07/6.03 tff(20010,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20009])).
% 6.07/6.03 tff(20011,plain,
% 6.07/6.03 (NSX6!13 = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[1550, 20010, 33])).
% 6.07/6.03 tff(20012,plain,
% 6.07/6.03 (pred(NSX6!13) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20011])).
% 6.07/6.03 tff(20013,plain,
% 6.07/6.03 (pred(NSX6!13) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20012, 16])).
% 6.07/6.03 tff(20014,plain,
% 6.07/6.03 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n4, n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20013, 19989])).
% 6.07/6.03 tff(20015,plain,
% 6.07/6.03 (sum(n4, n5) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 6.07/6.03 inference(symmetry,[status(thm)],[20014])).
% 6.07/6.03 tff(20016,plain,
% 6.07/6.03 (sum(pred(Y6!48), succ(X6!49)) = sum(n4, n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19909, 19991])).
% 6.07/6.03 tff(20017,plain,
% 6.07/6.03 (sum(pred(Y6!48), succ(X6!49)) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20016, 12])).
% 6.07/6.03 tff(20018,plain,
% 6.07/6.03 (sum(pred(X6!49), succ(Y6!48)) = sum(n4, n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[19965, 19933])).
% 6.07/6.03 tff(20019,plain,
% 6.07/6.03 (sum(pred(X6!49), succ(Y6!48)) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20018, 12])).
% 6.07/6.03 tff(20020,plain,
% 6.07/6.03 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n10, n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20019, 20017])).
% 6.07/6.03 tff(20021,plain,
% 6.07/6.03 (X7!47 = Y7!46),
% 6.07/6.03 inference(transitivity,[status(thm)],[785, 20020, 29, 10596, 20015, 794])).
% 6.07/6.03 tff(20022,plain,
% 6.07/6.03 ($false),
% 6.07/6.03 inference(unit_resolution,[status(thm)],[792, 20021])).
% 6.07/6.03 tff(20023,plain,((~(Y0!60 = n5)) | (X7!47 = Y7!46) | (~(X0!61 = n3))), inference(lemma,lemma(discharge,[]))).
% 6.07/6.03 tff(20024,plain,
% 6.07/6.03 (~(Y0!60 = n5)),
% 6.07/6.03 inference(unit_resolution,[status(thm)],[20023, 17987, 792])).
% 6.07/6.03 tff(20025,plain,
% 6.07/6.03 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n4, n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[18011, 1622])).
% 6.07/6.03 tff(20026,plain,
% 6.07/6.03 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20025, 7189])).
% 6.07/6.03 tff(20027,plain,
% 6.07/6.03 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n2, n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[18037, 20026])).
% 6.07/6.03 tff(20028,plain,
% 6.07/6.03 (Y1!58 = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[196, 20027, 18755])).
% 6.07/6.03 tff(20029,plain,
% 6.07/6.03 (pred(Y1!58) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20028])).
% 6.07/6.03 tff(20030,plain,
% 6.07/6.03 (pred(Y1!58) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[20029, 18])).
% 6.07/6.03 tff(20031,plain,
% 6.07/6.03 (pred(pred(Y1!58)) = pred(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20030])).
% 6.07/6.03 tff(20032,plain,
% 6.07/6.03 (pred(pred(Y1!58)) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20031, 17])).
% 6.07/6.03 tff(20033,plain,
% 6.07/6.03 (pred(pred(pred(Y1!58))) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20032])).
% 6.07/6.03 tff(20034,plain,
% 6.07/6.03 (pred(pred(pred(Y1!58))) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20033, 16])).
% 6.07/6.03 tff(20035,plain,
% 6.07/6.03 (pred(pred(pred(pred(Y1!58)))) = pred(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20034])).
% 6.07/6.03 tff(20036,plain,
% 6.07/6.03 (pred(pred(pred(pred(Y1!58)))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20035, 15])).
% 6.07/6.03 tff(20037,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20036])).
% 6.07/6.03 tff(20038,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(Y1!58))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20037, 25])).
% 6.07/6.03 tff(20039,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20038])).
% 6.07/6.03 tff(20040,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20039, 24])).
% 6.07/6.03 tff(20041,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20040])).
% 6.07/6.03 tff(20042,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20041, 23])).
% 6.07/6.03 tff(20043,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20042])).
% 6.07/6.03 tff(20044,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20043, 22])).
% 6.07/6.03 tff(20045,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20044])).
% 6.07/6.03 tff(20046,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20045, 21])).
% 6.07/6.03 tff(20047,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20046])).
% 6.07/6.03 tff(20048,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20047, 20])).
% 6.07/6.03 tff(20049,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20048])).
% 6.07/6.03 tff(20050,plain,
% 6.07/6.03 (NPY1!34 = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[232, 20049, 19])).
% 6.07/6.03 tff(20051,plain,
% 6.07/6.03 (succ(NPY1!34) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20050])).
% 6.07/6.03 tff(20052,plain,
% 6.07/6.03 (succ(NPY1!34) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20051, 53])).
% 6.07/6.03 tff(20053,plain,
% 6.07/6.03 (succ(Y1!58) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20028])).
% 6.07/6.03 tff(20054,plain,
% 6.07/6.03 (succ(Y1!58) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20053, 53])).
% 6.07/6.03 tff(20055,plain,
% 6.07/6.03 (succ(succ(Y1!58)) = succ(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20054])).
% 6.07/6.03 tff(20056,plain,
% 6.07/6.03 (succ(succ(Y1!58)) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20055, 45])).
% 6.07/6.03 tff(20057,plain,
% 6.07/6.03 (succ(succ(succ(Y1!58))) = succ(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20056])).
% 6.07/6.03 tff(20058,plain,
% 6.07/6.03 (succ(succ(succ(Y1!58))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20057, 28])).
% 6.07/6.03 tff(20059,plain,
% 6.07/6.03 (succ(succ(succ(succ(Y1!58)))) = succ(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20058])).
% 6.07/6.03 tff(20060,plain,
% 6.07/6.03 (succ(succ(succ(succ(Y1!58)))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20059, 42])).
% 6.07/6.03 tff(20061,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20060])).
% 6.07/6.03 tff(20062,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(Y1!58))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20061, 58])).
% 6.07/6.03 tff(20063,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20062])).
% 6.07/6.03 tff(20064,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20063, 36])).
% 6.07/6.03 tff(20065,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20064])).
% 6.07/6.03 tff(20066,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20065, 48])).
% 6.07/6.03 tff(20067,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20066])).
% 6.07/6.03 tff(20068,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20067, 14])).
% 6.07/6.03 tff(20069,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20068])).
% 6.07/6.03 tff(20070,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20069, 33])).
% 6.07/6.03 tff(20071,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20070])).
% 6.07/6.03 tff(20072,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[20071, 30])).
% 6.07/6.03 tff(20073,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20072])).
% 6.07/6.03 tff(20074,plain,
% 6.07/6.03 (NSY1!32 = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[255, 20073, 39])).
% 6.07/6.03 tff(20075,plain,
% 6.07/6.03 (pred(NSY1!32) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20074])).
% 6.07/6.03 tff(20076,plain,
% 6.07/6.03 (pred(NSY1!32) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[20075, 18])).
% 6.07/6.03 tff(20077,plain,
% 6.07/6.03 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n6, n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20076, 20052])).
% 6.07/6.03 tff(20078,plain,
% 6.07/6.03 (sum(pred(NSY1!32), succ(NPY1!34)) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20077, 52])).
% 6.07/6.03 tff(20079,plain,
% 6.07/6.03 (sum(pred(Y0!60), succ(X0!61)) = sum(n5, n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[1574, 18015])).
% 6.07/6.03 tff(20080,plain,
% 6.07/6.03 (sum(pred(Y0!60), succ(X0!61)) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20079, 848])).
% 6.07/6.03 tff(20081,plain,
% 6.07/6.03 (sum(n2, n7) = n9),
% 6.07/6.03 inference(and_elim,[status(thm)],[9])).
% 6.07/6.03 tff(20082,plain,
% 6.07/6.03 (sum(pred(X0!61), succ(Y0!60)) = sum(n2, n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[17989, 1598])).
% 6.07/6.03 tff(20083,plain,
% 6.07/6.03 (sum(pred(X0!61), succ(Y0!60)) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20082, 20081])).
% 6.07/6.03 tff(20084,plain,
% 6.07/6.03 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n9, n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20083, 20080])).
% 6.07/6.03 tff(20085,plain,
% 6.07/6.03 (X1!59 = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[93, 20084, 54])).
% 6.07/6.03 tff(20086,plain,
% 6.07/6.03 (pred(X1!59) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20085])).
% 6.07/6.03 tff(20087,plain,
% 6.07/6.03 (pred(X1!59) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[20086, 18])).
% 6.07/6.03 tff(20088,plain,
% 6.07/6.03 (pred(pred(X1!59)) = pred(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20087])).
% 6.07/6.03 tff(20089,plain,
% 6.07/6.03 (pred(pred(X1!59)) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20088, 17])).
% 6.07/6.03 tff(20090,plain,
% 6.07/6.03 (pred(pred(pred(X1!59))) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20089])).
% 6.07/6.03 tff(20091,plain,
% 6.07/6.03 (pred(pred(pred(X1!59))) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20090, 16])).
% 6.07/6.03 tff(20092,plain,
% 6.07/6.03 (pred(pred(pred(pred(X1!59)))) = pred(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20091])).
% 6.07/6.03 tff(20093,plain,
% 6.07/6.03 (pred(pred(pred(pred(X1!59)))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20092, 15])).
% 6.07/6.03 tff(20094,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(X1!59))))) = pred(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20093])).
% 6.07/6.03 tff(20095,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(X1!59))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20094, 25])).
% 6.07/6.03 tff(20096,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20095])).
% 6.07/6.03 tff(20097,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20096, 24])).
% 6.07/6.03 tff(20098,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20097])).
% 6.07/6.03 tff(20099,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20098, 23])).
% 6.07/6.03 tff(20100,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20099])).
% 6.07/6.03 tff(20101,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20100, 22])).
% 6.07/6.03 tff(20102,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20101])).
% 6.07/6.03 tff(20103,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20102, 21])).
% 6.07/6.03 tff(20104,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20103])).
% 6.07/6.03 tff(20105,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20104, 20])).
% 6.07/6.03 tff(20106,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20105])).
% 6.07/6.03 tff(20107,plain,
% 6.07/6.03 (NPX1!35 = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[280, 20106, 19])).
% 6.07/6.03 tff(20108,plain,
% 6.07/6.03 (succ(NPX1!35) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20107])).
% 6.07/6.03 tff(20109,plain,
% 6.07/6.03 (succ(NPX1!35) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20108, 53])).
% 6.07/6.03 tff(20110,plain,
% 6.07/6.03 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n8, n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20109, 20078])).
% 6.07/6.03 tff(20111,plain,
% 6.07/6.03 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20110, 64])).
% 6.07/6.03 tff(20112,plain,
% 6.07/6.03 (succ(X1!59) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20085])).
% 6.07/6.03 tff(20113,plain,
% 6.07/6.03 (succ(X1!59) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20112, 53])).
% 6.07/6.03 tff(20114,plain,
% 6.07/6.03 (succ(succ(X1!59)) = succ(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20113])).
% 6.07/6.03 tff(20115,plain,
% 6.07/6.03 (succ(succ(X1!59)) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20114, 45])).
% 6.07/6.03 tff(20116,plain,
% 6.07/6.03 (succ(succ(succ(X1!59))) = succ(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20115])).
% 6.07/6.03 tff(20117,plain,
% 6.07/6.03 (succ(succ(succ(X1!59))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20116, 28])).
% 6.07/6.03 tff(20118,plain,
% 6.07/6.03 (succ(succ(succ(succ(X1!59)))) = succ(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20117])).
% 6.07/6.03 tff(20119,plain,
% 6.07/6.03 (succ(succ(succ(succ(X1!59)))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20118, 42])).
% 6.07/6.03 tff(20120,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(X1!59))))) = succ(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20119])).
% 6.07/6.03 tff(20121,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(X1!59))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20120, 58])).
% 6.07/6.03 tff(20122,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20121])).
% 6.07/6.03 tff(20123,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20122, 36])).
% 6.07/6.03 tff(20124,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20123])).
% 6.07/6.03 tff(20125,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20124, 48])).
% 6.07/6.03 tff(20126,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20125])).
% 6.07/6.03 tff(20127,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20126, 14])).
% 6.07/6.03 tff(20128,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20127])).
% 6.07/6.03 tff(20129,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20128, 33])).
% 6.07/6.03 tff(20130,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20129])).
% 6.07/6.03 tff(20131,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[20130, 30])).
% 6.07/6.03 tff(20132,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20131])).
% 6.07/6.03 tff(20133,plain,
% 6.07/6.03 (NSX1!33 = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[305, 20132, 39])).
% 6.07/6.03 tff(20134,plain,
% 6.07/6.03 (pred(NSX1!33) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20133])).
% 6.07/6.03 tff(20135,plain,
% 6.07/6.03 (pred(NSX1!33) = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[20134, 18])).
% 6.07/6.03 tff(20136,plain,
% 6.07/6.03 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n6, n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20135, 20111])).
% 6.07/6.03 tff(20137,plain,
% 6.07/6.03 (Y2!56 = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[310, 20136, 788])).
% 6.07/6.03 tff(20138,plain,
% 6.07/6.03 (pred(Y2!56) = pred(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20137])).
% 6.07/6.03 tff(20139,plain,
% 6.07/6.03 (pred(Y2!56) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20138, 17])).
% 6.07/6.03 tff(20140,plain,
% 6.07/6.03 (pred(pred(Y2!56)) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20139])).
% 6.07/6.03 tff(20141,plain,
% 6.07/6.03 (pred(pred(Y2!56)) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20140, 16])).
% 6.07/6.03 tff(20142,plain,
% 6.07/6.03 (pred(pred(pred(Y2!56))) = pred(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20141])).
% 6.07/6.03 tff(20143,plain,
% 6.07/6.03 (pred(pred(pred(Y2!56))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20142, 15])).
% 6.07/6.03 tff(20144,plain,
% 6.07/6.03 (pred(pred(pred(pred(Y2!56)))) = pred(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20143])).
% 6.07/6.03 tff(20145,plain,
% 6.07/6.03 (pred(pred(pred(pred(Y2!56)))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20144, 25])).
% 6.07/6.03 tff(20146,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20145])).
% 6.07/6.03 tff(20147,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(Y2!56))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20146, 24])).
% 6.07/6.03 tff(20148,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20147])).
% 6.07/6.03 tff(20149,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20148, 23])).
% 6.07/6.03 tff(20150,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20149])).
% 6.07/6.03 tff(20151,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20150, 22])).
% 6.07/6.03 tff(20152,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20151])).
% 6.07/6.03 tff(20153,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20152, 21])).
% 6.07/6.03 tff(20154,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20153])).
% 6.07/6.03 tff(20155,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20154, 20])).
% 6.07/6.03 tff(20156,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20155])).
% 6.07/6.03 tff(20157,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[20156, 19])).
% 6.07/6.03 tff(20158,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20157])).
% 6.07/6.03 tff(20159,plain,
% 6.07/6.03 (NPY2!30 = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[347, 20158, 18])).
% 6.07/6.03 tff(20160,plain,
% 6.07/6.03 (succ(NPY2!30) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20159])).
% 6.07/6.03 tff(20161,plain,
% 6.07/6.03 (succ(NPY2!30) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[20160, 39])).
% 6.07/6.03 tff(20162,plain,
% 6.07/6.03 (succ(Y2!56) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20137])).
% 6.07/6.03 tff(20163,plain,
% 6.07/6.03 (succ(Y2!56) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[20162, 39])).
% 6.07/6.03 tff(20164,plain,
% 6.07/6.03 (succ(succ(Y2!56)) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20163])).
% 6.07/6.03 tff(20165,plain,
% 6.07/6.03 (succ(succ(Y2!56)) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20164, 53])).
% 6.07/6.03 tff(20166,plain,
% 6.07/6.03 (succ(succ(succ(Y2!56))) = succ(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20165])).
% 6.07/6.03 tff(20167,plain,
% 6.07/6.03 (succ(succ(succ(Y2!56))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20166, 45])).
% 6.07/6.03 tff(20168,plain,
% 6.07/6.03 (succ(succ(succ(succ(Y2!56)))) = succ(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20167])).
% 6.07/6.03 tff(20169,plain,
% 6.07/6.03 (succ(succ(succ(succ(Y2!56)))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20168, 28])).
% 6.07/6.03 tff(20170,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20169])).
% 6.07/6.03 tff(20171,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(Y2!56))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20170, 42])).
% 6.07/6.03 tff(20172,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20171])).
% 6.07/6.03 tff(20173,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20172, 58])).
% 6.07/6.03 tff(20174,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20173])).
% 6.07/6.03 tff(20175,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20174, 36])).
% 6.07/6.03 tff(20176,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20175])).
% 6.07/6.03 tff(20177,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20176, 48])).
% 6.07/6.03 tff(20178,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20177])).
% 6.07/6.03 tff(20179,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20178, 14])).
% 6.07/6.03 tff(20180,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20179])).
% 6.07/6.03 tff(20181,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20180, 33])).
% 6.07/6.03 tff(20182,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20181])).
% 6.07/6.03 tff(20183,plain,
% 6.07/6.03 (NSY2!28 = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[370, 20182, 30])).
% 6.07/6.03 tff(20184,plain,
% 6.07/6.03 (pred(NSY2!28) = pred(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20183])).
% 6.07/6.03 tff(20185,plain,
% 6.07/6.03 (pred(NSY2!28) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20184, 17])).
% 6.07/6.03 tff(20186,plain,
% 6.07/6.03 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n5, n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20185, 20161])).
% 6.07/6.03 tff(20187,plain,
% 6.07/6.03 (sum(pred(NSY2!28), succ(NPY2!30)) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20186, 50])).
% 6.07/6.03 tff(20188,plain,
% 6.07/6.03 (sum(pred(Y1!58), succ(X1!59)) = sum(n6, n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20030, 20113])).
% 6.07/6.03 tff(20189,plain,
% 6.07/6.03 (sum(pred(Y1!58), succ(X1!59)) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20188, 52])).
% 6.07/6.03 tff(20190,plain,
% 6.07/6.03 (sum(pred(X1!59), succ(Y1!58)) = sum(n6, n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20087, 20054])).
% 6.07/6.03 tff(20191,plain,
% 6.07/6.03 (sum(pred(X1!59), succ(Y1!58)) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20190, 52])).
% 6.07/6.03 tff(20192,plain,
% 6.07/6.03 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n3, n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20191, 20189])).
% 6.07/6.03 tff(20193,plain,
% 6.07/6.03 (X2!57 = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[209, 20192, 51])).
% 6.07/6.03 tff(20194,plain,
% 6.07/6.03 (pred(X2!57) = pred(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20193])).
% 6.07/6.03 tff(20195,plain,
% 6.07/6.03 (pred(X2!57) = n5),
% 6.07/6.03 inference(transitivity,[status(thm)],[20194, 17])).
% 6.07/6.03 tff(20196,plain,
% 6.07/6.03 (pred(pred(X2!57)) = pred(n5)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20195])).
% 6.07/6.03 tff(20197,plain,
% 6.07/6.03 (pred(pred(X2!57)) = n4),
% 6.07/6.03 inference(transitivity,[status(thm)],[20196, 16])).
% 6.07/6.03 tff(20198,plain,
% 6.07/6.03 (pred(pred(pred(X2!57))) = pred(n4)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20197])).
% 6.07/6.03 tff(20199,plain,
% 6.07/6.03 (pred(pred(pred(X2!57))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20198, 15])).
% 6.07/6.03 tff(20200,plain,
% 6.07/6.03 (pred(pred(pred(pred(X2!57)))) = pred(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20199])).
% 6.07/6.03 tff(20201,plain,
% 6.07/6.03 (pred(pred(pred(pred(X2!57)))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20200, 25])).
% 6.07/6.03 tff(20202,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(X2!57))))) = pred(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20201])).
% 6.07/6.03 tff(20203,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(X2!57))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20202, 24])).
% 6.07/6.03 tff(20204,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20203])).
% 6.07/6.03 tff(20205,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20204, 23])).
% 6.07/6.03 tff(20206,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20205])).
% 6.07/6.03 tff(20207,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20206, 22])).
% 6.07/6.03 tff(20208,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20207])).
% 6.07/6.03 tff(20209,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20208, 21])).
% 6.07/6.03 tff(20210,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20209])).
% 6.07/6.03 tff(20211,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20210, 20])).
% 6.07/6.03 tff(20212,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20211])).
% 6.07/6.03 tff(20213,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[20212, 19])).
% 6.07/6.03 tff(20214,plain,
% 6.07/6.03 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20213])).
% 6.07/6.03 tff(20215,plain,
% 6.07/6.03 (NPX2!31 = n6),
% 6.07/6.03 inference(transitivity,[status(thm)],[395, 20214, 18])).
% 6.07/6.03 tff(20216,plain,
% 6.07/6.03 (succ(NPX2!31) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20215])).
% 6.07/6.03 tff(20217,plain,
% 6.07/6.03 (succ(NPX2!31) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[20216, 39])).
% 6.07/6.03 tff(20218,plain,
% 6.07/6.03 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n7, n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20217, 20187])).
% 6.07/6.03 tff(20219,plain,
% 6.07/6.03 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20218, 787])).
% 6.07/6.03 tff(20220,plain,
% 6.07/6.03 (succ(X2!57) = succ(n6)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20193])).
% 6.07/6.03 tff(20221,plain,
% 6.07/6.03 (succ(X2!57) = n7),
% 6.07/6.03 inference(transitivity,[status(thm)],[20220, 39])).
% 6.07/6.03 tff(20222,plain,
% 6.07/6.03 (succ(succ(X2!57)) = succ(n7)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20221])).
% 6.07/6.03 tff(20223,plain,
% 6.07/6.03 (succ(succ(X2!57)) = n8),
% 6.07/6.03 inference(transitivity,[status(thm)],[20222, 53])).
% 6.07/6.03 tff(20224,plain,
% 6.07/6.03 (succ(succ(succ(X2!57))) = succ(n8)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20223])).
% 6.07/6.03 tff(20225,plain,
% 6.07/6.03 (succ(succ(succ(X2!57))) = n9),
% 6.07/6.03 inference(transitivity,[status(thm)],[20224, 45])).
% 6.07/6.03 tff(20226,plain,
% 6.07/6.03 (succ(succ(succ(succ(X2!57)))) = succ(n9)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20225])).
% 6.07/6.03 tff(20227,plain,
% 6.07/6.03 (succ(succ(succ(succ(X2!57)))) = n10),
% 6.07/6.03 inference(transitivity,[status(thm)],[20226, 28])).
% 6.07/6.03 tff(20228,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(X2!57))))) = succ(n10)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20227])).
% 6.07/6.03 tff(20229,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(X2!57))))) = n0),
% 6.07/6.03 inference(transitivity,[status(thm)],[20228, 42])).
% 6.07/6.03 tff(20230,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n0)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20229])).
% 6.07/6.03 tff(20231,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n1),
% 6.07/6.03 inference(transitivity,[status(thm)],[20230, 58])).
% 6.07/6.03 tff(20232,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n1)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20231])).
% 6.07/6.03 tff(20233,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n2),
% 6.07/6.03 inference(transitivity,[status(thm)],[20232, 36])).
% 6.07/6.03 tff(20234,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n2)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20233])).
% 6.07/6.03 tff(20235,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n3),
% 6.07/6.03 inference(transitivity,[status(thm)],[20234, 48])).
% 6.07/6.03 tff(20236,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n3)),
% 6.07/6.03 inference(monotonicity,[status(thm)],[20235])).
% 6.07/6.03 tff(20237,plain,
% 6.07/6.03 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20236, 14])).
% 6.07/6.04 tff(20238,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20237])).
% 6.07/6.04 tff(20239,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20238, 33])).
% 6.07/6.04 tff(20240,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20239])).
% 6.07/6.04 tff(20241,plain,
% 6.07/6.04 (NSX2!29 = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[420, 20240, 30])).
% 6.07/6.04 tff(20242,plain,
% 6.07/6.04 (pred(NSX2!29) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20241])).
% 6.07/6.04 tff(20243,plain,
% 6.07/6.04 (pred(NSX2!29) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20242, 17])).
% 6.07/6.04 tff(20244,plain,
% 6.07/6.04 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n5, n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20243, 20219])).
% 6.07/6.04 tff(20245,plain,
% 6.07/6.04 (Y3!54 = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[425, 20244, 558])).
% 6.07/6.04 tff(20246,plain,
% 6.07/6.04 (pred(Y3!54) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20245])).
% 6.07/6.04 tff(20247,plain,
% 6.07/6.04 (pred(Y3!54) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20246, 24])).
% 6.07/6.04 tff(20248,plain,
% 6.07/6.04 (pred(pred(Y3!54)) = pred(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20247])).
% 6.07/6.04 tff(20249,plain,
% 6.07/6.04 (pred(pred(Y3!54)) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20248, 23])).
% 6.07/6.04 tff(20250,plain,
% 6.07/6.04 (pred(pred(pred(Y3!54))) = pred(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20249])).
% 6.07/6.04 tff(20251,plain,
% 6.07/6.04 (pred(pred(pred(Y3!54))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20250, 22])).
% 6.07/6.04 tff(20252,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y3!54)))) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20251])).
% 6.07/6.04 tff(20253,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y3!54)))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20252, 21])).
% 6.07/6.04 tff(20254,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20253])).
% 6.07/6.04 tff(20255,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y3!54))))) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20254, 20])).
% 6.07/6.04 tff(20256,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20255])).
% 6.07/6.04 tff(20257,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20256, 19])).
% 6.07/6.04 tff(20258,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20257])).
% 6.07/6.04 tff(20259,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20258, 18])).
% 6.07/6.04 tff(20260,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20259])).
% 6.07/6.04 tff(20261,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20260, 17])).
% 6.07/6.04 tff(20262,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20261])).
% 6.07/6.04 tff(20263,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20262, 16])).
% 6.07/6.04 tff(20264,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20263])).
% 6.07/6.04 tff(20265,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20264, 15])).
% 6.07/6.04 tff(20266,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20265])).
% 6.07/6.04 tff(20267,plain,
% 6.07/6.04 (NPY3!26 = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[462, 20266, 25])).
% 6.07/6.04 tff(20268,plain,
% 6.07/6.04 (succ(NPY3!26) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20267])).
% 6.07/6.04 tff(20269,plain,
% 6.07/6.04 (succ(NPY3!26) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20268, 48])).
% 6.07/6.04 tff(20270,plain,
% 6.07/6.04 (succ(Y3!54) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20245])).
% 6.07/6.04 tff(20271,plain,
% 6.07/6.04 (succ(Y3!54) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20270, 48])).
% 6.07/6.04 tff(20272,plain,
% 6.07/6.04 (succ(succ(Y3!54)) = succ(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20271])).
% 6.07/6.04 tff(20273,plain,
% 6.07/6.04 (succ(succ(Y3!54)) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20272, 14])).
% 6.07/6.04 tff(20274,plain,
% 6.07/6.04 (succ(succ(succ(Y3!54))) = succ(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20273])).
% 6.07/6.04 tff(20275,plain,
% 6.07/6.04 (succ(succ(succ(Y3!54))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20274, 33])).
% 6.07/6.04 tff(20276,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y3!54)))) = succ(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20275])).
% 6.07/6.04 tff(20277,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y3!54)))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20276, 30])).
% 6.07/6.04 tff(20278,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20277])).
% 6.07/6.04 tff(20279,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(Y3!54))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20278, 39])).
% 6.07/6.04 tff(20280,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20279])).
% 6.07/6.04 tff(20281,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20280, 53])).
% 6.07/6.04 tff(20282,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20281])).
% 6.07/6.04 tff(20283,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20282, 45])).
% 6.07/6.04 tff(20284,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20283])).
% 6.07/6.04 tff(20285,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20284, 28])).
% 6.07/6.04 tff(20286,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20285])).
% 6.07/6.04 tff(20287,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20286, 42])).
% 6.07/6.04 tff(20288,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20287])).
% 6.07/6.04 tff(20289,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20288, 58])).
% 6.07/6.04 tff(20290,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20289])).
% 6.07/6.04 tff(20291,plain,
% 6.07/6.04 (NSY3!24 = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[485, 20290, 36])).
% 6.07/6.04 tff(20292,plain,
% 6.07/6.04 (pred(NSY3!24) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20291])).
% 6.07/6.04 tff(20293,plain,
% 6.07/6.04 (pred(NSY3!24) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20292, 24])).
% 6.07/6.04 tff(20294,plain,
% 6.07/6.04 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n1, n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20293, 20269])).
% 6.07/6.04 tff(20295,plain,
% 6.07/6.04 (sum(pred(NSY3!24), succ(NPY3!26)) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20294, 47])).
% 6.07/6.04 tff(20296,plain,
% 6.07/6.04 (sum(pred(Y2!56), succ(X2!57)) = sum(n5, n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20139, 20221])).
% 6.07/6.04 tff(20297,plain,
% 6.07/6.04 (sum(pred(Y2!56), succ(X2!57)) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20296, 50])).
% 6.07/6.04 tff(20298,plain,
% 6.07/6.04 (sum(pred(X2!57), succ(Y2!56)) = sum(n5, n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20195, 20163])).
% 6.07/6.04 tff(20299,plain,
% 6.07/6.04 (sum(pred(X2!57), succ(Y2!56)) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20298, 50])).
% 6.07/6.04 tff(20300,plain,
% 6.07/6.04 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n1, n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20299, 20297])).
% 6.07/6.04 tff(20301,plain,
% 6.07/6.04 (X3!55 = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[323, 20300, 49])).
% 6.07/6.04 tff(20302,plain,
% 6.07/6.04 (pred(X3!55) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20301])).
% 6.07/6.04 tff(20303,plain,
% 6.07/6.04 (pred(X3!55) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20302, 24])).
% 6.07/6.04 tff(20304,plain,
% 6.07/6.04 (pred(pred(X3!55)) = pred(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20303])).
% 6.07/6.04 tff(20305,plain,
% 6.07/6.04 (pred(pred(X3!55)) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20304, 23])).
% 6.07/6.04 tff(20306,plain,
% 6.07/6.04 (pred(pred(pred(X3!55))) = pred(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20305])).
% 6.07/6.04 tff(20307,plain,
% 6.07/6.04 (pred(pred(pred(X3!55))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20306, 22])).
% 6.07/6.04 tff(20308,plain,
% 6.07/6.04 (pred(pred(pred(pred(X3!55)))) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20307])).
% 6.07/6.04 tff(20309,plain,
% 6.07/6.04 (pred(pred(pred(pred(X3!55)))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20308, 21])).
% 6.07/6.04 tff(20310,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(X3!55))))) = pred(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20309])).
% 6.07/6.04 tff(20311,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(X3!55))))) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20310, 20])).
% 6.07/6.04 tff(20312,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20311])).
% 6.07/6.04 tff(20313,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20312, 19])).
% 6.07/6.04 tff(20314,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20313])).
% 6.07/6.04 tff(20315,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20314, 18])).
% 6.07/6.04 tff(20316,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20315])).
% 6.07/6.04 tff(20317,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20316, 17])).
% 6.07/6.04 tff(20318,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20317])).
% 6.07/6.04 tff(20319,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20318, 16])).
% 6.07/6.04 tff(20320,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20319])).
% 6.07/6.04 tff(20321,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20320, 15])).
% 6.07/6.04 tff(20322,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20321])).
% 6.07/6.04 tff(20323,plain,
% 6.07/6.04 (NPX3!27 = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[510, 20322, 25])).
% 6.07/6.04 tff(20324,plain,
% 6.07/6.04 (succ(NPX3!27) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20323])).
% 6.07/6.04 tff(20325,plain,
% 6.07/6.04 (succ(NPX3!27) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20324, 48])).
% 6.07/6.04 tff(20326,plain,
% 6.07/6.04 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n3, n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20325, 20295])).
% 6.07/6.04 tff(20327,plain,
% 6.07/6.04 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20326, 786])).
% 6.07/6.04 tff(20328,plain,
% 6.07/6.04 (succ(X3!55) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20301])).
% 6.07/6.04 tff(20329,plain,
% 6.07/6.04 (succ(X3!55) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20328, 48])).
% 6.07/6.04 tff(20330,plain,
% 6.07/6.04 (succ(succ(X3!55)) = succ(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20329])).
% 6.07/6.04 tff(20331,plain,
% 6.07/6.04 (succ(succ(X3!55)) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20330, 14])).
% 6.07/6.04 tff(20332,plain,
% 6.07/6.04 (succ(succ(succ(X3!55))) = succ(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20331])).
% 6.07/6.04 tff(20333,plain,
% 6.07/6.04 (succ(succ(succ(X3!55))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20332, 33])).
% 6.07/6.04 tff(20334,plain,
% 6.07/6.04 (succ(succ(succ(succ(X3!55)))) = succ(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20333])).
% 6.07/6.04 tff(20335,plain,
% 6.07/6.04 (succ(succ(succ(succ(X3!55)))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20334, 30])).
% 6.07/6.04 tff(20336,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(X3!55))))) = succ(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20335])).
% 6.07/6.04 tff(20337,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(X3!55))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20336, 39])).
% 6.07/6.04 tff(20338,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20337])).
% 6.07/6.04 tff(20339,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20338, 53])).
% 6.07/6.04 tff(20340,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20339])).
% 6.07/6.04 tff(20341,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20340, 45])).
% 6.07/6.04 tff(20342,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20341])).
% 6.07/6.04 tff(20343,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20342, 28])).
% 6.07/6.04 tff(20344,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20343])).
% 6.07/6.04 tff(20345,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20344, 42])).
% 6.07/6.04 tff(20346,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20345])).
% 6.07/6.04 tff(20347,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20346, 58])).
% 6.07/6.04 tff(20348,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20347])).
% 6.07/6.04 tff(20349,plain,
% 6.07/6.04 (NSX3!25 = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[535, 20348, 36])).
% 6.07/6.04 tff(20350,plain,
% 6.07/6.04 (pred(NSX3!25) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20349])).
% 6.07/6.04 tff(20351,plain,
% 6.07/6.04 (pred(NSX3!25) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20350, 24])).
% 6.07/6.04 tff(20352,plain,
% 6.07/6.04 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n1, n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20351, 20327])).
% 6.07/6.04 tff(20353,plain,
% 6.07/6.04 (Y4!52 = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[540, 20352, 791])).
% 6.07/6.04 tff(20354,plain,
% 6.07/6.04 (pred(Y4!52) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20353])).
% 6.07/6.04 tff(20355,plain,
% 6.07/6.04 (pred(Y4!52) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20354, 19])).
% 6.07/6.04 tff(20356,plain,
% 6.07/6.04 (pred(pred(Y4!52)) = pred(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20355])).
% 6.07/6.04 tff(20357,plain,
% 6.07/6.04 (pred(pred(Y4!52)) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20356, 18])).
% 6.07/6.04 tff(20358,plain,
% 6.07/6.04 (pred(pred(pred(Y4!52))) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20357])).
% 6.07/6.04 tff(20359,plain,
% 6.07/6.04 (pred(pred(pred(Y4!52))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20358, 17])).
% 6.07/6.04 tff(20360,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y4!52)))) = pred(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20359])).
% 6.07/6.04 tff(20361,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y4!52)))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20360, 16])).
% 6.07/6.04 tff(20362,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20361])).
% 6.07/6.04 tff(20363,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y4!52))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20362, 15])).
% 6.07/6.04 tff(20364,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20363])).
% 6.07/6.04 tff(20365,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20364, 25])).
% 6.07/6.04 tff(20366,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20365])).
% 6.07/6.04 tff(20367,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20366, 24])).
% 6.07/6.04 tff(20368,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20367])).
% 6.07/6.04 tff(20369,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20368, 23])).
% 6.07/6.04 tff(20370,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20369])).
% 6.07/6.04 tff(20371,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20370, 22])).
% 6.07/6.04 tff(20372,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20371])).
% 6.07/6.04 tff(20373,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20372, 21])).
% 6.07/6.04 tff(20374,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20373])).
% 6.07/6.04 tff(20375,plain,
% 6.07/6.04 (NPY4!22 = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[578, 20374, 20])).
% 6.07/6.04 tff(20376,plain,
% 6.07/6.04 (succ(NPY4!22) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20375])).
% 6.07/6.04 tff(20377,plain,
% 6.07/6.04 (succ(NPY4!22) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20376, 45])).
% 6.07/6.04 tff(20378,plain,
% 6.07/6.04 (succ(Y4!52) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20353])).
% 6.07/6.04 tff(20379,plain,
% 6.07/6.04 (succ(Y4!52) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20378, 45])).
% 6.07/6.04 tff(20380,plain,
% 6.07/6.04 (succ(succ(Y4!52)) = succ(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20379])).
% 6.07/6.04 tff(20381,plain,
% 6.07/6.04 (succ(succ(Y4!52)) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20380, 28])).
% 6.07/6.04 tff(20382,plain,
% 6.07/6.04 (succ(succ(succ(Y4!52))) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20381])).
% 6.07/6.04 tff(20383,plain,
% 6.07/6.04 (succ(succ(succ(Y4!52))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20382, 42])).
% 6.07/6.04 tff(20384,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y4!52)))) = succ(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20383])).
% 6.07/6.04 tff(20385,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y4!52)))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20384, 58])).
% 6.07/6.04 tff(20386,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20385])).
% 6.07/6.04 tff(20387,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(Y4!52))))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20386, 36])).
% 6.07/6.04 tff(20388,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20387])).
% 6.07/6.04 tff(20389,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20388, 48])).
% 6.07/6.04 tff(20390,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20389])).
% 6.07/6.04 tff(20391,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20390, 14])).
% 6.07/6.04 tff(20392,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20391])).
% 6.07/6.04 tff(20393,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20392, 33])).
% 6.07/6.04 tff(20394,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20393])).
% 6.07/6.04 tff(20395,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20394, 30])).
% 6.07/6.04 tff(20396,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20395])).
% 6.07/6.04 tff(20397,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20396, 39])).
% 6.07/6.04 tff(20398,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20397])).
% 6.07/6.04 tff(20399,plain,
% 6.07/6.04 (NSY4!20 = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[601, 20398, 53])).
% 6.07/6.04 tff(20400,plain,
% 6.07/6.04 (pred(NSY4!20) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20399])).
% 6.07/6.04 tff(20401,plain,
% 6.07/6.04 (pred(NSY4!20) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20400, 19])).
% 6.07/6.04 tff(20402,plain,
% 6.07/6.04 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n7, n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20401, 20377])).
% 6.07/6.04 tff(20403,plain,
% 6.07/6.04 (sum(pred(NSY4!20), succ(NPY4!22)) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20402, 44])).
% 6.07/6.04 tff(20404,plain,
% 6.07/6.04 (sum(pred(Y3!54), succ(X3!55)) = sum(n1, n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20247, 20329])).
% 6.07/6.04 tff(20405,plain,
% 6.07/6.04 (sum(pred(Y3!54), succ(X3!55)) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20404, 47])).
% 6.07/6.04 tff(20406,plain,
% 6.07/6.04 (sum(pred(X3!55), succ(Y3!54)) = sum(n1, n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20303, 20271])).
% 6.07/6.04 tff(20407,plain,
% 6.07/6.04 (sum(pred(X3!55), succ(Y3!54)) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20406, 47])).
% 6.07/6.04 tff(20408,plain,
% 6.07/6.04 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n4, n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20407, 20405])).
% 6.07/6.04 tff(20409,plain,
% 6.07/6.04 (X4!53 = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[438, 20408, 46])).
% 6.07/6.04 tff(20410,plain,
% 6.07/6.04 (pred(X4!53) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20409])).
% 6.07/6.04 tff(20411,plain,
% 6.07/6.04 (pred(X4!53) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20410, 19])).
% 6.07/6.04 tff(20412,plain,
% 6.07/6.04 (pred(pred(X4!53)) = pred(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20411])).
% 6.07/6.04 tff(20413,plain,
% 6.07/6.04 (pred(pred(X4!53)) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20412, 18])).
% 6.07/6.04 tff(20414,plain,
% 6.07/6.04 (pred(pred(pred(X4!53))) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20413])).
% 6.07/6.04 tff(20415,plain,
% 6.07/6.04 (pred(pred(pred(X4!53))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20414, 17])).
% 6.07/6.04 tff(20416,plain,
% 6.07/6.04 (pred(pred(pred(pred(X4!53)))) = pred(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20415])).
% 6.07/6.04 tff(20417,plain,
% 6.07/6.04 (pred(pred(pred(pred(X4!53)))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20416, 16])).
% 6.07/6.04 tff(20418,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(X4!53))))) = pred(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20417])).
% 6.07/6.04 tff(20419,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(X4!53))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20418, 15])).
% 6.07/6.04 tff(20420,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20419])).
% 6.07/6.04 tff(20421,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20420, 25])).
% 6.07/6.04 tff(20422,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20421])).
% 6.07/6.04 tff(20423,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20422, 24])).
% 6.07/6.04 tff(20424,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20423])).
% 6.07/6.04 tff(20425,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20424, 23])).
% 6.07/6.04 tff(20426,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20425])).
% 6.07/6.04 tff(20427,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20426, 22])).
% 6.07/6.04 tff(20428,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20427])).
% 6.07/6.04 tff(20429,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20428, 21])).
% 6.07/6.04 tff(20430,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20429])).
% 6.07/6.04 tff(20431,plain,
% 6.07/6.04 (NPX4!23 = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[626, 20430, 20])).
% 6.07/6.04 tff(20432,plain,
% 6.07/6.04 (succ(NPX4!23) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20431])).
% 6.07/6.04 tff(20433,plain,
% 6.07/6.04 (succ(NPX4!23) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20432, 45])).
% 6.07/6.04 tff(20434,plain,
% 6.07/6.04 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n9, n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20433, 20403])).
% 6.07/6.04 tff(20435,plain,
% 6.07/6.04 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20434, 790])).
% 6.07/6.04 tff(20436,plain,
% 6.07/6.04 (succ(X4!53) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20409])).
% 6.07/6.04 tff(20437,plain,
% 6.07/6.04 (succ(X4!53) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20436, 45])).
% 6.07/6.04 tff(20438,plain,
% 6.07/6.04 (succ(succ(X4!53)) = succ(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20437])).
% 6.07/6.04 tff(20439,plain,
% 6.07/6.04 (succ(succ(X4!53)) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20438, 28])).
% 6.07/6.04 tff(20440,plain,
% 6.07/6.04 (succ(succ(succ(X4!53))) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20439])).
% 6.07/6.04 tff(20441,plain,
% 6.07/6.04 (succ(succ(succ(X4!53))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20440, 42])).
% 6.07/6.04 tff(20442,plain,
% 6.07/6.04 (succ(succ(succ(succ(X4!53)))) = succ(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20441])).
% 6.07/6.04 tff(20443,plain,
% 6.07/6.04 (succ(succ(succ(succ(X4!53)))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20442, 58])).
% 6.07/6.04 tff(20444,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(X4!53))))) = succ(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20443])).
% 6.07/6.04 tff(20445,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(X4!53))))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20444, 36])).
% 6.07/6.04 tff(20446,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20445])).
% 6.07/6.04 tff(20447,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20446, 48])).
% 6.07/6.04 tff(20448,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20447])).
% 6.07/6.04 tff(20449,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20448, 14])).
% 6.07/6.04 tff(20450,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20449])).
% 6.07/6.04 tff(20451,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20450, 33])).
% 6.07/6.04 tff(20452,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20451])).
% 6.07/6.04 tff(20453,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20452, 30])).
% 6.07/6.04 tff(20454,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20453])).
% 6.07/6.04 tff(20455,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20454, 39])).
% 6.07/6.04 tff(20456,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20455])).
% 6.07/6.04 tff(20457,plain,
% 6.07/6.04 (NSX4!21 = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[651, 20456, 53])).
% 6.07/6.04 tff(20458,plain,
% 6.07/6.04 (pred(NSX4!21) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20457])).
% 6.07/6.04 tff(20459,plain,
% 6.07/6.04 (pred(NSX4!21) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20458, 19])).
% 6.07/6.04 tff(20460,plain,
% 6.07/6.04 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n7, n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20459, 20435])).
% 6.07/6.04 tff(20461,plain,
% 6.07/6.04 (Y5!50 = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[656, 20460, 789])).
% 6.07/6.04 tff(20462,plain,
% 6.07/6.04 (pred(Y5!50) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20461])).
% 6.07/6.04 tff(20463,plain,
% 6.07/6.04 (pred(Y5!50) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20462, 21])).
% 6.07/6.04 tff(20464,plain,
% 6.07/6.04 (pred(pred(Y5!50)) = pred(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20463])).
% 6.07/6.04 tff(20465,plain,
% 6.07/6.04 (pred(pred(Y5!50)) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20464, 20])).
% 6.07/6.04 tff(20466,plain,
% 6.07/6.04 (pred(pred(pred(Y5!50))) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20465])).
% 6.07/6.04 tff(20467,plain,
% 6.07/6.04 (pred(pred(pred(Y5!50))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20466, 19])).
% 6.07/6.04 tff(20468,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y5!50)))) = pred(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20467])).
% 6.07/6.04 tff(20469,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y5!50)))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20468, 18])).
% 6.07/6.04 tff(20470,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20469])).
% 6.07/6.04 tff(20471,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y5!50))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20470, 17])).
% 6.07/6.04 tff(20472,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20471])).
% 6.07/6.04 tff(20473,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20472, 16])).
% 6.07/6.04 tff(20474,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20473])).
% 6.07/6.04 tff(20475,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20474, 15])).
% 6.07/6.04 tff(20476,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20475])).
% 6.07/6.04 tff(20477,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20476, 25])).
% 6.07/6.04 tff(20478,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20477])).
% 6.07/6.04 tff(20479,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20478, 24])).
% 6.07/6.04 tff(20480,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20479])).
% 6.07/6.04 tff(20481,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20480, 23])).
% 6.07/6.04 tff(20482,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20481])).
% 6.07/6.04 tff(20483,plain,
% 6.07/6.04 (NPY5!18 = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[694, 20482, 22])).
% 6.07/6.04 tff(20484,plain,
% 6.07/6.04 (succ(NPY5!18) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20483])).
% 6.07/6.04 tff(20485,plain,
% 6.07/6.04 (succ(NPY5!18) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20484, 42])).
% 6.07/6.04 tff(20486,plain,
% 6.07/6.04 (succ(Y5!50) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20461])).
% 6.07/6.04 tff(20487,plain,
% 6.07/6.04 (succ(Y5!50) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20486, 42])).
% 6.07/6.04 tff(20488,plain,
% 6.07/6.04 (succ(succ(Y5!50)) = succ(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20487])).
% 6.07/6.04 tff(20489,plain,
% 6.07/6.04 (succ(succ(Y5!50)) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20488, 58])).
% 6.07/6.04 tff(20490,plain,
% 6.07/6.04 (succ(succ(succ(Y5!50))) = succ(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20489])).
% 6.07/6.04 tff(20491,plain,
% 6.07/6.04 (succ(succ(succ(Y5!50))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20490, 36])).
% 6.07/6.04 tff(20492,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y5!50)))) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20491])).
% 6.07/6.04 tff(20493,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y5!50)))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20492, 48])).
% 6.07/6.04 tff(20494,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20493])).
% 6.07/6.04 tff(20495,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(Y5!50))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20494, 14])).
% 6.07/6.04 tff(20496,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20495])).
% 6.07/6.04 tff(20497,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20496, 33])).
% 6.07/6.04 tff(20498,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20497])).
% 6.07/6.04 tff(20499,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20498, 30])).
% 6.07/6.04 tff(20500,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20499])).
% 6.07/6.04 tff(20501,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20500, 39])).
% 6.07/6.04 tff(20502,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20501])).
% 6.07/6.04 tff(20503,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20502, 53])).
% 6.07/6.04 tff(20504,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20503])).
% 6.07/6.04 tff(20505,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20504, 45])).
% 6.07/6.04 tff(20506,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20505])).
% 6.07/6.04 tff(20507,plain,
% 6.07/6.04 (NSY5!16 = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[717, 20506, 28])).
% 6.07/6.04 tff(20508,plain,
% 6.07/6.04 (pred(NSY5!16) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20507])).
% 6.07/6.04 tff(20509,plain,
% 6.07/6.04 (pred(NSY5!16) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20508, 21])).
% 6.07/6.04 tff(20510,plain,
% 6.07/6.04 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n9, n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20509, 20485])).
% 6.07/6.04 tff(20511,plain,
% 6.07/6.04 (sum(pred(NSY5!16), succ(NPY5!18)) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20510, 41])).
% 6.07/6.04 tff(20512,plain,
% 6.07/6.04 (sum(pred(Y4!52), succ(X4!53)) = sum(n7, n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20355, 20437])).
% 6.07/6.04 tff(20513,plain,
% 6.07/6.04 (sum(pred(Y4!52), succ(X4!53)) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20512, 44])).
% 6.07/6.04 tff(20514,plain,
% 6.07/6.04 (sum(pred(X4!53), succ(Y4!52)) = sum(n7, n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20411, 20379])).
% 6.07/6.04 tff(20515,plain,
% 6.07/6.04 (sum(pred(X4!53), succ(Y4!52)) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20514, 44])).
% 6.07/6.04 tff(20516,plain,
% 6.07/6.04 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n5, n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20515, 20513])).
% 6.07/6.04 tff(20517,plain,
% 6.07/6.04 (X5!51 = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[553, 20516, 43])).
% 6.07/6.04 tff(20518,plain,
% 6.07/6.04 (pred(X5!51) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20517])).
% 6.07/6.04 tff(20519,plain,
% 6.07/6.04 (pred(X5!51) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20518, 21])).
% 6.07/6.04 tff(20520,plain,
% 6.07/6.04 (pred(pred(X5!51)) = pred(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20519])).
% 6.07/6.04 tff(20521,plain,
% 6.07/6.04 (pred(pred(X5!51)) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20520, 20])).
% 6.07/6.04 tff(20522,plain,
% 6.07/6.04 (pred(pred(pred(X5!51))) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20521])).
% 6.07/6.04 tff(20523,plain,
% 6.07/6.04 (pred(pred(pred(X5!51))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20522, 19])).
% 6.07/6.04 tff(20524,plain,
% 6.07/6.04 (pred(pred(pred(pred(X5!51)))) = pred(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20523])).
% 6.07/6.04 tff(20525,plain,
% 6.07/6.04 (pred(pred(pred(pred(X5!51)))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20524, 18])).
% 6.07/6.04 tff(20526,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(X5!51))))) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20525])).
% 6.07/6.04 tff(20527,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(X5!51))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20526, 17])).
% 6.07/6.04 tff(20528,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20527])).
% 6.07/6.04 tff(20529,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20528, 16])).
% 6.07/6.04 tff(20530,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20529])).
% 6.07/6.04 tff(20531,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20530, 15])).
% 6.07/6.04 tff(20532,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20531])).
% 6.07/6.04 tff(20533,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20532, 25])).
% 6.07/6.04 tff(20534,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20533])).
% 6.07/6.04 tff(20535,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20534, 24])).
% 6.07/6.04 tff(20536,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20535])).
% 6.07/6.04 tff(20537,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20536, 23])).
% 6.07/6.04 tff(20538,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20537])).
% 6.07/6.04 tff(20539,plain,
% 6.07/6.04 (NPX5!19 = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[742, 20538, 22])).
% 6.07/6.04 tff(20540,plain,
% 6.07/6.04 (succ(NPX5!19) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20539])).
% 6.07/6.04 tff(20541,plain,
% 6.07/6.04 (succ(NPX5!19) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20540, 42])).
% 6.07/6.04 tff(20542,plain,
% 6.07/6.04 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n0, n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20541, 20511])).
% 6.07/6.04 tff(20543,plain,
% 6.07/6.04 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20542, 40])).
% 6.07/6.04 tff(20544,plain,
% 6.07/6.04 (succ(X5!51) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20517])).
% 6.07/6.04 tff(20545,plain,
% 6.07/6.04 (succ(X5!51) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20544, 42])).
% 6.07/6.04 tff(20546,plain,
% 6.07/6.04 (succ(succ(X5!51)) = succ(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20545])).
% 6.07/6.04 tff(20547,plain,
% 6.07/6.04 (succ(succ(X5!51)) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20546, 58])).
% 6.07/6.04 tff(20548,plain,
% 6.07/6.04 (succ(succ(succ(X5!51))) = succ(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20547])).
% 6.07/6.04 tff(20549,plain,
% 6.07/6.04 (succ(succ(succ(X5!51))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20548, 36])).
% 6.07/6.04 tff(20550,plain,
% 6.07/6.04 (succ(succ(succ(succ(X5!51)))) = succ(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20549])).
% 6.07/6.04 tff(20551,plain,
% 6.07/6.04 (succ(succ(succ(succ(X5!51)))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20550, 48])).
% 6.07/6.04 tff(20552,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(X5!51))))) = succ(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20551])).
% 6.07/6.04 tff(20553,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(X5!51))))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20552, 14])).
% 6.07/6.04 tff(20554,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20553])).
% 6.07/6.04 tff(20555,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20554, 33])).
% 6.07/6.04 tff(20556,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20555])).
% 6.07/6.04 tff(20557,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20556, 30])).
% 6.07/6.04 tff(20558,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20557])).
% 6.07/6.04 tff(20559,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[20558, 39])).
% 6.07/6.04 tff(20560,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20559])).
% 6.07/6.04 tff(20561,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20560, 53])).
% 6.07/6.04 tff(20562,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20561])).
% 6.07/6.04 tff(20563,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20562, 45])).
% 6.07/6.04 tff(20564,plain,
% 6.07/6.04 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20563])).
% 6.07/6.04 tff(20565,plain,
% 6.07/6.04 (NSX5!17 = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[767, 20564, 28])).
% 6.07/6.04 tff(20566,plain,
% 6.07/6.04 (pred(NSX5!17) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20565])).
% 6.07/6.04 tff(20567,plain,
% 6.07/6.04 (pred(NSX5!17) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20566, 21])).
% 6.07/6.04 tff(20568,plain,
% 6.07/6.04 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n9, n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20567, 20543])).
% 6.07/6.04 tff(20569,plain,
% 6.07/6.04 (Y6!48 = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[772, 20568, 54])).
% 6.07/6.04 tff(20570,plain,
% 6.07/6.04 (pred(Y6!48) = pred(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20569])).
% 6.07/6.04 tff(20571,plain,
% 6.07/6.04 (pred(Y6!48) = n6),
% 6.07/6.04 inference(transitivity,[status(thm)],[20570, 18])).
% 6.07/6.04 tff(20572,plain,
% 6.07/6.04 (pred(pred(Y6!48)) = pred(n6)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20571])).
% 6.07/6.04 tff(20573,plain,
% 6.07/6.04 (pred(pred(Y6!48)) = n5),
% 6.07/6.04 inference(transitivity,[status(thm)],[20572, 17])).
% 6.07/6.04 tff(20574,plain,
% 6.07/6.04 (pred(pred(pred(Y6!48))) = pred(n5)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20573])).
% 6.07/6.04 tff(20575,plain,
% 6.07/6.04 (pred(pred(pred(Y6!48))) = n4),
% 6.07/6.04 inference(transitivity,[status(thm)],[20574, 16])).
% 6.07/6.04 tff(20576,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y6!48)))) = pred(n4)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20575])).
% 6.07/6.04 tff(20577,plain,
% 6.07/6.04 (pred(pred(pred(pred(Y6!48)))) = n3),
% 6.07/6.04 inference(transitivity,[status(thm)],[20576, 15])).
% 6.07/6.04 tff(20578,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n3)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20577])).
% 6.07/6.04 tff(20579,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(Y6!48))))) = n2),
% 6.07/6.04 inference(transitivity,[status(thm)],[20578, 25])).
% 6.07/6.04 tff(20580,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n2)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20579])).
% 6.07/6.04 tff(20581,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n1),
% 6.07/6.04 inference(transitivity,[status(thm)],[20580, 24])).
% 6.07/6.04 tff(20582,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n1)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20581])).
% 6.07/6.04 tff(20583,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20582, 23])).
% 6.07/6.04 tff(20584,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n0)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20583])).
% 6.07/6.04 tff(20585,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20584, 22])).
% 6.07/6.04 tff(20586,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20585])).
% 6.07/6.04 tff(20587,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20586, 21])).
% 6.07/6.04 tff(20588,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20587])).
% 6.07/6.04 tff(20589,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20588, 20])).
% 6.07/6.04 tff(20590,plain,
% 6.07/6.04 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20589])).
% 6.07/6.04 tff(20591,plain,
% 6.07/6.04 (NPY6!14 = n7),
% 6.07/6.04 inference(transitivity,[status(thm)],[1465, 20590, 19])).
% 6.07/6.04 tff(20592,plain,
% 6.07/6.04 (succ(NPY6!14) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20591])).
% 6.07/6.04 tff(20593,plain,
% 6.07/6.04 (succ(NPY6!14) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20592, 53])).
% 6.07/6.04 tff(20594,plain,
% 6.07/6.04 (succ(Y6!48) = succ(n7)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20569])).
% 6.07/6.04 tff(20595,plain,
% 6.07/6.04 (succ(Y6!48) = n8),
% 6.07/6.04 inference(transitivity,[status(thm)],[20594, 53])).
% 6.07/6.04 tff(20596,plain,
% 6.07/6.04 (succ(succ(Y6!48)) = succ(n8)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20595])).
% 6.07/6.04 tff(20597,plain,
% 6.07/6.04 (succ(succ(Y6!48)) = n9),
% 6.07/6.04 inference(transitivity,[status(thm)],[20596, 45])).
% 6.07/6.04 tff(20598,plain,
% 6.07/6.04 (succ(succ(succ(Y6!48))) = succ(n9)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20597])).
% 6.07/6.04 tff(20599,plain,
% 6.07/6.04 (succ(succ(succ(Y6!48))) = n10),
% 6.07/6.04 inference(transitivity,[status(thm)],[20598, 28])).
% 6.07/6.04 tff(20600,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y6!48)))) = succ(n10)),
% 6.07/6.04 inference(monotonicity,[status(thm)],[20599])).
% 6.07/6.04 tff(20601,plain,
% 6.07/6.04 (succ(succ(succ(succ(Y6!48)))) = n0),
% 6.07/6.04 inference(transitivity,[status(thm)],[20600, 42])).
% 6.07/6.05 tff(20602,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20601])).
% 6.07/6.05 tff(20603,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(Y6!48))))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20602, 58])).
% 6.07/6.05 tff(20604,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20603])).
% 6.07/6.05 tff(20605,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20604, 36])).
% 6.07/6.05 tff(20606,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20605])).
% 6.07/6.05 tff(20607,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20606, 48])).
% 6.07/6.05 tff(20608,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20607])).
% 6.07/6.05 tff(20609,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20608, 14])).
% 6.07/6.05 tff(20610,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20609])).
% 6.07/6.05 tff(20611,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20610, 33])).
% 6.07/6.05 tff(20612,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20611])).
% 6.07/6.05 tff(20613,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20612, 30])).
% 6.07/6.05 tff(20614,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20613])).
% 6.07/6.05 tff(20615,plain,
% 6.07/6.05 (NSY6!12 = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[1490, 20614, 39])).
% 6.07/6.05 tff(20616,plain,
% 6.07/6.05 (pred(NSY6!12) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20615])).
% 6.07/6.05 tff(20617,plain,
% 6.07/6.05 (pred(NSY6!12) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20616, 18])).
% 6.07/6.05 tff(20618,plain,
% 6.07/6.05 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n6, n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20617, 20593])).
% 6.07/6.05 tff(20619,plain,
% 6.07/6.05 (sum(pred(NSY6!12), succ(NPY6!14)) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20618, 52])).
% 6.07/6.05 tff(20620,plain,
% 6.07/6.05 (sum(pred(Y5!50), succ(X5!51)) = sum(n9, n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20463, 20545])).
% 6.07/6.05 tff(20621,plain,
% 6.07/6.05 (sum(pred(Y5!50), succ(X5!51)) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20620, 41])).
% 6.07/6.05 tff(20622,plain,
% 6.07/6.05 (sum(pred(X5!51), succ(Y5!50)) = sum(n9, n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20519, 20487])).
% 6.07/6.05 tff(20623,plain,
% 6.07/6.05 (sum(pred(X5!51), succ(Y5!50)) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20622, 41])).
% 6.07/6.05 tff(20624,plain,
% 6.07/6.05 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n9, n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20623, 20621])).
% 6.07/6.05 tff(20625,plain,
% 6.07/6.05 (X6!49 = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[669, 20624, 54])).
% 6.07/6.05 tff(20626,plain,
% 6.07/6.05 (pred(X6!49) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20625])).
% 6.07/6.05 tff(20627,plain,
% 6.07/6.05 (pred(X6!49) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20626, 18])).
% 6.07/6.05 tff(20628,plain,
% 6.07/6.05 (pred(pred(X6!49)) = pred(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20627])).
% 6.07/6.05 tff(20629,plain,
% 6.07/6.05 (pred(pred(X6!49)) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20628, 17])).
% 6.07/6.05 tff(20630,plain,
% 6.07/6.05 (pred(pred(pred(X6!49))) = pred(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20629])).
% 6.07/6.05 tff(20631,plain,
% 6.07/6.05 (pred(pred(pred(X6!49))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20630, 16])).
% 6.07/6.05 tff(20632,plain,
% 6.07/6.05 (pred(pred(pred(pred(X6!49)))) = pred(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20631])).
% 6.07/6.05 tff(20633,plain,
% 6.07/6.05 (pred(pred(pred(pred(X6!49)))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20632, 15])).
% 6.07/6.05 tff(20634,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(X6!49))))) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20633])).
% 6.07/6.05 tff(20635,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(X6!49))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20634, 25])).
% 6.07/6.05 tff(20636,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20635])).
% 6.07/6.05 tff(20637,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20636, 24])).
% 6.07/6.05 tff(20638,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20637])).
% 6.07/6.05 tff(20639,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20638, 23])).
% 6.07/6.05 tff(20640,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20639])).
% 6.07/6.05 tff(20641,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20640, 22])).
% 6.07/6.05 tff(20642,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20641])).
% 6.07/6.05 tff(20643,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20642, 21])).
% 6.07/6.05 tff(20644,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20643])).
% 6.07/6.05 tff(20645,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20644, 20])).
% 6.07/6.05 tff(20646,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20645])).
% 6.07/6.05 tff(20647,plain,
% 6.07/6.05 (NPX6!15 = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[1523, 20646, 19])).
% 6.07/6.05 tff(20648,plain,
% 6.07/6.05 (succ(NPX6!15) = succ(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20647])).
% 6.07/6.05 tff(20649,plain,
% 6.07/6.05 (succ(NPX6!15) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20648, 53])).
% 6.07/6.05 tff(20650,plain,
% 6.07/6.05 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n8, n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20649, 20619])).
% 6.07/6.05 tff(20651,plain,
% 6.07/6.05 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20650, 64])).
% 6.07/6.05 tff(20652,plain,
% 6.07/6.05 (succ(X6!49) = succ(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20625])).
% 6.07/6.05 tff(20653,plain,
% 6.07/6.05 (succ(X6!49) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20652, 53])).
% 6.07/6.05 tff(20654,plain,
% 6.07/6.05 (succ(succ(X6!49)) = succ(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20653])).
% 6.07/6.05 tff(20655,plain,
% 6.07/6.05 (succ(succ(X6!49)) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20654, 45])).
% 6.07/6.05 tff(20656,plain,
% 6.07/6.05 (succ(succ(succ(X6!49))) = succ(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20655])).
% 6.07/6.05 tff(20657,plain,
% 6.07/6.05 (succ(succ(succ(X6!49))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20656, 28])).
% 6.07/6.05 tff(20658,plain,
% 6.07/6.05 (succ(succ(succ(succ(X6!49)))) = succ(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20657])).
% 6.07/6.05 tff(20659,plain,
% 6.07/6.05 (succ(succ(succ(succ(X6!49)))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20658, 42])).
% 6.07/6.05 tff(20660,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(X6!49))))) = succ(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20659])).
% 6.07/6.05 tff(20661,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(X6!49))))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20660, 58])).
% 6.07/6.05 tff(20662,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20661])).
% 6.07/6.05 tff(20663,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20662, 36])).
% 6.07/6.05 tff(20664,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20663])).
% 6.07/6.05 tff(20665,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20664, 48])).
% 6.07/6.05 tff(20666,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20665])).
% 6.07/6.05 tff(20667,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20666, 14])).
% 6.07/6.05 tff(20668,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20667])).
% 6.07/6.05 tff(20669,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20668, 33])).
% 6.07/6.05 tff(20670,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20669])).
% 6.07/6.05 tff(20671,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20670, 30])).
% 6.07/6.05 tff(20672,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20671])).
% 6.07/6.05 tff(20673,plain,
% 6.07/6.05 (NSX6!13 = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[1550, 20672, 39])).
% 6.07/6.05 tff(20674,plain,
% 6.07/6.05 (pred(NSX6!13) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20673])).
% 6.07/6.05 tff(20675,plain,
% 6.07/6.05 (pred(NSX6!13) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20674, 18])).
% 6.07/6.05 tff(20676,plain,
% 6.07/6.05 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n6, n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20675, 20651])).
% 6.07/6.05 tff(20677,plain,
% 6.07/6.05 (sum(n6, n0) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 6.07/6.05 inference(symmetry,[status(thm)],[20676])).
% 6.07/6.05 tff(20678,plain,
% 6.07/6.05 (sum(pred(Y6!48), succ(X6!49)) = sum(n6, n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20571, 20653])).
% 6.07/6.05 tff(20679,plain,
% 6.07/6.05 (sum(pred(Y6!48), succ(X6!49)) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20678, 52])).
% 6.07/6.05 tff(20680,plain,
% 6.07/6.05 (sum(pred(X6!49), succ(Y6!48)) = sum(n6, n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20627, 20595])).
% 6.07/6.05 tff(20681,plain,
% 6.07/6.05 (sum(pred(X6!49), succ(Y6!48)) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20680, 52])).
% 6.07/6.05 tff(20682,plain,
% 6.07/6.05 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n3, n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20681, 20679])).
% 6.07/6.05 tff(20683,plain,
% 6.07/6.05 (X7!47 = Y7!46),
% 6.07/6.05 inference(transitivity,[status(thm)],[785, 20682, 51, 11259, 20677, 794])).
% 6.07/6.05 tff(20684,plain,
% 6.07/6.05 ($false),
% 6.07/6.05 inference(unit_resolution,[status(thm)],[792, 20683])).
% 6.07/6.05 tff(20685,plain,((~(Y0!60 = n6)) | (X7!47 = Y7!46) | (~(X0!61 = n3))), inference(lemma,lemma(discharge,[]))).
% 6.07/6.05 tff(20686,plain,
% 6.07/6.05 (~(Y0!60 = n6)),
% 6.07/6.05 inference(unit_resolution,[status(thm)],[20685, 17987, 792])).
% 6.07/6.05 tff(20687,plain,
% 6.07/6.05 (sum(n4, n3) = n7),
% 6.07/6.05 inference(and_elim,[status(thm)],[9])).
% 6.07/6.05 tff(20688,plain,
% 6.07/6.05 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n4, n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[18011, 2335])).
% 6.07/6.05 tff(20689,plain,
% 6.07/6.05 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20688, 20687])).
% 6.07/6.05 tff(20690,plain,
% 6.07/6.05 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n2, n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[18037, 20689])).
% 6.07/6.05 tff(20691,plain,
% 6.07/6.05 (Y1!58 = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[196, 20690, 20081])).
% 6.07/6.05 tff(20692,plain,
% 6.07/6.05 (pred(Y1!58) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20691])).
% 6.07/6.05 tff(20693,plain,
% 6.07/6.05 (pred(Y1!58) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20692, 20])).
% 6.07/6.05 tff(20694,plain,
% 6.07/6.05 (pred(pred(Y1!58)) = pred(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20693])).
% 6.07/6.05 tff(20695,plain,
% 6.07/6.05 (pred(pred(Y1!58)) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20694, 19])).
% 6.07/6.05 tff(20696,plain,
% 6.07/6.05 (pred(pred(pred(Y1!58))) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20695])).
% 6.07/6.05 tff(20697,plain,
% 6.07/6.05 (pred(pred(pred(Y1!58))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20696, 18])).
% 6.07/6.05 tff(20698,plain,
% 6.07/6.05 (pred(pred(pred(pred(Y1!58)))) = pred(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20697])).
% 6.07/6.05 tff(20699,plain,
% 6.07/6.05 (pred(pred(pred(pred(Y1!58)))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20698, 17])).
% 6.07/6.05 tff(20700,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20699])).
% 6.07/6.05 tff(20701,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(Y1!58))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20700, 16])).
% 6.07/6.05 tff(20702,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20701])).
% 6.07/6.05 tff(20703,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20702, 15])).
% 6.07/6.05 tff(20704,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20703])).
% 6.07/6.05 tff(20705,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20704, 25])).
% 6.07/6.05 tff(20706,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20705])).
% 6.07/6.05 tff(20707,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20706, 24])).
% 6.07/6.05 tff(20708,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20707])).
% 6.07/6.05 tff(20709,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20708, 23])).
% 6.07/6.05 tff(20710,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20709])).
% 6.07/6.05 tff(20711,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20710, 22])).
% 6.07/6.05 tff(20712,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20711])).
% 6.07/6.05 tff(20713,plain,
% 6.07/6.05 (NPY1!34 = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[232, 20712, 21])).
% 6.07/6.05 tff(20714,plain,
% 6.07/6.05 (succ(NPY1!34) = succ(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20713])).
% 6.07/6.05 tff(20715,plain,
% 6.07/6.05 (succ(NPY1!34) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20714, 28])).
% 6.07/6.05 tff(20716,plain,
% 6.07/6.05 (succ(Y1!58) = succ(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20691])).
% 6.07/6.05 tff(20717,plain,
% 6.07/6.05 (succ(Y1!58) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20716, 28])).
% 6.07/6.05 tff(20718,plain,
% 6.07/6.05 (succ(succ(Y1!58)) = succ(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20717])).
% 6.07/6.05 tff(20719,plain,
% 6.07/6.05 (succ(succ(Y1!58)) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20718, 42])).
% 6.07/6.05 tff(20720,plain,
% 6.07/6.05 (succ(succ(succ(Y1!58))) = succ(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20719])).
% 6.07/6.05 tff(20721,plain,
% 6.07/6.05 (succ(succ(succ(Y1!58))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20720, 58])).
% 6.07/6.05 tff(20722,plain,
% 6.07/6.05 (succ(succ(succ(succ(Y1!58)))) = succ(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20721])).
% 6.07/6.05 tff(20723,plain,
% 6.07/6.05 (succ(succ(succ(succ(Y1!58)))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20722, 36])).
% 6.07/6.05 tff(20724,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20723])).
% 6.07/6.05 tff(20725,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(Y1!58))))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20724, 48])).
% 6.07/6.05 tff(20726,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20725])).
% 6.07/6.05 tff(20727,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20726, 14])).
% 6.07/6.05 tff(20728,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20727])).
% 6.07/6.05 tff(20729,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20728, 33])).
% 6.07/6.05 tff(20730,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20729])).
% 6.07/6.05 tff(20731,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20730, 30])).
% 6.07/6.05 tff(20732,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20731])).
% 6.07/6.05 tff(20733,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20732, 39])).
% 6.07/6.05 tff(20734,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20733])).
% 6.07/6.05 tff(20735,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20734, 53])).
% 6.07/6.05 tff(20736,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20735])).
% 6.07/6.05 tff(20737,plain,
% 6.07/6.05 (NSY1!32 = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[255, 20736, 45])).
% 6.07/6.05 tff(20738,plain,
% 6.07/6.05 (pred(NSY1!32) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20737])).
% 6.07/6.05 tff(20739,plain,
% 6.07/6.05 (pred(NSY1!32) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20738, 20])).
% 6.07/6.05 tff(20740,plain,
% 6.07/6.05 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n8, n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20739, 20715])).
% 6.07/6.05 tff(20741,plain,
% 6.07/6.05 (sum(pred(NSY1!32), succ(NPY1!34)) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20740, 27])).
% 6.07/6.05 tff(20742,plain,
% 6.07/6.05 (sum(pred(Y0!60), succ(X0!61)) = sum(n6, n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[2287, 18015])).
% 6.07/6.05 tff(20743,plain,
% 6.07/6.05 (sum(pred(Y0!60), succ(X0!61)) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20742, 85])).
% 6.07/6.05 tff(20744,plain,
% 6.07/6.05 (sum(pred(X0!61), succ(Y0!60)) = sum(n2, n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[17989, 2311])).
% 6.07/6.05 tff(20745,plain,
% 6.07/6.05 (sum(pred(X0!61), succ(Y0!60)) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20744, 79])).
% 6.07/6.05 tff(20746,plain,
% 6.07/6.05 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n10, n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20745, 20743])).
% 6.07/6.05 tff(20747,plain,
% 6.07/6.05 (X1!59 = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[93, 20746, 29])).
% 6.07/6.05 tff(20748,plain,
% 6.07/6.05 (pred(X1!59) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20747])).
% 6.07/6.05 tff(20749,plain,
% 6.07/6.05 (pred(X1!59) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20748, 20])).
% 6.07/6.05 tff(20750,plain,
% 6.07/6.05 (pred(pred(X1!59)) = pred(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20749])).
% 6.07/6.05 tff(20751,plain,
% 6.07/6.05 (pred(pred(X1!59)) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20750, 19])).
% 6.07/6.05 tff(20752,plain,
% 6.07/6.05 (pred(pred(pred(X1!59))) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20751])).
% 6.07/6.05 tff(20753,plain,
% 6.07/6.05 (pred(pred(pred(X1!59))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20752, 18])).
% 6.07/6.05 tff(20754,plain,
% 6.07/6.05 (pred(pred(pred(pred(X1!59)))) = pred(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20753])).
% 6.07/6.05 tff(20755,plain,
% 6.07/6.05 (pred(pred(pred(pred(X1!59)))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20754, 17])).
% 6.07/6.05 tff(20756,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(X1!59))))) = pred(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20755])).
% 6.07/6.05 tff(20757,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(X1!59))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20756, 16])).
% 6.07/6.05 tff(20758,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20757])).
% 6.07/6.05 tff(20759,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20758, 15])).
% 6.07/6.05 tff(20760,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20759])).
% 6.07/6.05 tff(20761,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20760, 25])).
% 6.07/6.05 tff(20762,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20761])).
% 6.07/6.05 tff(20763,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20762, 24])).
% 6.07/6.05 tff(20764,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20763])).
% 6.07/6.05 tff(20765,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20764, 23])).
% 6.07/6.05 tff(20766,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20765])).
% 6.07/6.05 tff(20767,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20766, 22])).
% 6.07/6.05 tff(20768,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20767])).
% 6.07/6.05 tff(20769,plain,
% 6.07/6.05 (NPX1!35 = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[280, 20768, 21])).
% 6.07/6.05 tff(20770,plain,
% 6.07/6.05 (succ(NPX1!35) = succ(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20769])).
% 6.07/6.05 tff(20771,plain,
% 6.07/6.05 (succ(NPX1!35) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20770, 28])).
% 6.07/6.05 tff(20772,plain,
% 6.07/6.05 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n10, n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20771, 20741])).
% 6.07/6.05 tff(20773,plain,
% 6.07/6.05 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20772, 69])).
% 6.07/6.05 tff(20774,plain,
% 6.07/6.05 (succ(X1!59) = succ(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20747])).
% 6.07/6.05 tff(20775,plain,
% 6.07/6.05 (succ(X1!59) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20774, 28])).
% 6.07/6.05 tff(20776,plain,
% 6.07/6.05 (succ(succ(X1!59)) = succ(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20775])).
% 6.07/6.05 tff(20777,plain,
% 6.07/6.05 (succ(succ(X1!59)) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20776, 42])).
% 6.07/6.05 tff(20778,plain,
% 6.07/6.05 (succ(succ(succ(X1!59))) = succ(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20777])).
% 6.07/6.05 tff(20779,plain,
% 6.07/6.05 (succ(succ(succ(X1!59))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20778, 58])).
% 6.07/6.05 tff(20780,plain,
% 6.07/6.05 (succ(succ(succ(succ(X1!59)))) = succ(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20779])).
% 6.07/6.05 tff(20781,plain,
% 6.07/6.05 (succ(succ(succ(succ(X1!59)))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20780, 36])).
% 6.07/6.05 tff(20782,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(X1!59))))) = succ(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20781])).
% 6.07/6.05 tff(20783,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(X1!59))))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20782, 48])).
% 6.07/6.05 tff(20784,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20783])).
% 6.07/6.05 tff(20785,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20784, 14])).
% 6.07/6.05 tff(20786,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20785])).
% 6.07/6.05 tff(20787,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20786, 33])).
% 6.07/6.05 tff(20788,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20787])).
% 6.07/6.05 tff(20789,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20788, 30])).
% 6.07/6.05 tff(20790,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20789])).
% 6.07/6.05 tff(20791,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20790, 39])).
% 6.07/6.05 tff(20792,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20791])).
% 6.07/6.05 tff(20793,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20792, 53])).
% 6.07/6.05 tff(20794,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20793])).
% 6.07/6.05 tff(20795,plain,
% 6.07/6.05 (NSX1!33 = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[305, 20794, 45])).
% 6.07/6.05 tff(20796,plain,
% 6.07/6.05 (pred(NSX1!33) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20795])).
% 6.07/6.05 tff(20797,plain,
% 6.07/6.05 (pred(NSX1!33) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20796, 20])).
% 6.07/6.05 tff(20798,plain,
% 6.07/6.05 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n8, n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20797, 20773])).
% 6.07/6.05 tff(20799,plain,
% 6.07/6.05 (Y2!56 = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[310, 20798, 98])).
% 6.07/6.05 tff(20800,plain,
% 6.07/6.05 (pred(Y2!56) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20799])).
% 6.07/6.05 tff(20801,plain,
% 6.07/6.05 (pred(Y2!56) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20800, 25])).
% 6.07/6.05 tff(20802,plain,
% 6.07/6.05 (pred(pred(Y2!56)) = pred(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20801])).
% 6.07/6.05 tff(20803,plain,
% 6.07/6.05 (pred(pred(Y2!56)) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20802, 24])).
% 6.07/6.05 tff(20804,plain,
% 6.07/6.05 (pred(pred(pred(Y2!56))) = pred(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20803])).
% 6.07/6.05 tff(20805,plain,
% 6.07/6.05 (pred(pred(pred(Y2!56))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20804, 23])).
% 6.07/6.05 tff(20806,plain,
% 6.07/6.05 (pred(pred(pred(pred(Y2!56)))) = pred(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20805])).
% 6.07/6.05 tff(20807,plain,
% 6.07/6.05 (pred(pred(pred(pred(Y2!56)))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20806, 22])).
% 6.07/6.05 tff(20808,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20807])).
% 6.07/6.05 tff(20809,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(Y2!56))))) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20808, 21])).
% 6.07/6.05 tff(20810,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20809])).
% 6.07/6.05 tff(20811,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20810, 20])).
% 6.07/6.05 tff(20812,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20811])).
% 6.07/6.05 tff(20813,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20812, 19])).
% 6.07/6.05 tff(20814,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20813])).
% 6.07/6.05 tff(20815,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20814, 18])).
% 6.07/6.05 tff(20816,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20815])).
% 6.07/6.05 tff(20817,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20816, 17])).
% 6.07/6.05 tff(20818,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20817])).
% 6.07/6.05 tff(20819,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20818, 16])).
% 6.07/6.05 tff(20820,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20819])).
% 6.07/6.05 tff(20821,plain,
% 6.07/6.05 (NPY2!30 = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[347, 20820, 15])).
% 6.07/6.05 tff(20822,plain,
% 6.07/6.05 (succ(NPY2!30) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20821])).
% 6.07/6.05 tff(20823,plain,
% 6.07/6.05 (succ(NPY2!30) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20822, 14])).
% 6.07/6.05 tff(20824,plain,
% 6.07/6.05 (succ(Y2!56) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20799])).
% 6.07/6.05 tff(20825,plain,
% 6.07/6.05 (succ(Y2!56) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20824, 14])).
% 6.07/6.05 tff(20826,plain,
% 6.07/6.05 (succ(succ(Y2!56)) = succ(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20825])).
% 6.07/6.05 tff(20827,plain,
% 6.07/6.05 (succ(succ(Y2!56)) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20826, 33])).
% 6.07/6.05 tff(20828,plain,
% 6.07/6.05 (succ(succ(succ(Y2!56))) = succ(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20827])).
% 6.07/6.05 tff(20829,plain,
% 6.07/6.05 (succ(succ(succ(Y2!56))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20828, 30])).
% 6.07/6.05 tff(20830,plain,
% 6.07/6.05 (succ(succ(succ(succ(Y2!56)))) = succ(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20829])).
% 6.07/6.05 tff(20831,plain,
% 6.07/6.05 (succ(succ(succ(succ(Y2!56)))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20830, 39])).
% 6.07/6.05 tff(20832,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20831])).
% 6.07/6.05 tff(20833,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(Y2!56))))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20832, 53])).
% 6.07/6.05 tff(20834,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20833])).
% 6.07/6.05 tff(20835,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20834, 45])).
% 6.07/6.05 tff(20836,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20835])).
% 6.07/6.05 tff(20837,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20836, 28])).
% 6.07/6.05 tff(20838,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20837])).
% 6.07/6.05 tff(20839,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20838, 42])).
% 6.07/6.05 tff(20840,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20839])).
% 6.07/6.05 tff(20841,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20840, 58])).
% 6.07/6.05 tff(20842,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20841])).
% 6.07/6.05 tff(20843,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20842, 36])).
% 6.07/6.05 tff(20844,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20843])).
% 6.07/6.05 tff(20845,plain,
% 6.07/6.05 (NSY2!28 = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[370, 20844, 48])).
% 6.07/6.05 tff(20846,plain,
% 6.07/6.05 (pred(NSY2!28) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20845])).
% 6.07/6.05 tff(20847,plain,
% 6.07/6.05 (pred(NSY2!28) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20846, 25])).
% 6.07/6.05 tff(20848,plain,
% 6.07/6.05 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n2, n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20847, 20823])).
% 6.07/6.05 tff(20849,plain,
% 6.07/6.05 (sum(pred(NSY2!28), succ(NPY2!30)) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20848, 13])).
% 6.07/6.05 tff(20850,plain,
% 6.07/6.05 (sum(pred(Y1!58), succ(X1!59)) = sum(n8, n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20693, 20775])).
% 6.07/6.05 tff(20851,plain,
% 6.07/6.05 (sum(pred(Y1!58), succ(X1!59)) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20850, 27])).
% 6.07/6.05 tff(20852,plain,
% 6.07/6.05 (sum(pred(X1!59), succ(Y1!58)) = sum(n8, n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20749, 20717])).
% 6.07/6.05 tff(20853,plain,
% 6.07/6.05 (sum(pred(X1!59), succ(Y1!58)) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20852, 27])).
% 6.07/6.05 tff(20854,plain,
% 6.07/6.05 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n7, n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20853, 20851])).
% 6.07/6.05 tff(20855,plain,
% 6.07/6.05 (X2!57 = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[209, 20854, 26])).
% 6.07/6.05 tff(20856,plain,
% 6.07/6.05 (pred(X2!57) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20855])).
% 6.07/6.05 tff(20857,plain,
% 6.07/6.05 (pred(X2!57) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20856, 25])).
% 6.07/6.05 tff(20858,plain,
% 6.07/6.05 (pred(pred(X2!57)) = pred(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20857])).
% 6.07/6.05 tff(20859,plain,
% 6.07/6.05 (pred(pred(X2!57)) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20858, 24])).
% 6.07/6.05 tff(20860,plain,
% 6.07/6.05 (pred(pred(pred(X2!57))) = pred(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20859])).
% 6.07/6.05 tff(20861,plain,
% 6.07/6.05 (pred(pred(pred(X2!57))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20860, 23])).
% 6.07/6.05 tff(20862,plain,
% 6.07/6.05 (pred(pred(pred(pred(X2!57)))) = pred(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20861])).
% 6.07/6.05 tff(20863,plain,
% 6.07/6.05 (pred(pred(pred(pred(X2!57)))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20862, 22])).
% 6.07/6.05 tff(20864,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(X2!57))))) = pred(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20863])).
% 6.07/6.05 tff(20865,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(X2!57))))) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20864, 21])).
% 6.07/6.05 tff(20866,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20865])).
% 6.07/6.05 tff(20867,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20866, 20])).
% 6.07/6.05 tff(20868,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20867])).
% 6.07/6.05 tff(20869,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20868, 19])).
% 6.07/6.05 tff(20870,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20869])).
% 6.07/6.05 tff(20871,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20870, 18])).
% 6.07/6.05 tff(20872,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20871])).
% 6.07/6.05 tff(20873,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20872, 17])).
% 6.07/6.05 tff(20874,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20873])).
% 6.07/6.05 tff(20875,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20874, 16])).
% 6.07/6.05 tff(20876,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20875])).
% 6.07/6.05 tff(20877,plain,
% 6.07/6.05 (NPX2!31 = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[395, 20876, 15])).
% 6.07/6.05 tff(20878,plain,
% 6.07/6.05 (succ(NPX2!31) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20877])).
% 6.07/6.05 tff(20879,plain,
% 6.07/6.05 (succ(NPX2!31) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20878, 14])).
% 6.07/6.05 tff(20880,plain,
% 6.07/6.05 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n4, n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20879, 20849])).
% 6.07/6.05 tff(20881,plain,
% 6.07/6.05 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20880, 12])).
% 6.07/6.05 tff(20882,plain,
% 6.07/6.05 (succ(X2!57) = succ(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20855])).
% 6.07/6.05 tff(20883,plain,
% 6.07/6.05 (succ(X2!57) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20882, 14])).
% 6.07/6.05 tff(20884,plain,
% 6.07/6.05 (succ(succ(X2!57)) = succ(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20883])).
% 6.07/6.05 tff(20885,plain,
% 6.07/6.05 (succ(succ(X2!57)) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20884, 33])).
% 6.07/6.05 tff(20886,plain,
% 6.07/6.05 (succ(succ(succ(X2!57))) = succ(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20885])).
% 6.07/6.05 tff(20887,plain,
% 6.07/6.05 (succ(succ(succ(X2!57))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20886, 30])).
% 6.07/6.05 tff(20888,plain,
% 6.07/6.05 (succ(succ(succ(succ(X2!57)))) = succ(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20887])).
% 6.07/6.05 tff(20889,plain,
% 6.07/6.05 (succ(succ(succ(succ(X2!57)))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20888, 39])).
% 6.07/6.05 tff(20890,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(X2!57))))) = succ(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20889])).
% 6.07/6.05 tff(20891,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(X2!57))))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20890, 53])).
% 6.07/6.05 tff(20892,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20891])).
% 6.07/6.05 tff(20893,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20892, 45])).
% 6.07/6.05 tff(20894,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20893])).
% 6.07/6.05 tff(20895,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20894, 28])).
% 6.07/6.05 tff(20896,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20895])).
% 6.07/6.05 tff(20897,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20896, 42])).
% 6.07/6.05 tff(20898,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20897])).
% 6.07/6.05 tff(20899,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[20898, 58])).
% 6.07/6.05 tff(20900,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20899])).
% 6.07/6.05 tff(20901,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20900, 36])).
% 6.07/6.05 tff(20902,plain,
% 6.07/6.05 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20901])).
% 6.07/6.05 tff(20903,plain,
% 6.07/6.05 (NSX2!29 = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[420, 20902, 48])).
% 6.07/6.05 tff(20904,plain,
% 6.07/6.05 (pred(NSX2!29) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20903])).
% 6.07/6.05 tff(20905,plain,
% 6.07/6.05 (pred(NSX2!29) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20904, 25])).
% 6.07/6.05 tff(20906,plain,
% 6.07/6.05 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n2, n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20905, 20881])).
% 6.07/6.05 tff(20907,plain,
% 6.07/6.05 (Y3!54 = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[425, 20906, 327])).
% 6.07/6.05 tff(20908,plain,
% 6.07/6.05 (pred(Y3!54) = pred(n1)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20907])).
% 6.07/6.05 tff(20909,plain,
% 6.07/6.05 (pred(Y3!54) = n0),
% 6.07/6.05 inference(transitivity,[status(thm)],[20908, 23])).
% 6.07/6.05 tff(20910,plain,
% 6.07/6.05 (pred(pred(Y3!54)) = pred(n0)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20909])).
% 6.07/6.05 tff(20911,plain,
% 6.07/6.05 (pred(pred(Y3!54)) = n10),
% 6.07/6.05 inference(transitivity,[status(thm)],[20910, 22])).
% 6.07/6.05 tff(20912,plain,
% 6.07/6.05 (pred(pred(pred(Y3!54))) = pred(n10)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20911])).
% 6.07/6.05 tff(20913,plain,
% 6.07/6.05 (pred(pred(pred(Y3!54))) = n9),
% 6.07/6.05 inference(transitivity,[status(thm)],[20912, 21])).
% 6.07/6.05 tff(20914,plain,
% 6.07/6.05 (pred(pred(pred(pred(Y3!54)))) = pred(n9)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20913])).
% 6.07/6.05 tff(20915,plain,
% 6.07/6.05 (pred(pred(pred(pred(Y3!54)))) = n8),
% 6.07/6.05 inference(transitivity,[status(thm)],[20914, 20])).
% 6.07/6.05 tff(20916,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n8)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20915])).
% 6.07/6.05 tff(20917,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(Y3!54))))) = n7),
% 6.07/6.05 inference(transitivity,[status(thm)],[20916, 19])).
% 6.07/6.05 tff(20918,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n7)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20917])).
% 6.07/6.05 tff(20919,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n6),
% 6.07/6.05 inference(transitivity,[status(thm)],[20918, 18])).
% 6.07/6.05 tff(20920,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n6)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20919])).
% 6.07/6.05 tff(20921,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n5),
% 6.07/6.05 inference(transitivity,[status(thm)],[20920, 17])).
% 6.07/6.05 tff(20922,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n5)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20921])).
% 6.07/6.05 tff(20923,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n4),
% 6.07/6.05 inference(transitivity,[status(thm)],[20922, 16])).
% 6.07/6.05 tff(20924,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n4)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20923])).
% 6.07/6.05 tff(20925,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n3),
% 6.07/6.05 inference(transitivity,[status(thm)],[20924, 15])).
% 6.07/6.05 tff(20926,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n3)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20925])).
% 6.07/6.05 tff(20927,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n2),
% 6.07/6.05 inference(transitivity,[status(thm)],[20926, 25])).
% 6.07/6.05 tff(20928,plain,
% 6.07/6.05 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n2)),
% 6.07/6.05 inference(monotonicity,[status(thm)],[20927])).
% 6.07/6.05 tff(20929,plain,
% 6.07/6.05 (NPY3!26 = n1),
% 6.07/6.05 inference(transitivity,[status(thm)],[462, 20928, 24])).
% 6.07/6.05 tff(20930,plain,
% 6.07/6.05 (succ(NPY3!26) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20929])).
% 6.07/6.06 tff(20931,plain,
% 6.07/6.06 (succ(NPY3!26) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[20930, 36])).
% 6.07/6.06 tff(20932,plain,
% 6.07/6.06 (succ(Y3!54) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20907])).
% 6.07/6.06 tff(20933,plain,
% 6.07/6.06 (succ(Y3!54) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[20932, 36])).
% 6.07/6.06 tff(20934,plain,
% 6.07/6.06 (succ(succ(Y3!54)) = succ(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20933])).
% 6.07/6.06 tff(20935,plain,
% 6.07/6.06 (succ(succ(Y3!54)) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[20934, 48])).
% 6.07/6.06 tff(20936,plain,
% 6.07/6.06 (succ(succ(succ(Y3!54))) = succ(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20935])).
% 6.07/6.06 tff(20937,plain,
% 6.07/6.06 (succ(succ(succ(Y3!54))) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[20936, 14])).
% 6.07/6.06 tff(20938,plain,
% 6.07/6.06 (succ(succ(succ(succ(Y3!54)))) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20937])).
% 6.07/6.06 tff(20939,plain,
% 6.07/6.06 (succ(succ(succ(succ(Y3!54)))) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[20938, 33])).
% 6.07/6.06 tff(20940,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20939])).
% 6.07/6.06 tff(20941,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(Y3!54))))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[20940, 30])).
% 6.07/6.06 tff(20942,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20941])).
% 6.07/6.06 tff(20943,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[20942, 39])).
% 6.07/6.06 tff(20944,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20943])).
% 6.07/6.06 tff(20945,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[20944, 53])).
% 6.07/6.06 tff(20946,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20945])).
% 6.07/6.06 tff(20947,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[20946, 45])).
% 6.07/6.06 tff(20948,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20947])).
% 6.07/6.06 tff(20949,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[20948, 28])).
% 6.07/6.06 tff(20950,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20949])).
% 6.07/6.06 tff(20951,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[20950, 42])).
% 6.07/6.06 tff(20952,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20951])).
% 6.07/6.06 tff(20953,plain,
% 6.07/6.06 (NSY3!24 = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[485, 20952, 58])).
% 6.07/6.06 tff(20954,plain,
% 6.07/6.06 (pred(NSY3!24) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20953])).
% 6.07/6.06 tff(20955,plain,
% 6.07/6.06 (pred(NSY3!24) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[20954, 23])).
% 6.07/6.06 tff(20956,plain,
% 6.07/6.06 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n0, n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20955, 20931])).
% 6.07/6.06 tff(20957,plain,
% 6.07/6.06 (sum(pred(NSY3!24), succ(NPY3!26)) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[20956, 35])).
% 6.07/6.06 tff(20958,plain,
% 6.07/6.06 (sum(pred(Y2!56), succ(X2!57)) = sum(n2, n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20801, 20883])).
% 6.07/6.06 tff(20959,plain,
% 6.07/6.06 (sum(pred(Y2!56), succ(X2!57)) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[20958, 13])).
% 6.07/6.06 tff(20960,plain,
% 6.07/6.06 (sum(pred(X2!57), succ(Y2!56)) = sum(n2, n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20857, 20825])).
% 6.07/6.06 tff(20961,plain,
% 6.07/6.06 (sum(pred(X2!57), succ(Y2!56)) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[20960, 13])).
% 6.07/6.06 tff(20962,plain,
% 6.07/6.06 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n6, n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20961, 20959])).
% 6.07/6.06 tff(20963,plain,
% 6.07/6.06 (X3!55 = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[323, 20962, 37])).
% 6.07/6.06 tff(20964,plain,
% 6.07/6.06 (pred(X3!55) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20963])).
% 6.07/6.06 tff(20965,plain,
% 6.07/6.06 (pred(X3!55) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[20964, 23])).
% 6.07/6.06 tff(20966,plain,
% 6.07/6.06 (pred(pred(X3!55)) = pred(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20965])).
% 6.07/6.06 tff(20967,plain,
% 6.07/6.06 (pred(pred(X3!55)) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[20966, 22])).
% 6.07/6.06 tff(20968,plain,
% 6.07/6.06 (pred(pred(pred(X3!55))) = pred(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20967])).
% 6.07/6.06 tff(20969,plain,
% 6.07/6.06 (pred(pred(pred(X3!55))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[20968, 21])).
% 6.07/6.06 tff(20970,plain,
% 6.07/6.06 (pred(pred(pred(pred(X3!55)))) = pred(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20969])).
% 6.07/6.06 tff(20971,plain,
% 6.07/6.06 (pred(pred(pred(pred(X3!55)))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[20970, 20])).
% 6.07/6.06 tff(20972,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(X3!55))))) = pred(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20971])).
% 6.07/6.06 tff(20973,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(X3!55))))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[20972, 19])).
% 6.07/6.06 tff(20974,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20973])).
% 6.07/6.06 tff(20975,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[20974, 18])).
% 6.07/6.06 tff(20976,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20975])).
% 6.07/6.06 tff(20977,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[20976, 17])).
% 6.07/6.06 tff(20978,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20977])).
% 6.07/6.06 tff(20979,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[20978, 16])).
% 6.07/6.06 tff(20980,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20979])).
% 6.07/6.06 tff(20981,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[20980, 15])).
% 6.07/6.06 tff(20982,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20981])).
% 6.07/6.06 tff(20983,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[20982, 25])).
% 6.07/6.06 tff(20984,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20983])).
% 6.07/6.06 tff(20985,plain,
% 6.07/6.06 (NPX3!27 = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[510, 20984, 24])).
% 6.07/6.06 tff(20986,plain,
% 6.07/6.06 (succ(NPX3!27) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20985])).
% 6.07/6.06 tff(20987,plain,
% 6.07/6.06 (succ(NPX3!27) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[20986, 36])).
% 6.07/6.06 tff(20988,plain,
% 6.07/6.06 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n2, n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20987, 20957])).
% 6.07/6.06 tff(20989,plain,
% 6.07/6.06 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[20988, 34])).
% 6.07/6.06 tff(20990,plain,
% 6.07/6.06 (succ(X3!55) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20963])).
% 6.07/6.06 tff(20991,plain,
% 6.07/6.06 (succ(X3!55) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[20990, 36])).
% 6.07/6.06 tff(20992,plain,
% 6.07/6.06 (succ(succ(X3!55)) = succ(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20991])).
% 6.07/6.06 tff(20993,plain,
% 6.07/6.06 (succ(succ(X3!55)) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[20992, 48])).
% 6.07/6.06 tff(20994,plain,
% 6.07/6.06 (succ(succ(succ(X3!55))) = succ(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20993])).
% 6.07/6.06 tff(20995,plain,
% 6.07/6.06 (succ(succ(succ(X3!55))) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[20994, 14])).
% 6.07/6.06 tff(20996,plain,
% 6.07/6.06 (succ(succ(succ(succ(X3!55)))) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20995])).
% 6.07/6.06 tff(20997,plain,
% 6.07/6.06 (succ(succ(succ(succ(X3!55)))) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[20996, 33])).
% 6.07/6.06 tff(20998,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(X3!55))))) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20997])).
% 6.07/6.06 tff(20999,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(X3!55))))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[20998, 30])).
% 6.07/6.06 tff(21000,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20999])).
% 6.07/6.06 tff(21001,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21000, 39])).
% 6.07/6.06 tff(21002,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21001])).
% 6.07/6.06 tff(21003,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21002, 53])).
% 6.07/6.06 tff(21004,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21003])).
% 6.07/6.06 tff(21005,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21004, 45])).
% 6.07/6.06 tff(21006,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21005])).
% 6.07/6.06 tff(21007,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21006, 28])).
% 6.07/6.06 tff(21008,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21007])).
% 6.07/6.06 tff(21009,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21008, 42])).
% 6.07/6.06 tff(21010,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21009])).
% 6.07/6.06 tff(21011,plain,
% 6.07/6.06 (NSX3!25 = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[535, 21010, 58])).
% 6.07/6.06 tff(21012,plain,
% 6.07/6.06 (pred(NSX3!25) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21011])).
% 6.07/6.06 tff(21013,plain,
% 6.07/6.06 (pred(NSX3!25) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21012, 23])).
% 6.07/6.06 tff(21014,plain,
% 6.07/6.06 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n0, n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21013, 20989])).
% 6.07/6.06 tff(21015,plain,
% 6.07/6.06 (Y4!52 = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[540, 21014, 442])).
% 6.07/6.06 tff(21016,plain,
% 6.07/6.06 (pred(Y4!52) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21015])).
% 6.07/6.06 tff(21017,plain,
% 6.07/6.06 (pred(Y4!52) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21016, 15])).
% 6.07/6.06 tff(21018,plain,
% 6.07/6.06 (pred(pred(Y4!52)) = pred(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21017])).
% 6.07/6.06 tff(21019,plain,
% 6.07/6.06 (pred(pred(Y4!52)) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21018, 25])).
% 6.07/6.06 tff(21020,plain,
% 6.07/6.06 (pred(pred(pred(Y4!52))) = pred(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21019])).
% 6.07/6.06 tff(21021,plain,
% 6.07/6.06 (pred(pred(pred(Y4!52))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21020, 24])).
% 6.07/6.06 tff(21022,plain,
% 6.07/6.06 (pred(pred(pred(pred(Y4!52)))) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21021])).
% 6.07/6.06 tff(21023,plain,
% 6.07/6.06 (pred(pred(pred(pred(Y4!52)))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21022, 23])).
% 6.07/6.06 tff(21024,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21023])).
% 6.07/6.06 tff(21025,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(Y4!52))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21024, 22])).
% 6.07/6.06 tff(21026,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21025])).
% 6.07/6.06 tff(21027,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21026, 21])).
% 6.07/6.06 tff(21028,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21027])).
% 6.07/6.06 tff(21029,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21028, 20])).
% 6.07/6.06 tff(21030,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21029])).
% 6.07/6.06 tff(21031,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21030, 19])).
% 6.07/6.06 tff(21032,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21031])).
% 6.07/6.06 tff(21033,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21032, 18])).
% 6.07/6.06 tff(21034,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21033])).
% 6.07/6.06 tff(21035,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21034, 17])).
% 6.07/6.06 tff(21036,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21035])).
% 6.07/6.06 tff(21037,plain,
% 6.07/6.06 (NPY4!22 = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[578, 21036, 16])).
% 6.07/6.06 tff(21038,plain,
% 6.07/6.06 (succ(NPY4!22) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21037])).
% 6.07/6.06 tff(21039,plain,
% 6.07/6.06 (succ(NPY4!22) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21038, 33])).
% 6.07/6.06 tff(21040,plain,
% 6.07/6.06 (succ(Y4!52) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21015])).
% 6.07/6.06 tff(21041,plain,
% 6.07/6.06 (succ(Y4!52) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21040, 33])).
% 6.07/6.06 tff(21042,plain,
% 6.07/6.06 (succ(succ(Y4!52)) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21041])).
% 6.07/6.06 tff(21043,plain,
% 6.07/6.06 (succ(succ(Y4!52)) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21042, 30])).
% 6.07/6.06 tff(21044,plain,
% 6.07/6.06 (succ(succ(succ(Y4!52))) = succ(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21043])).
% 6.07/6.06 tff(21045,plain,
% 6.07/6.06 (succ(succ(succ(Y4!52))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21044, 39])).
% 6.07/6.06 tff(21046,plain,
% 6.07/6.06 (succ(succ(succ(succ(Y4!52)))) = succ(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21045])).
% 6.07/6.06 tff(21047,plain,
% 6.07/6.06 (succ(succ(succ(succ(Y4!52)))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21046, 53])).
% 6.07/6.06 tff(21048,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21047])).
% 6.07/6.06 tff(21049,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(Y4!52))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21048, 45])).
% 6.07/6.06 tff(21050,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21049])).
% 6.07/6.06 tff(21051,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21050, 28])).
% 6.07/6.06 tff(21052,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21051])).
% 6.07/6.06 tff(21053,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21052, 42])).
% 6.07/6.06 tff(21054,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21053])).
% 6.07/6.06 tff(21055,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21054, 58])).
% 6.07/6.06 tff(21056,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21055])).
% 6.07/6.06 tff(21057,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21056, 36])).
% 6.07/6.06 tff(21058,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21057])).
% 6.07/6.06 tff(21059,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21058, 48])).
% 6.07/6.06 tff(21060,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21059])).
% 6.07/6.06 tff(21061,plain,
% 6.07/6.06 (NSY4!20 = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[601, 21060, 14])).
% 6.07/6.06 tff(21062,plain,
% 6.07/6.06 (pred(NSY4!20) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21061])).
% 6.07/6.06 tff(21063,plain,
% 6.07/6.06 (pred(NSY4!20) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21062, 15])).
% 6.07/6.06 tff(21064,plain,
% 6.07/6.06 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n3, n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21063, 21039])).
% 6.07/6.06 tff(21065,plain,
% 6.07/6.06 (sum(pred(NSY4!20), succ(NPY4!22)) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21064, 32])).
% 6.07/6.06 tff(21066,plain,
% 6.07/6.06 (sum(pred(Y3!54), succ(X3!55)) = sum(n0, n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20909, 20991])).
% 6.07/6.06 tff(21067,plain,
% 6.07/6.06 (sum(pred(Y3!54), succ(X3!55)) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21066, 35])).
% 6.07/6.06 tff(21068,plain,
% 6.07/6.06 (sum(pred(X3!55), succ(Y3!54)) = sum(n0, n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[20965, 20933])).
% 6.07/6.06 tff(21069,plain,
% 6.07/6.06 (sum(pred(X3!55), succ(Y3!54)) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21068, 35])).
% 6.07/6.06 tff(21070,plain,
% 6.07/6.06 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n2, n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21069, 21067])).
% 6.07/6.06 tff(21071,plain,
% 6.07/6.06 (X4!53 = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[438, 21070, 34])).
% 6.07/6.06 tff(21072,plain,
% 6.07/6.06 (pred(X4!53) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21071])).
% 6.07/6.06 tff(21073,plain,
% 6.07/6.06 (pred(X4!53) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21072, 15])).
% 6.07/6.06 tff(21074,plain,
% 6.07/6.06 (pred(pred(X4!53)) = pred(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21073])).
% 6.07/6.06 tff(21075,plain,
% 6.07/6.06 (pred(pred(X4!53)) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21074, 25])).
% 6.07/6.06 tff(21076,plain,
% 6.07/6.06 (pred(pred(pred(X4!53))) = pred(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21075])).
% 6.07/6.06 tff(21077,plain,
% 6.07/6.06 (pred(pred(pred(X4!53))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21076, 24])).
% 6.07/6.06 tff(21078,plain,
% 6.07/6.06 (pred(pred(pred(pred(X4!53)))) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21077])).
% 6.07/6.06 tff(21079,plain,
% 6.07/6.06 (pred(pred(pred(pred(X4!53)))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21078, 23])).
% 6.07/6.06 tff(21080,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(X4!53))))) = pred(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21079])).
% 6.07/6.06 tff(21081,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(X4!53))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21080, 22])).
% 6.07/6.06 tff(21082,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21081])).
% 6.07/6.06 tff(21083,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21082, 21])).
% 6.07/6.06 tff(21084,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21083])).
% 6.07/6.06 tff(21085,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21084, 20])).
% 6.07/6.06 tff(21086,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21085])).
% 6.07/6.06 tff(21087,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21086, 19])).
% 6.07/6.06 tff(21088,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21087])).
% 6.07/6.06 tff(21089,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21088, 18])).
% 6.07/6.06 tff(21090,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21089])).
% 6.07/6.06 tff(21091,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21090, 17])).
% 6.07/6.06 tff(21092,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21091])).
% 6.07/6.06 tff(21093,plain,
% 6.07/6.06 (NPX4!23 = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[626, 21092, 16])).
% 6.07/6.06 tff(21094,plain,
% 6.07/6.06 (succ(NPX4!23) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21093])).
% 6.07/6.06 tff(21095,plain,
% 6.07/6.06 (succ(NPX4!23) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21094, 33])).
% 6.07/6.06 tff(21096,plain,
% 6.07/6.06 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n5, n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21095, 21065])).
% 6.07/6.06 tff(21097,plain,
% 6.07/6.06 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21096, 558])).
% 6.07/6.06 tff(21098,plain,
% 6.07/6.06 (succ(X4!53) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21071])).
% 6.07/6.06 tff(21099,plain,
% 6.07/6.06 (succ(X4!53) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21098, 33])).
% 6.07/6.06 tff(21100,plain,
% 6.07/6.06 (succ(succ(X4!53)) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21099])).
% 6.07/6.06 tff(21101,plain,
% 6.07/6.06 (succ(succ(X4!53)) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21100, 30])).
% 6.07/6.06 tff(21102,plain,
% 6.07/6.06 (succ(succ(succ(X4!53))) = succ(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21101])).
% 6.07/6.06 tff(21103,plain,
% 6.07/6.06 (succ(succ(succ(X4!53))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21102, 39])).
% 6.07/6.06 tff(21104,plain,
% 6.07/6.06 (succ(succ(succ(succ(X4!53)))) = succ(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21103])).
% 6.07/6.06 tff(21105,plain,
% 6.07/6.06 (succ(succ(succ(succ(X4!53)))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21104, 53])).
% 6.07/6.06 tff(21106,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(X4!53))))) = succ(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21105])).
% 6.07/6.06 tff(21107,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(X4!53))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21106, 45])).
% 6.07/6.06 tff(21108,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21107])).
% 6.07/6.06 tff(21109,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21108, 28])).
% 6.07/6.06 tff(21110,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21109])).
% 6.07/6.06 tff(21111,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21110, 42])).
% 6.07/6.06 tff(21112,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21111])).
% 6.07/6.06 tff(21113,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21112, 58])).
% 6.07/6.06 tff(21114,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21113])).
% 6.07/6.06 tff(21115,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21114, 36])).
% 6.07/6.06 tff(21116,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21115])).
% 6.07/6.06 tff(21117,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21116, 48])).
% 6.07/6.06 tff(21118,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21117])).
% 6.07/6.06 tff(21119,plain,
% 6.07/6.06 (NSX4!21 = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[651, 21118, 14])).
% 6.07/6.06 tff(21120,plain,
% 6.07/6.06 (pred(NSX4!21) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21119])).
% 6.07/6.06 tff(21121,plain,
% 6.07/6.06 (pred(NSX4!21) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21120, 15])).
% 6.07/6.06 tff(21122,plain,
% 6.07/6.06 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n3, n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21121, 21097])).
% 6.07/6.06 tff(21123,plain,
% 6.07/6.06 (Y5!50 = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[656, 21122, 557])).
% 6.07/6.06 tff(21124,plain,
% 6.07/6.06 (pred(Y5!50) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21123])).
% 6.07/6.06 tff(21125,plain,
% 6.07/6.06 (pred(Y5!50) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[21124, 16])).
% 6.07/6.06 tff(21126,plain,
% 6.07/6.06 (pred(pred(Y5!50)) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21125])).
% 6.07/6.06 tff(21127,plain,
% 6.07/6.06 (pred(pred(Y5!50)) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21126, 15])).
% 6.07/6.06 tff(21128,plain,
% 6.07/6.06 (pred(pred(pred(Y5!50))) = pred(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21127])).
% 6.07/6.06 tff(21129,plain,
% 6.07/6.06 (pred(pred(pred(Y5!50))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21128, 25])).
% 6.07/6.06 tff(21130,plain,
% 6.07/6.06 (pred(pred(pred(pred(Y5!50)))) = pred(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21129])).
% 6.07/6.06 tff(21131,plain,
% 6.07/6.06 (pred(pred(pred(pred(Y5!50)))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21130, 24])).
% 6.07/6.06 tff(21132,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21131])).
% 6.07/6.06 tff(21133,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(Y5!50))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21132, 23])).
% 6.07/6.06 tff(21134,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21133])).
% 6.07/6.06 tff(21135,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21134, 22])).
% 6.07/6.06 tff(21136,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21135])).
% 6.07/6.06 tff(21137,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21136, 21])).
% 6.07/6.06 tff(21138,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21137])).
% 6.07/6.06 tff(21139,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21138, 20])).
% 6.07/6.06 tff(21140,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21139])).
% 6.07/6.06 tff(21141,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21140, 19])).
% 6.07/6.06 tff(21142,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21141])).
% 6.07/6.06 tff(21143,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21142, 18])).
% 6.07/6.06 tff(21144,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21143])).
% 6.07/6.06 tff(21145,plain,
% 6.07/6.06 (NPY5!18 = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[694, 21144, 17])).
% 6.07/6.06 tff(21146,plain,
% 6.07/6.06 (succ(NPY5!18) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21145])).
% 6.07/6.06 tff(21147,plain,
% 6.07/6.06 (succ(NPY5!18) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21146, 30])).
% 6.07/6.06 tff(21148,plain,
% 6.07/6.06 (succ(Y5!50) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21123])).
% 6.07/6.06 tff(21149,plain,
% 6.07/6.06 (succ(Y5!50) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21148, 30])).
% 6.07/6.06 tff(21150,plain,
% 6.07/6.06 (succ(succ(Y5!50)) = succ(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21149])).
% 6.07/6.06 tff(21151,plain,
% 6.07/6.06 (succ(succ(Y5!50)) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21150, 39])).
% 6.07/6.06 tff(21152,plain,
% 6.07/6.06 (succ(succ(succ(Y5!50))) = succ(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21151])).
% 6.07/6.06 tff(21153,plain,
% 6.07/6.06 (succ(succ(succ(Y5!50))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21152, 53])).
% 6.07/6.06 tff(21154,plain,
% 6.07/6.06 (succ(succ(succ(succ(Y5!50)))) = succ(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21153])).
% 6.07/6.06 tff(21155,plain,
% 6.07/6.06 (succ(succ(succ(succ(Y5!50)))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21154, 45])).
% 6.07/6.06 tff(21156,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21155])).
% 6.07/6.06 tff(21157,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(Y5!50))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21156, 28])).
% 6.07/6.06 tff(21158,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21157])).
% 6.07/6.06 tff(21159,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21158, 42])).
% 6.07/6.06 tff(21160,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21159])).
% 6.07/6.06 tff(21161,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21160, 58])).
% 6.07/6.06 tff(21162,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21161])).
% 6.07/6.06 tff(21163,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21162, 36])).
% 6.07/6.06 tff(21164,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21163])).
% 6.07/6.06 tff(21165,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21164, 48])).
% 6.07/6.06 tff(21166,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21165])).
% 6.07/6.06 tff(21167,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[21166, 14])).
% 6.07/6.06 tff(21168,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21167])).
% 6.07/6.06 tff(21169,plain,
% 6.07/6.06 (NSY5!16 = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[717, 21168, 33])).
% 6.07/6.06 tff(21170,plain,
% 6.07/6.06 (pred(NSY5!16) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21169])).
% 6.07/6.06 tff(21171,plain,
% 6.07/6.06 (pred(NSY5!16) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[21170, 16])).
% 6.07/6.06 tff(21172,plain,
% 6.07/6.06 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n4, n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21171, 21147])).
% 6.07/6.06 tff(21173,plain,
% 6.07/6.06 (sum(pred(NSY5!16), succ(NPY5!18)) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21172, 12])).
% 6.07/6.06 tff(21174,plain,
% 6.07/6.06 (sum(pred(Y4!52), succ(X4!53)) = sum(n3, n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21017, 21099])).
% 6.07/6.06 tff(21175,plain,
% 6.07/6.06 (sum(pred(Y4!52), succ(X4!53)) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21174, 32])).
% 6.07/6.06 tff(21176,plain,
% 6.07/6.06 (sum(pred(X4!53), succ(Y4!52)) = sum(n3, n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21073, 21041])).
% 6.07/6.06 tff(21177,plain,
% 6.07/6.06 (sum(pred(X4!53), succ(Y4!52)) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21176, 32])).
% 6.07/6.06 tff(21178,plain,
% 6.07/6.06 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n8, n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21177, 21175])).
% 6.07/6.06 tff(21179,plain,
% 6.07/6.06 (X5!51 = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[553, 21178, 31])).
% 6.07/6.06 tff(21180,plain,
% 6.07/6.06 (pred(X5!51) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21179])).
% 6.07/6.06 tff(21181,plain,
% 6.07/6.06 (pred(X5!51) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[21180, 16])).
% 6.07/6.06 tff(21182,plain,
% 6.07/6.06 (pred(pred(X5!51)) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21181])).
% 6.07/6.06 tff(21183,plain,
% 6.07/6.06 (pred(pred(X5!51)) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21182, 15])).
% 6.07/6.06 tff(21184,plain,
% 6.07/6.06 (pred(pred(pred(X5!51))) = pred(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21183])).
% 6.07/6.06 tff(21185,plain,
% 6.07/6.06 (pred(pred(pred(X5!51))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21184, 25])).
% 6.07/6.06 tff(21186,plain,
% 6.07/6.06 (pred(pred(pred(pred(X5!51)))) = pred(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21185])).
% 6.07/6.06 tff(21187,plain,
% 6.07/6.06 (pred(pred(pred(pred(X5!51)))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21186, 24])).
% 6.07/6.06 tff(21188,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(X5!51))))) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21187])).
% 6.07/6.06 tff(21189,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(X5!51))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21188, 23])).
% 6.07/6.06 tff(21190,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21189])).
% 6.07/6.06 tff(21191,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21190, 22])).
% 6.07/6.06 tff(21192,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21191])).
% 6.07/6.06 tff(21193,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21192, 21])).
% 6.07/6.06 tff(21194,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21193])).
% 6.07/6.06 tff(21195,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21194, 20])).
% 6.07/6.06 tff(21196,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21195])).
% 6.07/6.06 tff(21197,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21196, 19])).
% 6.07/6.06 tff(21198,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21197])).
% 6.07/6.06 tff(21199,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21198, 18])).
% 6.07/6.06 tff(21200,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21199])).
% 6.07/6.06 tff(21201,plain,
% 6.07/6.06 (NPX5!19 = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[742, 21200, 17])).
% 6.07/6.06 tff(21202,plain,
% 6.07/6.06 (succ(NPX5!19) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21201])).
% 6.07/6.06 tff(21203,plain,
% 6.07/6.06 (succ(NPX5!19) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21202, 30])).
% 6.07/6.06 tff(21204,plain,
% 6.07/6.06 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n6, n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21203, 21173])).
% 6.07/6.06 tff(21205,plain,
% 6.07/6.06 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21204, 674])).
% 6.07/6.06 tff(21206,plain,
% 6.07/6.06 (succ(X5!51) = succ(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21179])).
% 6.07/6.06 tff(21207,plain,
% 6.07/6.06 (succ(X5!51) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21206, 30])).
% 6.07/6.06 tff(21208,plain,
% 6.07/6.06 (succ(succ(X5!51)) = succ(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21207])).
% 6.07/6.06 tff(21209,plain,
% 6.07/6.06 (succ(succ(X5!51)) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21208, 39])).
% 6.07/6.06 tff(21210,plain,
% 6.07/6.06 (succ(succ(succ(X5!51))) = succ(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21209])).
% 6.07/6.06 tff(21211,plain,
% 6.07/6.06 (succ(succ(succ(X5!51))) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21210, 53])).
% 6.07/6.06 tff(21212,plain,
% 6.07/6.06 (succ(succ(succ(succ(X5!51)))) = succ(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21211])).
% 6.07/6.06 tff(21213,plain,
% 6.07/6.06 (succ(succ(succ(succ(X5!51)))) = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[21212, 45])).
% 6.07/6.06 tff(21214,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(X5!51))))) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21213])).
% 6.07/6.06 tff(21215,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(X5!51))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21214, 28])).
% 6.07/6.06 tff(21216,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21215])).
% 6.07/6.06 tff(21217,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21216, 42])).
% 6.07/6.06 tff(21218,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21217])).
% 6.07/6.06 tff(21219,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21218, 58])).
% 6.07/6.06 tff(21220,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21219])).
% 6.07/6.06 tff(21221,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21220, 36])).
% 6.07/6.06 tff(21222,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21221])).
% 6.07/6.06 tff(21223,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21222, 48])).
% 6.07/6.06 tff(21224,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21223])).
% 6.07/6.06 tff(21225,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[21224, 14])).
% 6.07/6.06 tff(21226,plain,
% 6.07/6.06 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21225])).
% 6.07/6.06 tff(21227,plain,
% 6.07/6.06 (NSX5!17 = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[767, 21226, 33])).
% 6.07/6.06 tff(21228,plain,
% 6.07/6.06 (pred(NSX5!17) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21227])).
% 6.07/6.06 tff(21229,plain,
% 6.07/6.06 (pred(NSX5!17) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[21228, 16])).
% 6.07/6.06 tff(21230,plain,
% 6.07/6.06 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n4, n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21229, 21205])).
% 6.07/6.06 tff(21231,plain,
% 6.07/6.06 (Y6!48 = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[772, 21230, 673])).
% 6.07/6.06 tff(21232,plain,
% 6.07/6.06 (pred(Y6!48) = pred(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21231])).
% 6.07/6.06 tff(21233,plain,
% 6.07/6.06 (pred(Y6!48) = n8),
% 6.07/6.06 inference(transitivity,[status(thm)],[21232, 20])).
% 6.07/6.06 tff(21234,plain,
% 6.07/6.06 (pred(pred(Y6!48)) = pred(n8)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21233])).
% 6.07/6.06 tff(21235,plain,
% 6.07/6.06 (pred(pred(Y6!48)) = n7),
% 6.07/6.06 inference(transitivity,[status(thm)],[21234, 19])).
% 6.07/6.06 tff(21236,plain,
% 6.07/6.06 (pred(pred(pred(Y6!48))) = pred(n7)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21235])).
% 6.07/6.06 tff(21237,plain,
% 6.07/6.06 (pred(pred(pred(Y6!48))) = n6),
% 6.07/6.06 inference(transitivity,[status(thm)],[21236, 18])).
% 6.07/6.06 tff(21238,plain,
% 6.07/6.06 (pred(pred(pred(pred(Y6!48)))) = pred(n6)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21237])).
% 6.07/6.06 tff(21239,plain,
% 6.07/6.06 (pred(pred(pred(pred(Y6!48)))) = n5),
% 6.07/6.06 inference(transitivity,[status(thm)],[21238, 17])).
% 6.07/6.06 tff(21240,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n5)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21239])).
% 6.07/6.06 tff(21241,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(Y6!48))))) = n4),
% 6.07/6.06 inference(transitivity,[status(thm)],[21240, 16])).
% 6.07/6.06 tff(21242,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n4)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21241])).
% 6.07/6.06 tff(21243,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n3),
% 6.07/6.06 inference(transitivity,[status(thm)],[21242, 15])).
% 6.07/6.06 tff(21244,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n3)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21243])).
% 6.07/6.06 tff(21245,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n2),
% 6.07/6.06 inference(transitivity,[status(thm)],[21244, 25])).
% 6.07/6.06 tff(21246,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n2)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21245])).
% 6.07/6.06 tff(21247,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21246, 24])).
% 6.07/6.06 tff(21248,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n1)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21247])).
% 6.07/6.06 tff(21249,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21248, 23])).
% 6.07/6.06 tff(21250,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21249])).
% 6.07/6.06 tff(21251,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21250, 22])).
% 6.07/6.06 tff(21252,plain,
% 6.07/6.06 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21251])).
% 6.07/6.06 tff(21253,plain,
% 6.07/6.06 (NPY6!14 = n9),
% 6.07/6.06 inference(transitivity,[status(thm)],[1465, 21252, 21])).
% 6.07/6.06 tff(21254,plain,
% 6.07/6.06 (succ(NPY6!14) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21253])).
% 6.07/6.06 tff(21255,plain,
% 6.07/6.06 (succ(NPY6!14) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21254, 28])).
% 6.07/6.06 tff(21256,plain,
% 6.07/6.06 (succ(Y6!48) = succ(n9)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21231])).
% 6.07/6.06 tff(21257,plain,
% 6.07/6.06 (succ(Y6!48) = n10),
% 6.07/6.06 inference(transitivity,[status(thm)],[21256, 28])).
% 6.07/6.06 tff(21258,plain,
% 6.07/6.06 (succ(succ(Y6!48)) = succ(n10)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21257])).
% 6.07/6.06 tff(21259,plain,
% 6.07/6.06 (succ(succ(Y6!48)) = n0),
% 6.07/6.06 inference(transitivity,[status(thm)],[21258, 42])).
% 6.07/6.06 tff(21260,plain,
% 6.07/6.06 (succ(succ(succ(Y6!48))) = succ(n0)),
% 6.07/6.06 inference(monotonicity,[status(thm)],[21259])).
% 6.07/6.06 tff(21261,plain,
% 6.07/6.06 (succ(succ(succ(Y6!48))) = n1),
% 6.07/6.06 inference(transitivity,[status(thm)],[21260, 58])).
% 6.07/6.07 tff(21262,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y6!48)))) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21261])).
% 6.07/6.07 tff(21263,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y6!48)))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21262, 36])).
% 6.07/6.07 tff(21264,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21263])).
% 6.07/6.07 tff(21265,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y6!48))))) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21264, 48])).
% 6.07/6.07 tff(21266,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21265])).
% 6.07/6.07 tff(21267,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21266, 14])).
% 6.07/6.07 tff(21268,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21267])).
% 6.07/6.07 tff(21269,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21268, 33])).
% 6.07/6.07 tff(21270,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21269])).
% 6.07/6.07 tff(21271,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21270, 30])).
% 6.07/6.07 tff(21272,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21271])).
% 6.07/6.07 tff(21273,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21272, 39])).
% 6.07/6.07 tff(21274,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21273])).
% 6.07/6.07 tff(21275,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21274, 53])).
% 6.07/6.07 tff(21276,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21275])).
% 6.07/6.07 tff(21277,plain,
% 6.07/6.07 (NSY6!12 = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[1490, 21276, 45])).
% 6.07/6.07 tff(21278,plain,
% 6.07/6.07 (pred(NSY6!12) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21277])).
% 6.07/6.07 tff(21279,plain,
% 6.07/6.07 (pred(NSY6!12) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21278, 20])).
% 6.07/6.07 tff(21280,plain,
% 6.07/6.07 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n8, n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21279, 21255])).
% 6.07/6.07 tff(21281,plain,
% 6.07/6.07 (sum(pred(NSY6!12), succ(NPY6!14)) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21280, 27])).
% 6.07/6.07 tff(21282,plain,
% 6.07/6.07 (sum(pred(Y5!50), succ(X5!51)) = sum(n4, n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21125, 21207])).
% 6.07/6.07 tff(21283,plain,
% 6.07/6.07 (sum(pred(Y5!50), succ(X5!51)) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21282, 12])).
% 6.07/6.07 tff(21284,plain,
% 6.07/6.07 (sum(pred(X5!51), succ(Y5!50)) = sum(n4, n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21181, 21149])).
% 6.07/6.07 tff(21285,plain,
% 6.07/6.07 (sum(pred(X5!51), succ(Y5!50)) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21284, 12])).
% 6.07/6.07 tff(21286,plain,
% 6.07/6.07 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n10, n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21285, 21283])).
% 6.07/6.07 tff(21287,plain,
% 6.07/6.07 (X6!49 = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[669, 21286, 29])).
% 6.07/6.07 tff(21288,plain,
% 6.07/6.07 (pred(X6!49) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21287])).
% 6.07/6.07 tff(21289,plain,
% 6.07/6.07 (pred(X6!49) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21288, 20])).
% 6.07/6.07 tff(21290,plain,
% 6.07/6.07 (pred(pred(X6!49)) = pred(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21289])).
% 6.07/6.07 tff(21291,plain,
% 6.07/6.07 (pred(pred(X6!49)) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21290, 19])).
% 6.07/6.07 tff(21292,plain,
% 6.07/6.07 (pred(pred(pred(X6!49))) = pred(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21291])).
% 6.07/6.07 tff(21293,plain,
% 6.07/6.07 (pred(pred(pred(X6!49))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21292, 18])).
% 6.07/6.07 tff(21294,plain,
% 6.07/6.07 (pred(pred(pred(pred(X6!49)))) = pred(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21293])).
% 6.07/6.07 tff(21295,plain,
% 6.07/6.07 (pred(pred(pred(pred(X6!49)))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21294, 17])).
% 6.07/6.07 tff(21296,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(X6!49))))) = pred(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21295])).
% 6.07/6.07 tff(21297,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(X6!49))))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21296, 16])).
% 6.07/6.07 tff(21298,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21297])).
% 6.07/6.07 tff(21299,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21298, 15])).
% 6.07/6.07 tff(21300,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21299])).
% 6.07/6.07 tff(21301,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21300, 25])).
% 6.07/6.07 tff(21302,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21301])).
% 6.07/6.07 tff(21303,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[21302, 24])).
% 6.07/6.07 tff(21304,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21303])).
% 6.07/6.07 tff(21305,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21304, 23])).
% 6.07/6.07 tff(21306,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21305])).
% 6.07/6.07 tff(21307,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21306, 22])).
% 6.07/6.07 tff(21308,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21307])).
% 6.07/6.07 tff(21309,plain,
% 6.07/6.07 (NPX6!15 = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[1523, 21308, 21])).
% 6.07/6.07 tff(21310,plain,
% 6.07/6.07 (succ(NPX6!15) = succ(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21309])).
% 6.07/6.07 tff(21311,plain,
% 6.07/6.07 (succ(NPX6!15) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21310, 28])).
% 6.07/6.07 tff(21312,plain,
% 6.07/6.07 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n10, n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21311, 21281])).
% 6.07/6.07 tff(21313,plain,
% 6.07/6.07 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21312, 69])).
% 6.07/6.07 tff(21314,plain,
% 6.07/6.07 (succ(X6!49) = succ(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21287])).
% 6.07/6.07 tff(21315,plain,
% 6.07/6.07 (succ(X6!49) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21314, 28])).
% 6.07/6.07 tff(21316,plain,
% 6.07/6.07 (succ(succ(X6!49)) = succ(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21315])).
% 6.07/6.07 tff(21317,plain,
% 6.07/6.07 (succ(succ(X6!49)) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21316, 42])).
% 6.07/6.07 tff(21318,plain,
% 6.07/6.07 (succ(succ(succ(X6!49))) = succ(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21317])).
% 6.07/6.07 tff(21319,plain,
% 6.07/6.07 (succ(succ(succ(X6!49))) = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[21318, 58])).
% 6.07/6.07 tff(21320,plain,
% 6.07/6.07 (succ(succ(succ(succ(X6!49)))) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21319])).
% 6.07/6.07 tff(21321,plain,
% 6.07/6.07 (succ(succ(succ(succ(X6!49)))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21320, 36])).
% 6.07/6.07 tff(21322,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(X6!49))))) = succ(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21321])).
% 6.07/6.07 tff(21323,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(X6!49))))) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21322, 48])).
% 6.07/6.07 tff(21324,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21323])).
% 6.07/6.07 tff(21325,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21324, 14])).
% 6.07/6.07 tff(21326,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21325])).
% 6.07/6.07 tff(21327,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21326, 33])).
% 6.07/6.07 tff(21328,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21327])).
% 6.07/6.07 tff(21329,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21328, 30])).
% 6.07/6.07 tff(21330,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21329])).
% 6.07/6.07 tff(21331,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21330, 39])).
% 6.07/6.07 tff(21332,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21331])).
% 6.07/6.07 tff(21333,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21332, 53])).
% 6.07/6.07 tff(21334,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21333])).
% 6.07/6.07 tff(21335,plain,
% 6.07/6.07 (NSX6!13 = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[1550, 21334, 45])).
% 6.07/6.07 tff(21336,plain,
% 6.07/6.07 (pred(NSX6!13) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21335])).
% 6.07/6.07 tff(21337,plain,
% 6.07/6.07 (pred(NSX6!13) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21336, 20])).
% 6.07/6.07 tff(21338,plain,
% 6.07/6.07 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n8, n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21337, 21313])).
% 6.07/6.07 tff(21339,plain,
% 6.07/6.07 (sum(n8, n6) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 6.07/6.07 inference(symmetry,[status(thm)],[21338])).
% 6.07/6.07 tff(21340,plain,
% 6.07/6.07 (sum(pred(Y6!48), succ(X6!49)) = sum(n8, n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21233, 21315])).
% 6.07/6.07 tff(21341,plain,
% 6.07/6.07 (sum(pred(Y6!48), succ(X6!49)) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21340, 27])).
% 6.07/6.07 tff(21342,plain,
% 6.07/6.07 (sum(pred(X6!49), succ(Y6!48)) = sum(n8, n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21289, 21257])).
% 6.07/6.07 tff(21343,plain,
% 6.07/6.07 (sum(pred(X6!49), succ(Y6!48)) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21342, 27])).
% 6.07/6.07 tff(21344,plain,
% 6.07/6.07 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n7, n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21343, 21341])).
% 6.07/6.07 tff(21345,plain,
% 6.07/6.07 (X7!47 = Y7!46),
% 6.07/6.07 inference(transitivity,[status(thm)],[785, 21344, 26, 1556, 21339, 794])).
% 6.07/6.07 tff(21346,plain,
% 6.07/6.07 ($false),
% 6.07/6.07 inference(unit_resolution,[status(thm)],[792, 21345])).
% 6.07/6.07 tff(21347,plain,((~(Y0!60 = n7)) | (X7!47 = Y7!46) | (~(X0!61 = n3))), inference(lemma,lemma(discharge,[]))).
% 6.07/6.07 tff(21348,plain,
% 6.07/6.07 (~(Y0!60 = n7)),
% 6.07/6.07 inference(unit_resolution,[status(thm)],[21347, 17987, 792])).
% 6.07/6.07 tff(21349,assumption,(Y0!60 = n1), introduced(assumption)).
% 6.07/6.07 tff(21350,plain,
% 6.07/6.07 (pred(Y0!60) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21349])).
% 6.07/6.07 tff(21351,plain,
% 6.07/6.07 (pred(Y0!60) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21350, 23])).
% 6.07/6.07 tff(21352,plain,
% 6.07/6.07 (pred(pred(Y0!60)) = pred(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21351])).
% 6.07/6.07 tff(21353,plain,
% 6.07/6.07 (pred(pred(Y0!60)) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21352, 22])).
% 6.07/6.07 tff(21354,plain,
% 6.07/6.07 (pred(pred(pred(Y0!60))) = pred(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21353])).
% 6.07/6.07 tff(21355,plain,
% 6.07/6.07 (pred(pred(pred(Y0!60))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21354, 21])).
% 6.07/6.07 tff(21356,plain,
% 6.07/6.07 (pred(pred(pred(pred(Y0!60)))) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21355])).
% 6.07/6.07 tff(21357,plain,
% 6.07/6.07 (pred(pred(pred(pred(Y0!60)))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21356, 20])).
% 6.07/6.07 tff(21358,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(Y0!60))))) = pred(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21357])).
% 6.07/6.07 tff(21359,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(Y0!60))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21358, 19])).
% 6.07/6.07 tff(21360,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = pred(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21359])).
% 6.07/6.07 tff(21361,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(Y0!60)))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21360, 18])).
% 6.07/6.07 tff(21362,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = pred(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21361])).
% 6.07/6.07 tff(21363,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(Y0!60))))))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21362, 17])).
% 6.07/6.07 tff(21364,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = pred(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21363])).
% 6.07/6.07 tff(21365,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21364, 16])).
% 6.07/6.07 tff(21366,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = pred(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21365])).
% 6.07/6.07 tff(21367,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21366, 15])).
% 6.07/6.07 tff(21368,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = pred(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21367])).
% 6.07/6.07 tff(21369,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60)))))))))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21368, 25])).
% 6.07/6.07 tff(21370,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y0!60))))))))))) = pred(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21369])).
% 6.07/6.07 tff(21371,plain,
% 6.07/6.07 (NPY0!38 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[118, 21370, 24])).
% 6.07/6.07 tff(21372,plain,
% 6.07/6.07 (succ(NPY0!38) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21371])).
% 6.07/6.07 tff(21373,plain,
% 6.07/6.07 (succ(NPY0!38) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21372, 36])).
% 6.07/6.07 tff(21374,plain,
% 6.07/6.07 (succ(Y0!60) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21349])).
% 6.07/6.07 tff(21375,plain,
% 6.07/6.07 (succ(Y0!60) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21374, 36])).
% 6.07/6.07 tff(21376,plain,
% 6.07/6.07 (succ(succ(Y0!60)) = succ(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21375])).
% 6.07/6.07 tff(21377,plain,
% 6.07/6.07 (succ(succ(Y0!60)) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21376, 48])).
% 6.07/6.07 tff(21378,plain,
% 6.07/6.07 (succ(succ(succ(Y0!60))) = succ(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21377])).
% 6.07/6.07 tff(21379,plain,
% 6.07/6.07 (succ(succ(succ(Y0!60))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21378, 14])).
% 6.07/6.07 tff(21380,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y0!60)))) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21379])).
% 6.07/6.07 tff(21381,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y0!60)))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21380, 33])).
% 6.07/6.07 tff(21382,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y0!60))))) = succ(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21381])).
% 6.07/6.07 tff(21383,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y0!60))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21382, 30])).
% 6.07/6.07 tff(21384,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = succ(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21383])).
% 6.07/6.07 tff(21385,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y0!60)))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21384, 39])).
% 6.07/6.07 tff(21386,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = succ(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21385])).
% 6.07/6.07 tff(21387,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y0!60))))))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21386, 53])).
% 6.07/6.07 tff(21388,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = succ(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21387])).
% 6.07/6.07 tff(21389,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21388, 45])).
% 6.07/6.07 tff(21390,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = succ(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21389])).
% 6.07/6.07 tff(21391,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21390, 28])).
% 6.07/6.07 tff(21392,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = succ(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21391])).
% 6.07/6.07 tff(21393,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60)))))))))) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21392, 42])).
% 6.07/6.07 tff(21394,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y0!60))))))))))) = succ(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21393])).
% 6.07/6.07 tff(21395,plain,
% 6.07/6.07 (NSY0!36 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[141, 21394, 58])).
% 6.07/6.07 tff(21396,plain,
% 6.07/6.07 (pred(NSY0!36) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21395])).
% 6.07/6.07 tff(21397,plain,
% 6.07/6.07 (pred(NSY0!36) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21396, 23])).
% 6.07/6.07 tff(21398,plain,
% 6.07/6.07 (sum(pred(NSY0!36), succ(NPY0!38)) = sum(n0, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21397, 21373])).
% 6.07/6.07 tff(21399,plain,
% 6.07/6.07 (sum(pred(NSY0!36), succ(NPY0!38)) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21398, 35])).
% 6.07/6.07 tff(21400,plain,
% 6.07/6.07 (sum(n6, n2) = n8),
% 6.07/6.07 inference(and_elim,[status(thm)],[9])).
% 6.07/6.07 tff(21401,plain,
% 6.07/6.07 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n6, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[7214, 21399])).
% 6.07/6.07 tff(21402,plain,
% 6.07/6.07 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21401, 21400])).
% 6.07/6.07 tff(21403,plain,
% 6.07/6.07 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n4, n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[7240, 21402])).
% 6.07/6.07 tff(21404,plain,
% 6.07/6.07 (Y1!58 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[196, 21403, 8619])).
% 6.07/6.07 tff(21405,plain,
% 6.07/6.07 (pred(Y1!58) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21404])).
% 6.07/6.07 tff(21406,plain,
% 6.07/6.07 (pred(Y1!58) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21405, 23])).
% 6.07/6.07 tff(21407,plain,
% 6.07/6.07 (pred(pred(Y1!58)) = pred(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21406])).
% 6.07/6.07 tff(21408,plain,
% 6.07/6.07 (pred(pred(Y1!58)) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21407, 22])).
% 6.07/6.07 tff(21409,plain,
% 6.07/6.07 (pred(pred(pred(Y1!58))) = pred(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21408])).
% 6.07/6.07 tff(21410,plain,
% 6.07/6.07 (pred(pred(pred(Y1!58))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21409, 21])).
% 6.07/6.07 tff(21411,plain,
% 6.07/6.07 (pred(pred(pred(pred(Y1!58)))) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21410])).
% 6.07/6.07 tff(21412,plain,
% 6.07/6.07 (pred(pred(pred(pred(Y1!58)))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21411, 20])).
% 6.07/6.07 tff(21413,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21412])).
% 6.07/6.07 tff(21414,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(Y1!58))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21413, 19])).
% 6.07/6.07 tff(21415,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21414])).
% 6.07/6.07 tff(21416,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21415, 18])).
% 6.07/6.07 tff(21417,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21416])).
% 6.07/6.07 tff(21418,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21417, 17])).
% 6.07/6.07 tff(21419,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21418])).
% 6.07/6.07 tff(21420,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21419, 16])).
% 6.07/6.07 tff(21421,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21420])).
% 6.07/6.07 tff(21422,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21421, 15])).
% 6.07/6.07 tff(21423,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21422])).
% 6.07/6.07 tff(21424,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21423, 25])).
% 6.07/6.07 tff(21425,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21424])).
% 6.07/6.07 tff(21426,plain,
% 6.07/6.07 (NPY1!34 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[232, 21425, 24])).
% 6.07/6.07 tff(21427,plain,
% 6.07/6.07 (succ(NPY1!34) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21426])).
% 6.07/6.07 tff(21428,plain,
% 6.07/6.07 (succ(NPY1!34) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21427, 36])).
% 6.07/6.07 tff(21429,plain,
% 6.07/6.07 (succ(Y1!58) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21404])).
% 6.07/6.07 tff(21430,plain,
% 6.07/6.07 (succ(Y1!58) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21429, 36])).
% 6.07/6.07 tff(21431,plain,
% 6.07/6.07 (succ(succ(Y1!58)) = succ(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21430])).
% 6.07/6.07 tff(21432,plain,
% 6.07/6.07 (succ(succ(Y1!58)) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21431, 48])).
% 6.07/6.07 tff(21433,plain,
% 6.07/6.07 (succ(succ(succ(Y1!58))) = succ(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21432])).
% 6.07/6.07 tff(21434,plain,
% 6.07/6.07 (succ(succ(succ(Y1!58))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21433, 14])).
% 6.07/6.07 tff(21435,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y1!58)))) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21434])).
% 6.07/6.07 tff(21436,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y1!58)))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21435, 33])).
% 6.07/6.07 tff(21437,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21436])).
% 6.07/6.07 tff(21438,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y1!58))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21437, 30])).
% 6.07/6.07 tff(21439,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21438])).
% 6.07/6.07 tff(21440,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21439, 39])).
% 6.07/6.07 tff(21441,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21440])).
% 6.07/6.07 tff(21442,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21441, 53])).
% 6.07/6.07 tff(21443,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21442])).
% 6.07/6.07 tff(21444,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21443, 45])).
% 6.07/6.07 tff(21445,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21444])).
% 6.07/6.07 tff(21446,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21445, 28])).
% 6.07/6.07 tff(21447,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21446])).
% 6.07/6.07 tff(21448,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21447, 42])).
% 6.07/6.07 tff(21449,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21448])).
% 6.07/6.07 tff(21450,plain,
% 6.07/6.07 (NSY1!32 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[255, 21449, 58])).
% 6.07/6.07 tff(21451,plain,
% 6.07/6.07 (pred(NSY1!32) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21450])).
% 6.07/6.07 tff(21452,plain,
% 6.07/6.07 (pred(NSY1!32) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21451, 23])).
% 6.07/6.07 tff(21453,plain,
% 6.07/6.07 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n0, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21452, 21428])).
% 6.07/6.07 tff(21454,plain,
% 6.07/6.07 (sum(pred(NSY1!32), succ(NPY1!34)) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21453, 35])).
% 6.07/6.07 tff(21455,plain,
% 6.07/6.07 (sum(pred(Y0!60), succ(X0!61)) = sum(n0, n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21351, 7218])).
% 6.07/6.07 tff(21456,plain,
% 6.07/6.07 (sum(pred(Y0!60), succ(X0!61)) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21455, 6525])).
% 6.07/6.07 tff(21457,plain,
% 6.07/6.07 (sum(pred(X0!61), succ(Y0!60)) = sum(n4, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[7192, 21375])).
% 6.07/6.07 tff(21458,plain,
% 6.07/6.07 (sum(pred(X0!61), succ(Y0!60)) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21457, 70])).
% 6.07/6.07 tff(21459,plain,
% 6.07/6.07 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n6, n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21458, 21456])).
% 6.07/6.07 tff(21460,plain,
% 6.07/6.07 (X1!59 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[93, 21459, 37])).
% 6.07/6.07 tff(21461,plain,
% 6.07/6.07 (pred(X1!59) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21460])).
% 6.07/6.07 tff(21462,plain,
% 6.07/6.07 (pred(X1!59) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21461, 23])).
% 6.07/6.07 tff(21463,plain,
% 6.07/6.07 (pred(pred(X1!59)) = pred(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21462])).
% 6.07/6.07 tff(21464,plain,
% 6.07/6.07 (pred(pred(X1!59)) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21463, 22])).
% 6.07/6.07 tff(21465,plain,
% 6.07/6.07 (pred(pred(pred(X1!59))) = pred(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21464])).
% 6.07/6.07 tff(21466,plain,
% 6.07/6.07 (pred(pred(pred(X1!59))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21465, 21])).
% 6.07/6.07 tff(21467,plain,
% 6.07/6.07 (pred(pred(pred(pred(X1!59)))) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21466])).
% 6.07/6.07 tff(21468,plain,
% 6.07/6.07 (pred(pred(pred(pred(X1!59)))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21467, 20])).
% 6.07/6.07 tff(21469,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(X1!59))))) = pred(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21468])).
% 6.07/6.07 tff(21470,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(X1!59))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21469, 19])).
% 6.07/6.07 tff(21471,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21470])).
% 6.07/6.07 tff(21472,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21471, 18])).
% 6.07/6.07 tff(21473,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21472])).
% 6.07/6.07 tff(21474,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21473, 17])).
% 6.07/6.07 tff(21475,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21474])).
% 6.07/6.07 tff(21476,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21475, 16])).
% 6.07/6.07 tff(21477,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21476])).
% 6.07/6.07 tff(21478,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21477, 15])).
% 6.07/6.07 tff(21479,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21478])).
% 6.07/6.07 tff(21480,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21479, 25])).
% 6.07/6.07 tff(21481,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21480])).
% 6.07/6.07 tff(21482,plain,
% 6.07/6.07 (NPX1!35 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[280, 21481, 24])).
% 6.07/6.07 tff(21483,plain,
% 6.07/6.07 (succ(NPX1!35) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21482])).
% 6.07/6.07 tff(21484,plain,
% 6.07/6.07 (succ(NPX1!35) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21483, 36])).
% 6.07/6.07 tff(21485,plain,
% 6.07/6.07 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n2, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21484, 21454])).
% 6.07/6.07 tff(21486,plain,
% 6.07/6.07 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21485, 34])).
% 6.07/6.07 tff(21487,plain,
% 6.07/6.07 (succ(X1!59) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21460])).
% 6.07/6.07 tff(21488,plain,
% 6.07/6.07 (succ(X1!59) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21487, 36])).
% 6.07/6.07 tff(21489,plain,
% 6.07/6.07 (succ(succ(X1!59)) = succ(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21488])).
% 6.07/6.07 tff(21490,plain,
% 6.07/6.07 (succ(succ(X1!59)) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21489, 48])).
% 6.07/6.07 tff(21491,plain,
% 6.07/6.07 (succ(succ(succ(X1!59))) = succ(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21490])).
% 6.07/6.07 tff(21492,plain,
% 6.07/6.07 (succ(succ(succ(X1!59))) = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[21491, 14])).
% 6.07/6.07 tff(21493,plain,
% 6.07/6.07 (succ(succ(succ(succ(X1!59)))) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21492])).
% 6.07/6.07 tff(21494,plain,
% 6.07/6.07 (succ(succ(succ(succ(X1!59)))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21493, 33])).
% 6.07/6.07 tff(21495,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(X1!59))))) = succ(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21494])).
% 6.07/6.07 tff(21496,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(X1!59))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21495, 30])).
% 6.07/6.07 tff(21497,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21496])).
% 6.07/6.07 tff(21498,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21497, 39])).
% 6.07/6.07 tff(21499,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21498])).
% 6.07/6.07 tff(21500,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21499, 53])).
% 6.07/6.07 tff(21501,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21500])).
% 6.07/6.07 tff(21502,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21501, 45])).
% 6.07/6.07 tff(21503,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21502])).
% 6.07/6.07 tff(21504,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21503, 28])).
% 6.07/6.07 tff(21505,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21504])).
% 6.07/6.07 tff(21506,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21505, 42])).
% 6.07/6.07 tff(21507,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21506])).
% 6.07/6.07 tff(21508,plain,
% 6.07/6.07 (NSX1!33 = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[305, 21507, 58])).
% 6.07/6.07 tff(21509,plain,
% 6.07/6.07 (pred(NSX1!33) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21508])).
% 6.07/6.07 tff(21510,plain,
% 6.07/6.07 (pred(NSX1!33) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21509, 23])).
% 6.07/6.07 tff(21511,plain,
% 6.07/6.07 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n0, n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21510, 21486])).
% 6.07/6.07 tff(21512,plain,
% 6.07/6.07 (Y2!56 = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[310, 21511, 442])).
% 6.07/6.07 tff(21513,plain,
% 6.07/6.07 (pred(Y2!56) = pred(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21512])).
% 6.07/6.07 tff(21514,plain,
% 6.07/6.07 (pred(Y2!56) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21513, 15])).
% 6.07/6.07 tff(21515,plain,
% 6.07/6.07 (pred(pred(Y2!56)) = pred(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21514])).
% 6.07/6.07 tff(21516,plain,
% 6.07/6.07 (pred(pred(Y2!56)) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21515, 25])).
% 6.07/6.07 tff(21517,plain,
% 6.07/6.07 (pred(pred(pred(Y2!56))) = pred(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21516])).
% 6.07/6.07 tff(21518,plain,
% 6.07/6.07 (pred(pred(pred(Y2!56))) = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[21517, 24])).
% 6.07/6.07 tff(21519,plain,
% 6.07/6.07 (pred(pred(pred(pred(Y2!56)))) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21518])).
% 6.07/6.07 tff(21520,plain,
% 6.07/6.07 (pred(pred(pred(pred(Y2!56)))) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21519, 23])).
% 6.07/6.07 tff(21521,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21520])).
% 6.07/6.07 tff(21522,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(Y2!56))))) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21521, 22])).
% 6.07/6.07 tff(21523,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21522])).
% 6.07/6.07 tff(21524,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21523, 21])).
% 6.07/6.07 tff(21525,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21524])).
% 6.07/6.07 tff(21526,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21525, 20])).
% 6.07/6.07 tff(21527,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21526])).
% 6.07/6.07 tff(21528,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21527, 19])).
% 6.07/6.07 tff(21529,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21528])).
% 6.07/6.07 tff(21530,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21529, 18])).
% 6.07/6.07 tff(21531,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21530])).
% 6.07/6.07 tff(21532,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21531, 17])).
% 6.07/6.07 tff(21533,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21532])).
% 6.07/6.07 tff(21534,plain,
% 6.07/6.07 (NPY2!30 = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[347, 21533, 16])).
% 6.07/6.07 tff(21535,plain,
% 6.07/6.07 (succ(NPY2!30) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21534])).
% 6.07/6.07 tff(21536,plain,
% 6.07/6.07 (succ(NPY2!30) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21535, 33])).
% 6.07/6.07 tff(21537,plain,
% 6.07/6.07 (succ(Y2!56) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21512])).
% 6.07/6.07 tff(21538,plain,
% 6.07/6.07 (succ(Y2!56) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21537, 33])).
% 6.07/6.07 tff(21539,plain,
% 6.07/6.07 (succ(succ(Y2!56)) = succ(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21538])).
% 6.07/6.07 tff(21540,plain,
% 6.07/6.07 (succ(succ(Y2!56)) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21539, 30])).
% 6.07/6.07 tff(21541,plain,
% 6.07/6.07 (succ(succ(succ(Y2!56))) = succ(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21540])).
% 6.07/6.07 tff(21542,plain,
% 6.07/6.07 (succ(succ(succ(Y2!56))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21541, 39])).
% 6.07/6.07 tff(21543,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y2!56)))) = succ(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21542])).
% 6.07/6.07 tff(21544,plain,
% 6.07/6.07 (succ(succ(succ(succ(Y2!56)))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21543, 53])).
% 6.07/6.07 tff(21545,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21544])).
% 6.07/6.07 tff(21546,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(Y2!56))))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21545, 45])).
% 6.07/6.07 tff(21547,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21546])).
% 6.07/6.07 tff(21548,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21547, 28])).
% 6.07/6.07 tff(21549,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21548])).
% 6.07/6.07 tff(21550,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21549, 42])).
% 6.07/6.07 tff(21551,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21550])).
% 6.07/6.07 tff(21552,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[21551, 58])).
% 6.07/6.07 tff(21553,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21552])).
% 6.07/6.07 tff(21554,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21553, 36])).
% 6.07/6.07 tff(21555,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21554])).
% 6.07/6.07 tff(21556,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21555, 48])).
% 6.07/6.07 tff(21557,plain,
% 6.07/6.07 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21556])).
% 6.07/6.07 tff(21558,plain,
% 6.07/6.07 (NSY2!28 = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[370, 21557, 14])).
% 6.07/6.07 tff(21559,plain,
% 6.07/6.07 (pred(NSY2!28) = pred(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21558])).
% 6.07/6.07 tff(21560,plain,
% 6.07/6.07 (pred(NSY2!28) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21559, 15])).
% 6.07/6.07 tff(21561,plain,
% 6.07/6.07 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n3, n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21560, 21536])).
% 6.07/6.07 tff(21562,plain,
% 6.07/6.07 (sum(pred(NSY2!28), succ(NPY2!30)) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21561, 32])).
% 6.07/6.07 tff(21563,plain,
% 6.07/6.07 (sum(pred(Y1!58), succ(X1!59)) = sum(n0, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21406, 21488])).
% 6.07/6.07 tff(21564,plain,
% 6.07/6.07 (sum(pred(Y1!58), succ(X1!59)) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21563, 35])).
% 6.07/6.07 tff(21565,plain,
% 6.07/6.07 (sum(pred(X1!59), succ(Y1!58)) = sum(n0, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21462, 21430])).
% 6.07/6.07 tff(21566,plain,
% 6.07/6.07 (sum(pred(X1!59), succ(Y1!58)) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21565, 35])).
% 6.07/6.07 tff(21567,plain,
% 6.07/6.07 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n2, n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21566, 21564])).
% 6.07/6.07 tff(21568,plain,
% 6.07/6.07 (X2!57 = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[209, 21567, 34])).
% 6.07/6.07 tff(21569,plain,
% 6.07/6.07 (pred(X2!57) = pred(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21568])).
% 6.07/6.07 tff(21570,plain,
% 6.07/6.07 (pred(X2!57) = n3),
% 6.07/6.07 inference(transitivity,[status(thm)],[21569, 15])).
% 6.07/6.07 tff(21571,plain,
% 6.07/6.07 (pred(pred(X2!57)) = pred(n3)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21570])).
% 6.07/6.07 tff(21572,plain,
% 6.07/6.07 (pred(pred(X2!57)) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21571, 25])).
% 6.07/6.07 tff(21573,plain,
% 6.07/6.07 (pred(pred(pred(X2!57))) = pred(n2)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21572])).
% 6.07/6.07 tff(21574,plain,
% 6.07/6.07 (pred(pred(pred(X2!57))) = n1),
% 6.07/6.07 inference(transitivity,[status(thm)],[21573, 24])).
% 6.07/6.07 tff(21575,plain,
% 6.07/6.07 (pred(pred(pred(pred(X2!57)))) = pred(n1)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21574])).
% 6.07/6.07 tff(21576,plain,
% 6.07/6.07 (pred(pred(pred(pred(X2!57)))) = n0),
% 6.07/6.07 inference(transitivity,[status(thm)],[21575, 23])).
% 6.07/6.07 tff(21577,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(X2!57))))) = pred(n0)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21576])).
% 6.07/6.07 tff(21578,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(X2!57))))) = n10),
% 6.07/6.07 inference(transitivity,[status(thm)],[21577, 22])).
% 6.07/6.07 tff(21579,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n10)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21578])).
% 6.07/6.07 tff(21580,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n9),
% 6.07/6.07 inference(transitivity,[status(thm)],[21579, 21])).
% 6.07/6.07 tff(21581,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n9)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21580])).
% 6.07/6.07 tff(21582,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n8),
% 6.07/6.07 inference(transitivity,[status(thm)],[21581, 20])).
% 6.07/6.07 tff(21583,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21582])).
% 6.07/6.07 tff(21584,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21583, 19])).
% 6.07/6.07 tff(21585,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n7)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21584])).
% 6.07/6.07 tff(21586,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21585, 18])).
% 6.07/6.07 tff(21587,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21586])).
% 6.07/6.07 tff(21588,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21587, 17])).
% 6.07/6.07 tff(21589,plain,
% 6.07/6.07 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21588])).
% 6.07/6.07 tff(21590,plain,
% 6.07/6.07 (NPX2!31 = n4),
% 6.07/6.07 inference(transitivity,[status(thm)],[395, 21589, 16])).
% 6.07/6.07 tff(21591,plain,
% 6.07/6.07 (succ(NPX2!31) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21590])).
% 6.07/6.07 tff(21592,plain,
% 6.07/6.07 (succ(NPX2!31) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21591, 33])).
% 6.07/6.07 tff(21593,plain,
% 6.07/6.07 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n5, n8)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21592, 21562])).
% 6.07/6.07 tff(21594,plain,
% 6.07/6.07 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n2),
% 6.07/6.07 inference(transitivity,[status(thm)],[21593, 558])).
% 6.07/6.07 tff(21595,plain,
% 6.07/6.07 (succ(X2!57) = succ(n4)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21568])).
% 6.07/6.07 tff(21596,plain,
% 6.07/6.07 (succ(X2!57) = n5),
% 6.07/6.07 inference(transitivity,[status(thm)],[21595, 33])).
% 6.07/6.07 tff(21597,plain,
% 6.07/6.07 (succ(succ(X2!57)) = succ(n5)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21596])).
% 6.07/6.07 tff(21598,plain,
% 6.07/6.07 (succ(succ(X2!57)) = n6),
% 6.07/6.07 inference(transitivity,[status(thm)],[21597, 30])).
% 6.07/6.07 tff(21599,plain,
% 6.07/6.07 (succ(succ(succ(X2!57))) = succ(n6)),
% 6.07/6.07 inference(monotonicity,[status(thm)],[21598])).
% 6.07/6.07 tff(21600,plain,
% 6.07/6.07 (succ(succ(succ(X2!57))) = n7),
% 6.07/6.07 inference(transitivity,[status(thm)],[21599, 39])).
% 6.07/6.08 tff(21601,plain,
% 6.07/6.08 (succ(succ(succ(succ(X2!57)))) = succ(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21600])).
% 6.07/6.08 tff(21602,plain,
% 6.07/6.08 (succ(succ(succ(succ(X2!57)))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21601, 53])).
% 6.07/6.08 tff(21603,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X2!57))))) = succ(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21602])).
% 6.07/6.08 tff(21604,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X2!57))))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21603, 45])).
% 6.07/6.08 tff(21605,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21604])).
% 6.07/6.08 tff(21606,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21605, 28])).
% 6.07/6.08 tff(21607,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21606])).
% 6.07/6.08 tff(21608,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21607, 42])).
% 6.07/6.08 tff(21609,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21608])).
% 6.07/6.08 tff(21610,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21609, 58])).
% 6.07/6.08 tff(21611,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21610])).
% 6.07/6.08 tff(21612,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21611, 36])).
% 6.07/6.08 tff(21613,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21612])).
% 6.07/6.08 tff(21614,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21613, 48])).
% 6.07/6.08 tff(21615,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21614])).
% 6.07/6.08 tff(21616,plain,
% 6.07/6.08 (NSX2!29 = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[420, 21615, 14])).
% 6.07/6.08 tff(21617,plain,
% 6.07/6.08 (pred(NSX2!29) = pred(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21616])).
% 6.07/6.08 tff(21618,plain,
% 6.07/6.08 (pred(NSX2!29) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21617, 15])).
% 6.07/6.08 tff(21619,plain,
% 6.07/6.08 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n3, n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21618, 21594])).
% 6.07/6.08 tff(21620,plain,
% 6.07/6.08 (Y3!54 = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[425, 21619, 557])).
% 6.07/6.08 tff(21621,plain,
% 6.07/6.08 (pred(Y3!54) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21620])).
% 6.07/6.08 tff(21622,plain,
% 6.07/6.08 (pred(Y3!54) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21621, 16])).
% 6.07/6.08 tff(21623,plain,
% 6.07/6.08 (pred(pred(Y3!54)) = pred(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21622])).
% 6.07/6.08 tff(21624,plain,
% 6.07/6.08 (pred(pred(Y3!54)) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21623, 15])).
% 6.07/6.08 tff(21625,plain,
% 6.07/6.08 (pred(pred(pred(Y3!54))) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21624])).
% 6.07/6.08 tff(21626,plain,
% 6.07/6.08 (pred(pred(pred(Y3!54))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21625, 25])).
% 6.07/6.08 tff(21627,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y3!54)))) = pred(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21626])).
% 6.07/6.08 tff(21628,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y3!54)))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21627, 24])).
% 6.07/6.08 tff(21629,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21628])).
% 6.07/6.08 tff(21630,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y3!54))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21629, 23])).
% 6.07/6.08 tff(21631,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21630])).
% 6.07/6.08 tff(21632,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21631, 22])).
% 6.07/6.08 tff(21633,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21632])).
% 6.07/6.08 tff(21634,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21633, 21])).
% 6.07/6.08 tff(21635,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21634])).
% 6.07/6.08 tff(21636,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21635, 20])).
% 6.07/6.08 tff(21637,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21636])).
% 6.07/6.08 tff(21638,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21637, 19])).
% 6.07/6.08 tff(21639,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21638])).
% 6.07/6.08 tff(21640,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21639, 18])).
% 6.07/6.08 tff(21641,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21640])).
% 6.07/6.08 tff(21642,plain,
% 6.07/6.08 (NPY3!26 = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[462, 21641, 17])).
% 6.07/6.08 tff(21643,plain,
% 6.07/6.08 (succ(NPY3!26) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21642])).
% 6.07/6.08 tff(21644,plain,
% 6.07/6.08 (succ(NPY3!26) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21643, 30])).
% 6.07/6.08 tff(21645,plain,
% 6.07/6.08 (succ(Y3!54) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21620])).
% 6.07/6.08 tff(21646,plain,
% 6.07/6.08 (succ(Y3!54) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21645, 30])).
% 6.07/6.08 tff(21647,plain,
% 6.07/6.08 (succ(succ(Y3!54)) = succ(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21646])).
% 6.07/6.08 tff(21648,plain,
% 6.07/6.08 (succ(succ(Y3!54)) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21647, 39])).
% 6.07/6.08 tff(21649,plain,
% 6.07/6.08 (succ(succ(succ(Y3!54))) = succ(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21648])).
% 6.07/6.08 tff(21650,plain,
% 6.07/6.08 (succ(succ(succ(Y3!54))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21649, 53])).
% 6.07/6.08 tff(21651,plain,
% 6.07/6.08 (succ(succ(succ(succ(Y3!54)))) = succ(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21650])).
% 6.07/6.08 tff(21652,plain,
% 6.07/6.08 (succ(succ(succ(succ(Y3!54)))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21651, 45])).
% 6.07/6.08 tff(21653,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21652])).
% 6.07/6.08 tff(21654,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(Y3!54))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21653, 28])).
% 6.07/6.08 tff(21655,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21654])).
% 6.07/6.08 tff(21656,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21655, 42])).
% 6.07/6.08 tff(21657,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21656])).
% 6.07/6.08 tff(21658,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21657, 58])).
% 6.07/6.08 tff(21659,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21658])).
% 6.07/6.08 tff(21660,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21659, 36])).
% 6.07/6.08 tff(21661,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21660])).
% 6.07/6.08 tff(21662,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21661, 48])).
% 6.07/6.08 tff(21663,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21662])).
% 6.07/6.08 tff(21664,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21663, 14])).
% 6.07/6.08 tff(21665,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21664])).
% 6.07/6.08 tff(21666,plain,
% 6.07/6.08 (NSY3!24 = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[485, 21665, 33])).
% 6.07/6.08 tff(21667,plain,
% 6.07/6.08 (pred(NSY3!24) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21666])).
% 6.07/6.08 tff(21668,plain,
% 6.07/6.08 (pred(NSY3!24) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21667, 16])).
% 6.07/6.08 tff(21669,plain,
% 6.07/6.08 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n4, n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21668, 21644])).
% 6.07/6.08 tff(21670,plain,
% 6.07/6.08 (sum(pred(NSY3!24), succ(NPY3!26)) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21669, 12])).
% 6.07/6.08 tff(21671,plain,
% 6.07/6.08 (sum(pred(Y2!56), succ(X2!57)) = sum(n3, n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21514, 21596])).
% 6.07/6.08 tff(21672,plain,
% 6.07/6.08 (sum(pred(Y2!56), succ(X2!57)) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21671, 32])).
% 6.07/6.08 tff(21673,plain,
% 6.07/6.08 (sum(pred(X2!57), succ(Y2!56)) = sum(n3, n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21570, 21538])).
% 6.07/6.08 tff(21674,plain,
% 6.07/6.08 (sum(pred(X2!57), succ(Y2!56)) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21673, 32])).
% 6.07/6.08 tff(21675,plain,
% 6.07/6.08 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n8, n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21674, 21672])).
% 6.07/6.08 tff(21676,plain,
% 6.07/6.08 (X3!55 = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[323, 21675, 31])).
% 6.07/6.08 tff(21677,plain,
% 6.07/6.08 (pred(X3!55) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21676])).
% 6.07/6.08 tff(21678,plain,
% 6.07/6.08 (pred(X3!55) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21677, 16])).
% 6.07/6.08 tff(21679,plain,
% 6.07/6.08 (pred(pred(X3!55)) = pred(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21678])).
% 6.07/6.08 tff(21680,plain,
% 6.07/6.08 (pred(pred(X3!55)) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21679, 15])).
% 6.07/6.08 tff(21681,plain,
% 6.07/6.08 (pred(pred(pred(X3!55))) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21680])).
% 6.07/6.08 tff(21682,plain,
% 6.07/6.08 (pred(pred(pred(X3!55))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21681, 25])).
% 6.07/6.08 tff(21683,plain,
% 6.07/6.08 (pred(pred(pred(pred(X3!55)))) = pred(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21682])).
% 6.07/6.08 tff(21684,plain,
% 6.07/6.08 (pred(pred(pred(pred(X3!55)))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21683, 24])).
% 6.07/6.08 tff(21685,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(X3!55))))) = pred(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21684])).
% 6.07/6.08 tff(21686,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(X3!55))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21685, 23])).
% 6.07/6.08 tff(21687,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21686])).
% 6.07/6.08 tff(21688,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21687, 22])).
% 6.07/6.08 tff(21689,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21688])).
% 6.07/6.08 tff(21690,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21689, 21])).
% 6.07/6.08 tff(21691,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21690])).
% 6.07/6.08 tff(21692,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21691, 20])).
% 6.07/6.08 tff(21693,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21692])).
% 6.07/6.08 tff(21694,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21693, 19])).
% 6.07/6.08 tff(21695,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21694])).
% 6.07/6.08 tff(21696,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21695, 18])).
% 6.07/6.08 tff(21697,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21696])).
% 6.07/6.08 tff(21698,plain,
% 6.07/6.08 (NPX3!27 = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[510, 21697, 17])).
% 6.07/6.08 tff(21699,plain,
% 6.07/6.08 (succ(NPX3!27) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21698])).
% 6.07/6.08 tff(21700,plain,
% 6.07/6.08 (succ(NPX3!27) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21699, 30])).
% 6.07/6.08 tff(21701,plain,
% 6.07/6.08 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n6, n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21700, 21670])).
% 6.07/6.08 tff(21702,plain,
% 6.07/6.08 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21701, 674])).
% 6.07/6.08 tff(21703,plain,
% 6.07/6.08 (succ(X3!55) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21676])).
% 6.07/6.08 tff(21704,plain,
% 6.07/6.08 (succ(X3!55) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21703, 30])).
% 6.07/6.08 tff(21705,plain,
% 6.07/6.08 (succ(succ(X3!55)) = succ(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21704])).
% 6.07/6.08 tff(21706,plain,
% 6.07/6.08 (succ(succ(X3!55)) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21705, 39])).
% 6.07/6.08 tff(21707,plain,
% 6.07/6.08 (succ(succ(succ(X3!55))) = succ(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21706])).
% 6.07/6.08 tff(21708,plain,
% 6.07/6.08 (succ(succ(succ(X3!55))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21707, 53])).
% 6.07/6.08 tff(21709,plain,
% 6.07/6.08 (succ(succ(succ(succ(X3!55)))) = succ(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21708])).
% 6.07/6.08 tff(21710,plain,
% 6.07/6.08 (succ(succ(succ(succ(X3!55)))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21709, 45])).
% 6.07/6.08 tff(21711,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X3!55))))) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21710])).
% 6.07/6.08 tff(21712,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X3!55))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21711, 28])).
% 6.07/6.08 tff(21713,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X3!55)))))) = succ(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21712])).
% 6.07/6.08 tff(21714,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X3!55)))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21713, 42])).
% 6.07/6.08 tff(21715,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = succ(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21714])).
% 6.07/6.08 tff(21716,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X3!55))))))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21715, 58])).
% 6.07/6.08 tff(21717,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = succ(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21716])).
% 6.07/6.08 tff(21718,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21717, 36])).
% 6.07/6.08 tff(21719,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = succ(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21718])).
% 6.07/6.08 tff(21720,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21719, 48])).
% 6.07/6.08 tff(21721,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21720])).
% 6.07/6.08 tff(21722,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55)))))))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21721, 14])).
% 6.07/6.08 tff(21723,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X3!55))))))))))) = succ(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21722])).
% 6.07/6.08 tff(21724,plain,
% 6.07/6.08 (NSX3!25 = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[535, 21723, 33])).
% 6.07/6.08 tff(21725,plain,
% 6.07/6.08 (pred(NSX3!25) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21724])).
% 6.07/6.08 tff(21726,plain,
% 6.07/6.08 (pred(NSX3!25) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21725, 16])).
% 6.07/6.08 tff(21727,plain,
% 6.07/6.08 (sum(pred(NSX3!25), sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26)))) = sum(n4, n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21726, 21702])).
% 6.07/6.08 tff(21728,plain,
% 6.07/6.08 (Y4!52 = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[540, 21727, 673])).
% 6.07/6.08 tff(21729,plain,
% 6.07/6.08 (pred(Y4!52) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21728])).
% 6.07/6.08 tff(21730,plain,
% 6.07/6.08 (pred(Y4!52) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21729, 20])).
% 6.07/6.08 tff(21731,plain,
% 6.07/6.08 (pred(pred(Y4!52)) = pred(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21730])).
% 6.07/6.08 tff(21732,plain,
% 6.07/6.08 (pred(pred(Y4!52)) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21731, 19])).
% 6.07/6.08 tff(21733,plain,
% 6.07/6.08 (pred(pred(pred(Y4!52))) = pred(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21732])).
% 6.07/6.08 tff(21734,plain,
% 6.07/6.08 (pred(pred(pred(Y4!52))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21733, 18])).
% 6.07/6.08 tff(21735,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y4!52)))) = pred(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21734])).
% 6.07/6.08 tff(21736,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y4!52)))) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21735, 17])).
% 6.07/6.08 tff(21737,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y4!52))))) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21736])).
% 6.07/6.08 tff(21738,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y4!52))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21737, 16])).
% 6.07/6.08 tff(21739,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = pred(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21738])).
% 6.07/6.08 tff(21740,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(Y4!52)))))) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21739, 15])).
% 6.07/6.08 tff(21741,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21740])).
% 6.07/6.08 tff(21742,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(Y4!52))))))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21741, 25])).
% 6.07/6.08 tff(21743,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = pred(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21742])).
% 6.07/6.08 tff(21744,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21743, 24])).
% 6.07/6.08 tff(21745,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = pred(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21744])).
% 6.07/6.08 tff(21746,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21745, 23])).
% 6.07/6.08 tff(21747,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = pred(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21746])).
% 6.07/6.08 tff(21748,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52)))))))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21747, 22])).
% 6.07/6.08 tff(21749,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y4!52))))))))))) = pred(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21748])).
% 6.07/6.08 tff(21750,plain,
% 6.07/6.08 (NPY4!22 = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[578, 21749, 21])).
% 6.07/6.08 tff(21751,plain,
% 6.07/6.08 (succ(NPY4!22) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21750])).
% 6.07/6.08 tff(21752,plain,
% 6.07/6.08 (succ(NPY4!22) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21751, 28])).
% 6.07/6.08 tff(21753,plain,
% 6.07/6.08 (succ(Y4!52) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21728])).
% 6.07/6.08 tff(21754,plain,
% 6.07/6.08 (succ(Y4!52) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21753, 28])).
% 6.07/6.08 tff(21755,plain,
% 6.07/6.08 (succ(succ(Y4!52)) = succ(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21754])).
% 6.07/6.08 tff(21756,plain,
% 6.07/6.08 (succ(succ(Y4!52)) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21755, 42])).
% 6.07/6.08 tff(21757,plain,
% 6.07/6.08 (succ(succ(succ(Y4!52))) = succ(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21756])).
% 6.07/6.08 tff(21758,plain,
% 6.07/6.08 (succ(succ(succ(Y4!52))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21757, 58])).
% 6.07/6.08 tff(21759,plain,
% 6.07/6.08 (succ(succ(succ(succ(Y4!52)))) = succ(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21758])).
% 6.07/6.08 tff(21760,plain,
% 6.07/6.08 (succ(succ(succ(succ(Y4!52)))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21759, 36])).
% 6.07/6.08 tff(21761,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(Y4!52))))) = succ(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21760])).
% 6.07/6.08 tff(21762,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(Y4!52))))) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21761, 48])).
% 6.07/6.08 tff(21763,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21762])).
% 6.07/6.08 tff(21764,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(Y4!52)))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21763, 14])).
% 6.07/6.08 tff(21765,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = succ(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21764])).
% 6.07/6.08 tff(21766,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(Y4!52))))))) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21765, 33])).
% 6.07/6.08 tff(21767,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21766])).
% 6.07/6.08 tff(21768,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21767, 30])).
% 6.07/6.08 tff(21769,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = succ(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21768])).
% 6.07/6.08 tff(21770,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21769, 39])).
% 6.07/6.08 tff(21771,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = succ(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21770])).
% 6.07/6.08 tff(21772,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52)))))))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21771, 53])).
% 6.07/6.08 tff(21773,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y4!52))))))))))) = succ(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21772])).
% 6.07/6.08 tff(21774,plain,
% 6.07/6.08 (NSY4!20 = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[601, 21773, 45])).
% 6.07/6.08 tff(21775,plain,
% 6.07/6.08 (pred(NSY4!20) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21774])).
% 6.07/6.08 tff(21776,plain,
% 6.07/6.08 (pred(NSY4!20) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21775, 20])).
% 6.07/6.08 tff(21777,plain,
% 6.07/6.08 (sum(pred(NSY4!20), succ(NPY4!22)) = sum(n8, n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21776, 21752])).
% 6.07/6.08 tff(21778,plain,
% 6.07/6.08 (sum(pred(NSY4!20), succ(NPY4!22)) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21777, 27])).
% 6.07/6.08 tff(21779,plain,
% 6.07/6.08 (sum(pred(Y3!54), succ(X3!55)) = sum(n4, n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21622, 21704])).
% 6.07/6.08 tff(21780,plain,
% 6.07/6.08 (sum(pred(Y3!54), succ(X3!55)) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21779, 12])).
% 6.07/6.08 tff(21781,plain,
% 6.07/6.08 (sum(pred(X3!55), succ(Y3!54)) = sum(n4, n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21678, 21646])).
% 6.07/6.08 tff(21782,plain,
% 6.07/6.08 (sum(pred(X3!55), succ(Y3!54)) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21781, 12])).
% 6.07/6.08 tff(21783,plain,
% 6.07/6.08 (sum(sum(pred(X3!55), succ(Y3!54)), sum(pred(Y3!54), succ(X3!55))) = sum(n10, n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21782, 21780])).
% 6.07/6.08 tff(21784,plain,
% 6.07/6.08 (X4!53 = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[438, 21783, 29])).
% 6.07/6.08 tff(21785,plain,
% 6.07/6.08 (pred(X4!53) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21784])).
% 6.07/6.08 tff(21786,plain,
% 6.07/6.08 (pred(X4!53) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21785, 20])).
% 6.07/6.08 tff(21787,plain,
% 6.07/6.08 (pred(pred(X4!53)) = pred(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21786])).
% 6.07/6.08 tff(21788,plain,
% 6.07/6.08 (pred(pred(X4!53)) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21787, 19])).
% 6.07/6.08 tff(21789,plain,
% 6.07/6.08 (pred(pred(pred(X4!53))) = pred(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21788])).
% 6.07/6.08 tff(21790,plain,
% 6.07/6.08 (pred(pred(pred(X4!53))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21789, 18])).
% 6.07/6.08 tff(21791,plain,
% 6.07/6.08 (pred(pred(pred(pred(X4!53)))) = pred(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21790])).
% 6.07/6.08 tff(21792,plain,
% 6.07/6.08 (pred(pred(pred(pred(X4!53)))) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21791, 17])).
% 6.07/6.08 tff(21793,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(X4!53))))) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21792])).
% 6.07/6.08 tff(21794,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(X4!53))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21793, 16])).
% 6.07/6.08 tff(21795,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(X4!53)))))) = pred(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21794])).
% 6.07/6.08 tff(21796,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(X4!53)))))) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21795, 15])).
% 6.07/6.08 tff(21797,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21796])).
% 6.07/6.08 tff(21798,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(X4!53))))))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21797, 25])).
% 6.07/6.08 tff(21799,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = pred(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21798])).
% 6.07/6.08 tff(21800,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21799, 24])).
% 6.07/6.08 tff(21801,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = pred(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21800])).
% 6.07/6.08 tff(21802,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21801, 23])).
% 6.07/6.08 tff(21803,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = pred(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21802])).
% 6.07/6.08 tff(21804,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53)))))))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21803, 22])).
% 6.07/6.08 tff(21805,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X4!53))))))))))) = pred(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21804])).
% 6.07/6.08 tff(21806,plain,
% 6.07/6.08 (NPX4!23 = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[626, 21805, 21])).
% 6.07/6.08 tff(21807,plain,
% 6.07/6.08 (succ(NPX4!23) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21806])).
% 6.07/6.08 tff(21808,plain,
% 6.07/6.08 (succ(NPX4!23) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21807, 28])).
% 6.07/6.08 tff(21809,plain,
% 6.07/6.08 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = sum(n10, n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21808, 21778])).
% 6.07/6.08 tff(21810,plain,
% 6.07/6.08 (sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21809, 69])).
% 6.07/6.08 tff(21811,plain,
% 6.07/6.08 (succ(X4!53) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21784])).
% 6.07/6.08 tff(21812,plain,
% 6.07/6.08 (succ(X4!53) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21811, 28])).
% 6.07/6.08 tff(21813,plain,
% 6.07/6.08 (succ(succ(X4!53)) = succ(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21812])).
% 6.07/6.08 tff(21814,plain,
% 6.07/6.08 (succ(succ(X4!53)) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21813, 42])).
% 6.07/6.08 tff(21815,plain,
% 6.07/6.08 (succ(succ(succ(X4!53))) = succ(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21814])).
% 6.07/6.08 tff(21816,plain,
% 6.07/6.08 (succ(succ(succ(X4!53))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21815, 58])).
% 6.07/6.08 tff(21817,plain,
% 6.07/6.08 (succ(succ(succ(succ(X4!53)))) = succ(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21816])).
% 6.07/6.08 tff(21818,plain,
% 6.07/6.08 (succ(succ(succ(succ(X4!53)))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21817, 36])).
% 6.07/6.08 tff(21819,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X4!53))))) = succ(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21818])).
% 6.07/6.08 tff(21820,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X4!53))))) = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[21819, 48])).
% 6.07/6.08 tff(21821,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X4!53)))))) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21820])).
% 6.07/6.08 tff(21822,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X4!53)))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21821, 14])).
% 6.07/6.08 tff(21823,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = succ(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21822])).
% 6.07/6.08 tff(21824,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X4!53))))))) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21823, 33])).
% 6.07/6.08 tff(21825,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21824])).
% 6.07/6.08 tff(21826,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21825, 30])).
% 6.07/6.08 tff(21827,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = succ(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21826])).
% 6.07/6.08 tff(21828,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21827, 39])).
% 6.07/6.08 tff(21829,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = succ(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21828])).
% 6.07/6.08 tff(21830,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53)))))))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21829, 53])).
% 6.07/6.08 tff(21831,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X4!53))))))))))) = succ(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21830])).
% 6.07/6.08 tff(21832,plain,
% 6.07/6.08 (NSX4!21 = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[651, 21831, 45])).
% 6.07/6.08 tff(21833,plain,
% 6.07/6.08 (pred(NSX4!21) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21832])).
% 6.07/6.08 tff(21834,plain,
% 6.07/6.08 (pred(NSX4!21) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21833, 20])).
% 6.07/6.08 tff(21835,plain,
% 6.07/6.08 (sum(pred(NSX4!21), sum(succ(NPX4!23), sum(pred(NSY4!20), succ(NPY4!22)))) = sum(n8, n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21834, 21810])).
% 6.07/6.08 tff(21836,plain,
% 6.07/6.08 (Y5!50 = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[656, 21835, 98])).
% 6.07/6.08 tff(21837,plain,
% 6.07/6.08 (pred(Y5!50) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21836])).
% 6.07/6.08 tff(21838,plain,
% 6.07/6.08 (pred(Y5!50) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21837, 25])).
% 6.07/6.08 tff(21839,plain,
% 6.07/6.08 (pred(pred(Y5!50)) = pred(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21838])).
% 6.07/6.08 tff(21840,plain,
% 6.07/6.08 (pred(pred(Y5!50)) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21839, 24])).
% 6.07/6.08 tff(21841,plain,
% 6.07/6.08 (pred(pred(pred(Y5!50))) = pred(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21840])).
% 6.07/6.08 tff(21842,plain,
% 6.07/6.08 (pred(pred(pred(Y5!50))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21841, 23])).
% 6.07/6.08 tff(21843,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y5!50)))) = pred(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21842])).
% 6.07/6.08 tff(21844,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y5!50)))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21843, 22])).
% 6.07/6.08 tff(21845,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y5!50))))) = pred(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21844])).
% 6.07/6.08 tff(21846,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y5!50))))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21845, 21])).
% 6.07/6.08 tff(21847,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21846])).
% 6.07/6.08 tff(21848,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(Y5!50)))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21847, 20])).
% 6.07/6.08 tff(21849,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = pred(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21848])).
% 6.07/6.08 tff(21850,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(Y5!50))))))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21849, 19])).
% 6.07/6.08 tff(21851,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = pred(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21850])).
% 6.07/6.08 tff(21852,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21851, 18])).
% 6.07/6.08 tff(21853,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = pred(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21852])).
% 6.07/6.08 tff(21854,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21853, 17])).
% 6.07/6.08 tff(21855,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21854])).
% 6.07/6.08 tff(21856,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50)))))))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21855, 16])).
% 6.07/6.08 tff(21857,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y5!50))))))))))) = pred(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21856])).
% 6.07/6.08 tff(21858,plain,
% 6.07/6.08 (NPY5!18 = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[694, 21857, 15])).
% 6.07/6.08 tff(21859,plain,
% 6.07/6.08 (succ(NPY5!18) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21858])).
% 6.07/6.08 tff(21860,plain,
% 6.07/6.08 (succ(NPY5!18) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21859, 14])).
% 6.07/6.08 tff(21861,plain,
% 6.07/6.08 (succ(Y5!50) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21836])).
% 6.07/6.08 tff(21862,plain,
% 6.07/6.08 (succ(Y5!50) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21861, 14])).
% 6.07/6.08 tff(21863,plain,
% 6.07/6.08 (succ(succ(Y5!50)) = succ(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21862])).
% 6.07/6.08 tff(21864,plain,
% 6.07/6.08 (succ(succ(Y5!50)) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21863, 33])).
% 6.07/6.08 tff(21865,plain,
% 6.07/6.08 (succ(succ(succ(Y5!50))) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21864])).
% 6.07/6.08 tff(21866,plain,
% 6.07/6.08 (succ(succ(succ(Y5!50))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21865, 30])).
% 6.07/6.08 tff(21867,plain,
% 6.07/6.08 (succ(succ(succ(succ(Y5!50)))) = succ(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21866])).
% 6.07/6.08 tff(21868,plain,
% 6.07/6.08 (succ(succ(succ(succ(Y5!50)))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21867, 39])).
% 6.07/6.08 tff(21869,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(Y5!50))))) = succ(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21868])).
% 6.07/6.08 tff(21870,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(Y5!50))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21869, 53])).
% 6.07/6.08 tff(21871,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = succ(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21870])).
% 6.07/6.08 tff(21872,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(Y5!50)))))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21871, 45])).
% 6.07/6.08 tff(21873,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21872])).
% 6.07/6.08 tff(21874,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(Y5!50))))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21873, 28])).
% 6.07/6.08 tff(21875,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = succ(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21874])).
% 6.07/6.08 tff(21876,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21875, 42])).
% 6.07/6.08 tff(21877,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = succ(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21876])).
% 6.07/6.08 tff(21878,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21877, 58])).
% 6.07/6.08 tff(21879,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = succ(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21878])).
% 6.07/6.08 tff(21880,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50)))))))))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21879, 36])).
% 6.07/6.08 tff(21881,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y5!50))))))))))) = succ(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21880])).
% 6.07/6.08 tff(21882,plain,
% 6.07/6.08 (NSY5!16 = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[717, 21881, 48])).
% 6.07/6.08 tff(21883,plain,
% 6.07/6.08 (pred(NSY5!16) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21882])).
% 6.07/6.08 tff(21884,plain,
% 6.07/6.08 (pred(NSY5!16) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21883, 25])).
% 6.07/6.08 tff(21885,plain,
% 6.07/6.08 (sum(pred(NSY5!16), succ(NPY5!18)) = sum(n2, n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21884, 21860])).
% 6.07/6.08 tff(21886,plain,
% 6.07/6.08 (sum(pred(NSY5!16), succ(NPY5!18)) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21885, 13])).
% 6.07/6.08 tff(21887,plain,
% 6.07/6.08 (sum(pred(Y4!52), succ(X4!53)) = sum(n8, n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21730, 21812])).
% 6.07/6.08 tff(21888,plain,
% 6.07/6.08 (sum(pred(Y4!52), succ(X4!53)) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21887, 27])).
% 6.07/6.08 tff(21889,plain,
% 6.07/6.08 (sum(pred(X4!53), succ(Y4!52)) = sum(n8, n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21786, 21754])).
% 6.07/6.08 tff(21890,plain,
% 6.07/6.08 (sum(pred(X4!53), succ(Y4!52)) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21889, 27])).
% 6.07/6.08 tff(21891,plain,
% 6.07/6.08 (sum(sum(pred(X4!53), succ(Y4!52)), sum(pred(Y4!52), succ(X4!53))) = sum(n7, n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21890, 21888])).
% 6.07/6.08 tff(21892,plain,
% 6.07/6.08 (X5!51 = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[553, 21891, 26])).
% 6.07/6.08 tff(21893,plain,
% 6.07/6.08 (pred(X5!51) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21892])).
% 6.07/6.08 tff(21894,plain,
% 6.07/6.08 (pred(X5!51) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21893, 25])).
% 6.07/6.08 tff(21895,plain,
% 6.07/6.08 (pred(pred(X5!51)) = pred(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21894])).
% 6.07/6.08 tff(21896,plain,
% 6.07/6.08 (pred(pred(X5!51)) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21895, 24])).
% 6.07/6.08 tff(21897,plain,
% 6.07/6.08 (pred(pred(pred(X5!51))) = pred(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21896])).
% 6.07/6.08 tff(21898,plain,
% 6.07/6.08 (pred(pred(pred(X5!51))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21897, 23])).
% 6.07/6.08 tff(21899,plain,
% 6.07/6.08 (pred(pred(pred(pred(X5!51)))) = pred(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21898])).
% 6.07/6.08 tff(21900,plain,
% 6.07/6.08 (pred(pred(pred(pred(X5!51)))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21899, 22])).
% 6.07/6.08 tff(21901,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(X5!51))))) = pred(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21900])).
% 6.07/6.08 tff(21902,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(X5!51))))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21901, 21])).
% 6.07/6.08 tff(21903,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(X5!51)))))) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21902])).
% 6.07/6.08 tff(21904,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(X5!51)))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21903, 20])).
% 6.07/6.08 tff(21905,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = pred(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21904])).
% 6.07/6.08 tff(21906,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(X5!51))))))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21905, 19])).
% 6.07/6.08 tff(21907,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = pred(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21906])).
% 6.07/6.08 tff(21908,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21907, 18])).
% 6.07/6.08 tff(21909,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = pred(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21908])).
% 6.07/6.08 tff(21910,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21909, 17])).
% 6.07/6.08 tff(21911,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = pred(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21910])).
% 6.07/6.08 tff(21912,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51)))))))))) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21911, 16])).
% 6.07/6.08 tff(21913,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X5!51))))))))))) = pred(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21912])).
% 6.07/6.08 tff(21914,plain,
% 6.07/6.08 (NPX5!19 = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[742, 21913, 15])).
% 6.07/6.08 tff(21915,plain,
% 6.07/6.08 (succ(NPX5!19) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21914])).
% 6.07/6.08 tff(21916,plain,
% 6.07/6.08 (succ(NPX5!19) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21915, 14])).
% 6.07/6.08 tff(21917,plain,
% 6.07/6.08 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = sum(n4, n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21916, 21886])).
% 6.07/6.08 tff(21918,plain,
% 6.07/6.08 (sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21917, 12])).
% 6.07/6.08 tff(21919,plain,
% 6.07/6.08 (succ(X5!51) = succ(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21892])).
% 6.07/6.08 tff(21920,plain,
% 6.07/6.08 (succ(X5!51) = n4),
% 6.07/6.08 inference(transitivity,[status(thm)],[21919, 14])).
% 6.07/6.08 tff(21921,plain,
% 6.07/6.08 (succ(succ(X5!51)) = succ(n4)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21920])).
% 6.07/6.08 tff(21922,plain,
% 6.07/6.08 (succ(succ(X5!51)) = n5),
% 6.07/6.08 inference(transitivity,[status(thm)],[21921, 33])).
% 6.07/6.08 tff(21923,plain,
% 6.07/6.08 (succ(succ(succ(X5!51))) = succ(n5)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21922])).
% 6.07/6.08 tff(21924,plain,
% 6.07/6.08 (succ(succ(succ(X5!51))) = n6),
% 6.07/6.08 inference(transitivity,[status(thm)],[21923, 30])).
% 6.07/6.08 tff(21925,plain,
% 6.07/6.08 (succ(succ(succ(succ(X5!51)))) = succ(n6)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21924])).
% 6.07/6.08 tff(21926,plain,
% 6.07/6.08 (succ(succ(succ(succ(X5!51)))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21925, 39])).
% 6.07/6.08 tff(21927,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X5!51))))) = succ(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21926])).
% 6.07/6.08 tff(21928,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(X5!51))))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21927, 53])).
% 6.07/6.08 tff(21929,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X5!51)))))) = succ(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21928])).
% 6.07/6.08 tff(21930,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(X5!51)))))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21929, 45])).
% 6.07/6.08 tff(21931,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = succ(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21930])).
% 6.07/6.08 tff(21932,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(X5!51))))))) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21931, 28])).
% 6.07/6.08 tff(21933,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = succ(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21932])).
% 6.07/6.08 tff(21934,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21933, 42])).
% 6.07/6.08 tff(21935,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = succ(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21934])).
% 6.07/6.08 tff(21936,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))) = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[21935, 58])).
% 6.07/6.08 tff(21937,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = succ(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21936])).
% 6.07/6.08 tff(21938,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51)))))))))) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21937, 36])).
% 6.07/6.08 tff(21939,plain,
% 6.07/6.08 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X5!51))))))))))) = succ(n2)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21938])).
% 6.07/6.08 tff(21940,plain,
% 6.07/6.08 (NSX5!17 = n3),
% 6.07/6.08 inference(transitivity,[status(thm)],[767, 21939, 48])).
% 6.07/6.08 tff(21941,plain,
% 6.07/6.08 (pred(NSX5!17) = pred(n3)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21940])).
% 6.07/6.08 tff(21942,plain,
% 6.07/6.08 (pred(NSX5!17) = n2),
% 6.07/6.08 inference(transitivity,[status(thm)],[21941, 25])).
% 6.07/6.08 tff(21943,plain,
% 6.07/6.08 (sum(pred(NSX5!17), sum(succ(NPX5!19), sum(pred(NSY5!16), succ(NPY5!18)))) = sum(n2, n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21942, 21918])).
% 6.07/6.08 tff(21944,plain,
% 6.07/6.08 (Y6!48 = n1),
% 6.07/6.08 inference(transitivity,[status(thm)],[772, 21943, 327])).
% 6.07/6.08 tff(21945,plain,
% 6.07/6.08 (pred(Y6!48) = pred(n1)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21944])).
% 6.07/6.08 tff(21946,plain,
% 6.07/6.08 (pred(Y6!48) = n0),
% 6.07/6.08 inference(transitivity,[status(thm)],[21945, 23])).
% 6.07/6.08 tff(21947,plain,
% 6.07/6.08 (pred(pred(Y6!48)) = pred(n0)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21946])).
% 6.07/6.08 tff(21948,plain,
% 6.07/6.08 (pred(pred(Y6!48)) = n10),
% 6.07/6.08 inference(transitivity,[status(thm)],[21947, 22])).
% 6.07/6.08 tff(21949,plain,
% 6.07/6.08 (pred(pred(pred(Y6!48))) = pred(n10)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21948])).
% 6.07/6.08 tff(21950,plain,
% 6.07/6.08 (pred(pred(pred(Y6!48))) = n9),
% 6.07/6.08 inference(transitivity,[status(thm)],[21949, 21])).
% 6.07/6.08 tff(21951,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y6!48)))) = pred(n9)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21950])).
% 6.07/6.08 tff(21952,plain,
% 6.07/6.08 (pred(pred(pred(pred(Y6!48)))) = n8),
% 6.07/6.08 inference(transitivity,[status(thm)],[21951, 20])).
% 6.07/6.08 tff(21953,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y6!48))))) = pred(n8)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21952])).
% 6.07/6.08 tff(21954,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(Y6!48))))) = n7),
% 6.07/6.08 inference(transitivity,[status(thm)],[21953, 19])).
% 6.07/6.08 tff(21955,plain,
% 6.07/6.08 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = pred(n7)),
% 6.07/6.08 inference(monotonicity,[status(thm)],[21954])).
% 6.07/6.08 tff(21956,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(Y6!48)))))) = n6),
% 6.07/6.09 inference(transitivity,[status(thm)],[21955, 18])).
% 6.07/6.09 tff(21957,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = pred(n6)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21956])).
% 6.07/6.09 tff(21958,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(Y6!48))))))) = n5),
% 6.07/6.09 inference(transitivity,[status(thm)],[21957, 17])).
% 6.07/6.09 tff(21959,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = pred(n5)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21958])).
% 6.07/6.09 tff(21960,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))) = n4),
% 6.07/6.09 inference(transitivity,[status(thm)],[21959, 16])).
% 6.07/6.09 tff(21961,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = pred(n4)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21960])).
% 6.07/6.09 tff(21962,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))) = n3),
% 6.07/6.09 inference(transitivity,[status(thm)],[21961, 15])).
% 6.07/6.09 tff(21963,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = pred(n3)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21962])).
% 6.07/6.09 tff(21964,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48)))))))))) = n2),
% 6.07/6.09 inference(transitivity,[status(thm)],[21963, 25])).
% 6.07/6.09 tff(21965,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y6!48))))))))))) = pred(n2)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21964])).
% 6.07/6.09 tff(21966,plain,
% 6.07/6.09 (NPY6!14 = n1),
% 6.07/6.09 inference(transitivity,[status(thm)],[1465, 21965, 24])).
% 6.07/6.09 tff(21967,plain,
% 6.07/6.09 (succ(NPY6!14) = succ(n1)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21966])).
% 6.07/6.09 tff(21968,plain,
% 6.07/6.09 (succ(NPY6!14) = n2),
% 6.07/6.09 inference(transitivity,[status(thm)],[21967, 36])).
% 6.07/6.09 tff(21969,plain,
% 6.07/6.09 (succ(Y6!48) = succ(n1)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21944])).
% 6.07/6.09 tff(21970,plain,
% 6.07/6.09 (succ(Y6!48) = n2),
% 6.07/6.09 inference(transitivity,[status(thm)],[21969, 36])).
% 6.07/6.09 tff(21971,plain,
% 6.07/6.09 (succ(succ(Y6!48)) = succ(n2)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21970])).
% 6.07/6.09 tff(21972,plain,
% 6.07/6.09 (succ(succ(Y6!48)) = n3),
% 6.07/6.09 inference(transitivity,[status(thm)],[21971, 48])).
% 6.07/6.09 tff(21973,plain,
% 6.07/6.09 (succ(succ(succ(Y6!48))) = succ(n3)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21972])).
% 6.07/6.09 tff(21974,plain,
% 6.07/6.09 (succ(succ(succ(Y6!48))) = n4),
% 6.07/6.09 inference(transitivity,[status(thm)],[21973, 14])).
% 6.07/6.09 tff(21975,plain,
% 6.07/6.09 (succ(succ(succ(succ(Y6!48)))) = succ(n4)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21974])).
% 6.07/6.09 tff(21976,plain,
% 6.07/6.09 (succ(succ(succ(succ(Y6!48)))) = n5),
% 6.07/6.09 inference(transitivity,[status(thm)],[21975, 33])).
% 6.07/6.09 tff(21977,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(Y6!48))))) = succ(n5)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21976])).
% 6.07/6.09 tff(21978,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(Y6!48))))) = n6),
% 6.07/6.09 inference(transitivity,[status(thm)],[21977, 30])).
% 6.07/6.09 tff(21979,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = succ(n6)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21978])).
% 6.07/6.09 tff(21980,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(Y6!48)))))) = n7),
% 6.07/6.09 inference(transitivity,[status(thm)],[21979, 39])).
% 6.07/6.09 tff(21981,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = succ(n7)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21980])).
% 6.07/6.09 tff(21982,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(Y6!48))))))) = n8),
% 6.07/6.09 inference(transitivity,[status(thm)],[21981, 53])).
% 6.07/6.09 tff(21983,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = succ(n8)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21982])).
% 6.07/6.09 tff(21984,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))) = n9),
% 6.07/6.09 inference(transitivity,[status(thm)],[21983, 45])).
% 6.07/6.09 tff(21985,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = succ(n9)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21984])).
% 6.07/6.09 tff(21986,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))) = n10),
% 6.07/6.09 inference(transitivity,[status(thm)],[21985, 28])).
% 6.07/6.09 tff(21987,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = succ(n10)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21986])).
% 6.07/6.09 tff(21988,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48)))))))))) = n0),
% 6.07/6.09 inference(transitivity,[status(thm)],[21987, 42])).
% 6.07/6.09 tff(21989,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y6!48))))))))))) = succ(n0)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21988])).
% 6.07/6.09 tff(21990,plain,
% 6.07/6.09 (NSY6!12 = n1),
% 6.07/6.09 inference(transitivity,[status(thm)],[1490, 21989, 58])).
% 6.07/6.09 tff(21991,plain,
% 6.07/6.09 (pred(NSY6!12) = pred(n1)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21990])).
% 6.07/6.09 tff(21992,plain,
% 6.07/6.09 (pred(NSY6!12) = n0),
% 6.07/6.09 inference(transitivity,[status(thm)],[21991, 23])).
% 6.07/6.09 tff(21993,plain,
% 6.07/6.09 (sum(pred(NSY6!12), succ(NPY6!14)) = sum(n0, n2)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21992, 21968])).
% 6.07/6.09 tff(21994,plain,
% 6.07/6.09 (sum(pred(NSY6!12), succ(NPY6!14)) = n2),
% 6.07/6.09 inference(transitivity,[status(thm)],[21993, 35])).
% 6.07/6.09 tff(21995,plain,
% 6.07/6.09 (sum(pred(Y5!50), succ(X5!51)) = sum(n2, n4)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21838, 21920])).
% 6.07/6.09 tff(21996,plain,
% 6.07/6.09 (sum(pred(Y5!50), succ(X5!51)) = n6),
% 6.07/6.09 inference(transitivity,[status(thm)],[21995, 13])).
% 6.07/6.09 tff(21997,plain,
% 6.07/6.09 (sum(pred(X5!51), succ(Y5!50)) = sum(n2, n4)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21894, 21862])).
% 6.07/6.09 tff(21998,plain,
% 6.07/6.09 (sum(pred(X5!51), succ(Y5!50)) = n6),
% 6.07/6.09 inference(transitivity,[status(thm)],[21997, 13])).
% 6.07/6.09 tff(21999,plain,
% 6.07/6.09 (sum(sum(pred(X5!51), succ(Y5!50)), sum(pred(Y5!50), succ(X5!51))) = sum(n6, n6)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21998, 21996])).
% 6.07/6.09 tff(22000,plain,
% 6.07/6.09 (X6!49 = n1),
% 6.07/6.09 inference(transitivity,[status(thm)],[669, 21999, 37])).
% 6.07/6.09 tff(22001,plain,
% 6.07/6.09 (pred(X6!49) = pred(n1)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22000])).
% 6.07/6.09 tff(22002,plain,
% 6.07/6.09 (pred(X6!49) = n0),
% 6.07/6.09 inference(transitivity,[status(thm)],[22001, 23])).
% 6.07/6.09 tff(22003,plain,
% 6.07/6.09 (pred(pred(X6!49)) = pred(n0)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22002])).
% 6.07/6.09 tff(22004,plain,
% 6.07/6.09 (pred(pred(X6!49)) = n10),
% 6.07/6.09 inference(transitivity,[status(thm)],[22003, 22])).
% 6.07/6.09 tff(22005,plain,
% 6.07/6.09 (pred(pred(pred(X6!49))) = pred(n10)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22004])).
% 6.07/6.09 tff(22006,plain,
% 6.07/6.09 (pred(pred(pred(X6!49))) = n9),
% 6.07/6.09 inference(transitivity,[status(thm)],[22005, 21])).
% 6.07/6.09 tff(22007,plain,
% 6.07/6.09 (pred(pred(pred(pred(X6!49)))) = pred(n9)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22006])).
% 6.07/6.09 tff(22008,plain,
% 6.07/6.09 (pred(pred(pred(pred(X6!49)))) = n8),
% 6.07/6.09 inference(transitivity,[status(thm)],[22007, 20])).
% 6.07/6.09 tff(22009,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(X6!49))))) = pred(n8)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22008])).
% 6.07/6.09 tff(22010,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(X6!49))))) = n7),
% 6.07/6.09 inference(transitivity,[status(thm)],[22009, 19])).
% 6.07/6.09 tff(22011,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(X6!49)))))) = pred(n7)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22010])).
% 6.07/6.09 tff(22012,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(X6!49)))))) = n6),
% 6.07/6.09 inference(transitivity,[status(thm)],[22011, 18])).
% 6.07/6.09 tff(22013,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = pred(n6)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22012])).
% 6.07/6.09 tff(22014,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(X6!49))))))) = n5),
% 6.07/6.09 inference(transitivity,[status(thm)],[22013, 17])).
% 6.07/6.09 tff(22015,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = pred(n5)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22014])).
% 6.07/6.09 tff(22016,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))) = n4),
% 6.07/6.09 inference(transitivity,[status(thm)],[22015, 16])).
% 6.07/6.09 tff(22017,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = pred(n4)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22016])).
% 6.07/6.09 tff(22018,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))) = n3),
% 6.07/6.09 inference(transitivity,[status(thm)],[22017, 15])).
% 6.07/6.09 tff(22019,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = pred(n3)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22018])).
% 6.07/6.09 tff(22020,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49)))))))))) = n2),
% 6.07/6.09 inference(transitivity,[status(thm)],[22019, 25])).
% 6.07/6.09 tff(22021,plain,
% 6.07/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X6!49))))))))))) = pred(n2)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22020])).
% 6.07/6.09 tff(22022,plain,
% 6.07/6.09 (NPX6!15 = n1),
% 6.07/6.09 inference(transitivity,[status(thm)],[1523, 22021, 24])).
% 6.07/6.09 tff(22023,plain,
% 6.07/6.09 (succ(NPX6!15) = succ(n1)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22022])).
% 6.07/6.09 tff(22024,plain,
% 6.07/6.09 (succ(NPX6!15) = n2),
% 6.07/6.09 inference(transitivity,[status(thm)],[22023, 36])).
% 6.07/6.09 tff(22025,plain,
% 6.07/6.09 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = sum(n2, n2)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22024, 21994])).
% 6.07/6.09 tff(22026,plain,
% 6.07/6.09 (sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))) = n4),
% 6.07/6.09 inference(transitivity,[status(thm)],[22025, 34])).
% 6.07/6.09 tff(22027,plain,
% 6.07/6.09 (succ(X6!49) = succ(n1)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22000])).
% 6.07/6.09 tff(22028,plain,
% 6.07/6.09 (succ(X6!49) = n2),
% 6.07/6.09 inference(transitivity,[status(thm)],[22027, 36])).
% 6.07/6.09 tff(22029,plain,
% 6.07/6.09 (succ(succ(X6!49)) = succ(n2)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22028])).
% 6.07/6.09 tff(22030,plain,
% 6.07/6.09 (succ(succ(X6!49)) = n3),
% 6.07/6.09 inference(transitivity,[status(thm)],[22029, 48])).
% 6.07/6.09 tff(22031,plain,
% 6.07/6.09 (succ(succ(succ(X6!49))) = succ(n3)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22030])).
% 6.07/6.09 tff(22032,plain,
% 6.07/6.09 (succ(succ(succ(X6!49))) = n4),
% 6.07/6.09 inference(transitivity,[status(thm)],[22031, 14])).
% 6.07/6.09 tff(22033,plain,
% 6.07/6.09 (succ(succ(succ(succ(X6!49)))) = succ(n4)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22032])).
% 6.07/6.09 tff(22034,plain,
% 6.07/6.09 (succ(succ(succ(succ(X6!49)))) = n5),
% 6.07/6.09 inference(transitivity,[status(thm)],[22033, 33])).
% 6.07/6.09 tff(22035,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(X6!49))))) = succ(n5)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22034])).
% 6.07/6.09 tff(22036,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(X6!49))))) = n6),
% 6.07/6.09 inference(transitivity,[status(thm)],[22035, 30])).
% 6.07/6.09 tff(22037,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(X6!49)))))) = succ(n6)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22036])).
% 6.07/6.09 tff(22038,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(X6!49)))))) = n7),
% 6.07/6.09 inference(transitivity,[status(thm)],[22037, 39])).
% 6.07/6.09 tff(22039,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = succ(n7)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22038])).
% 6.07/6.09 tff(22040,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(X6!49))))))) = n8),
% 6.07/6.09 inference(transitivity,[status(thm)],[22039, 53])).
% 6.07/6.09 tff(22041,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = succ(n8)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22040])).
% 6.07/6.09 tff(22042,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))) = n9),
% 6.07/6.09 inference(transitivity,[status(thm)],[22041, 45])).
% 6.07/6.09 tff(22043,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = succ(n9)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22042])).
% 6.07/6.09 tff(22044,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))) = n10),
% 6.07/6.09 inference(transitivity,[status(thm)],[22043, 28])).
% 6.07/6.09 tff(22045,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = succ(n10)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22044])).
% 6.07/6.09 tff(22046,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49)))))))))) = n0),
% 6.07/6.09 inference(transitivity,[status(thm)],[22045, 42])).
% 6.07/6.09 tff(22047,plain,
% 6.07/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X6!49))))))))))) = succ(n0)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22046])).
% 6.07/6.09 tff(22048,plain,
% 6.07/6.09 (NSX6!13 = n1),
% 6.07/6.09 inference(transitivity,[status(thm)],[1550, 22047, 58])).
% 6.07/6.09 tff(22049,plain,
% 6.07/6.09 (pred(NSX6!13) = pred(n1)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22048])).
% 6.07/6.09 tff(22050,plain,
% 6.07/6.09 (pred(NSX6!13) = n0),
% 6.07/6.09 inference(transitivity,[status(thm)],[22049, 23])).
% 6.07/6.09 tff(22051,plain,
% 6.07/6.09 (sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14)))) = sum(n0, n4)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[22050, 22026])).
% 6.07/6.09 tff(22052,plain,
% 6.07/6.09 (sum(n0, n4) = sum(pred(NSX6!13), sum(succ(NPX6!15), sum(pred(NSY6!12), succ(NPY6!14))))),
% 6.07/6.09 inference(symmetry,[status(thm)],[22051])).
% 6.07/6.09 tff(22053,plain,
% 6.07/6.09 (sum(pred(Y6!48), succ(X6!49)) = sum(n0, n2)),
% 6.07/6.09 inference(monotonicity,[status(thm)],[21946, 22028])).
% 6.15/6.09 tff(22054,plain,
% 6.15/6.09 (sum(pred(Y6!48), succ(X6!49)) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22053, 35])).
% 6.15/6.09 tff(22055,plain,
% 6.15/6.09 (sum(pred(X6!49), succ(Y6!48)) = sum(n0, n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22002, 21970])).
% 6.15/6.09 tff(22056,plain,
% 6.15/6.09 (sum(pred(X6!49), succ(Y6!48)) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22055, 35])).
% 6.15/6.09 tff(22057,plain,
% 6.15/6.09 (sum(sum(pred(X6!49), succ(Y6!48)), sum(pred(Y6!48), succ(X6!49))) = sum(n2, n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22056, 22054])).
% 6.15/6.09 tff(22058,plain,
% 6.15/6.09 (X7!47 = Y7!46),
% 6.15/6.09 inference(transitivity,[status(thm)],[785, 22057, 34, 18688, 22052, 794])).
% 6.15/6.09 tff(22059,plain,
% 6.15/6.09 ($false),
% 6.15/6.09 inference(unit_resolution,[status(thm)],[792, 22058])).
% 6.15/6.09 tff(22060,plain,((~(X0!61 = n5)) | (X7!47 = Y7!46) | (~(Y0!60 = n1))), inference(lemma,lemma(discharge,[]))).
% 6.15/6.09 tff(22061,plain,
% 6.15/6.09 (~(X0!61 = n5)),
% 6.15/6.09 inference(unit_resolution,[status(thm)],[22060, 21349, 792])).
% 6.15/6.09 tff(22062,plain,
% 6.15/6.09 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = sum(n7, n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[874, 21399])).
% 6.15/6.09 tff(22063,plain,
% 6.15/6.09 (sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22062, 16000])).
% 6.15/6.09 tff(22064,plain,
% 6.15/6.09 (sum(pred(NSX0!37), sum(succ(NPX0!39), sum(pred(NSY0!36), succ(NPY0!38)))) = sum(n5, n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[900, 22063])).
% 6.15/6.09 tff(22065,plain,
% 6.15/6.09 (Y1!58 = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[196, 22064, 62])).
% 6.15/6.09 tff(22066,plain,
% 6.15/6.09 (pred(Y1!58) = pred(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22065])).
% 6.15/6.09 tff(22067,plain,
% 6.15/6.09 (pred(Y1!58) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22066, 25])).
% 6.15/6.09 tff(22068,plain,
% 6.15/6.09 (pred(pred(Y1!58)) = pred(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22067])).
% 6.15/6.09 tff(22069,plain,
% 6.15/6.09 (pred(pred(Y1!58)) = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[22068, 24])).
% 6.15/6.09 tff(22070,plain,
% 6.15/6.09 (pred(pred(pred(Y1!58))) = pred(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22069])).
% 6.15/6.09 tff(22071,plain,
% 6.15/6.09 (pred(pred(pred(Y1!58))) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22070, 23])).
% 6.15/6.09 tff(22072,plain,
% 6.15/6.09 (pred(pred(pred(pred(Y1!58)))) = pred(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22071])).
% 6.15/6.09 tff(22073,plain,
% 6.15/6.09 (pred(pred(pred(pred(Y1!58)))) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22072, 22])).
% 6.15/6.09 tff(22074,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(Y1!58))))) = pred(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22073])).
% 6.15/6.09 tff(22075,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(Y1!58))))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22074, 21])).
% 6.15/6.09 tff(22076,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = pred(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22075])).
% 6.15/6.09 tff(22077,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(Y1!58)))))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22076, 20])).
% 6.15/6.09 tff(22078,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = pred(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22077])).
% 6.15/6.09 tff(22079,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(Y1!58))))))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22078, 19])).
% 6.15/6.09 tff(22080,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = pred(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22079])).
% 6.15/6.09 tff(22081,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22080, 18])).
% 6.15/6.09 tff(22082,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = pred(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22081])).
% 6.15/6.09 tff(22083,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22082, 17])).
% 6.15/6.09 tff(22084,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = pred(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22083])).
% 6.15/6.09 tff(22085,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58)))))))))) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22084, 16])).
% 6.15/6.09 tff(22086,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y1!58))))))))))) = pred(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22085])).
% 6.15/6.09 tff(22087,plain,
% 6.15/6.09 (NPY1!34 = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[232, 22086, 15])).
% 6.15/6.09 tff(22088,plain,
% 6.15/6.09 (succ(NPY1!34) = succ(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22087])).
% 6.15/6.09 tff(22089,plain,
% 6.15/6.09 (succ(NPY1!34) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22088, 14])).
% 6.15/6.09 tff(22090,plain,
% 6.15/6.09 (succ(Y1!58) = succ(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22065])).
% 6.15/6.09 tff(22091,plain,
% 6.15/6.09 (succ(Y1!58) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22090, 14])).
% 6.15/6.09 tff(22092,plain,
% 6.15/6.09 (succ(succ(Y1!58)) = succ(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22091])).
% 6.15/6.09 tff(22093,plain,
% 6.15/6.09 (succ(succ(Y1!58)) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22092, 33])).
% 6.15/6.09 tff(22094,plain,
% 6.15/6.09 (succ(succ(succ(Y1!58))) = succ(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22093])).
% 6.15/6.09 tff(22095,plain,
% 6.15/6.09 (succ(succ(succ(Y1!58))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22094, 30])).
% 6.15/6.09 tff(22096,plain,
% 6.15/6.09 (succ(succ(succ(succ(Y1!58)))) = succ(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22095])).
% 6.15/6.09 tff(22097,plain,
% 6.15/6.09 (succ(succ(succ(succ(Y1!58)))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22096, 39])).
% 6.15/6.09 tff(22098,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(Y1!58))))) = succ(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22097])).
% 6.15/6.09 tff(22099,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(Y1!58))))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22098, 53])).
% 6.15/6.09 tff(22100,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = succ(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22099])).
% 6.15/6.09 tff(22101,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(Y1!58)))))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22100, 45])).
% 6.15/6.09 tff(22102,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = succ(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22101])).
% 6.15/6.09 tff(22103,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(Y1!58))))))) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22102, 28])).
% 6.15/6.09 tff(22104,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = succ(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22103])).
% 6.15/6.09 tff(22105,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22104, 42])).
% 6.15/6.09 tff(22106,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = succ(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22105])).
% 6.15/6.09 tff(22107,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))) = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[22106, 58])).
% 6.15/6.09 tff(22108,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = succ(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22107])).
% 6.15/6.09 tff(22109,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58)))))))))) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22108, 36])).
% 6.15/6.09 tff(22110,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y1!58))))))))))) = succ(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22109])).
% 6.15/6.09 tff(22111,plain,
% 6.15/6.09 (NSY1!32 = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[255, 22110, 48])).
% 6.15/6.09 tff(22112,plain,
% 6.15/6.09 (pred(NSY1!32) = pred(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22111])).
% 6.15/6.09 tff(22113,plain,
% 6.15/6.09 (pred(NSY1!32) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22112, 25])).
% 6.15/6.09 tff(22114,plain,
% 6.15/6.09 (sum(pred(NSY1!32), succ(NPY1!34)) = sum(n2, n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22113, 22089])).
% 6.15/6.09 tff(22115,plain,
% 6.15/6.09 (sum(pred(NSY1!32), succ(NPY1!34)) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22114, 13])).
% 6.15/6.09 tff(22116,plain,
% 6.15/6.09 (sum(n0, n7) = n7),
% 6.15/6.09 inference(and_elim,[status(thm)],[9])).
% 6.15/6.09 tff(22117,plain,
% 6.15/6.09 (sum(pred(Y0!60), succ(X0!61)) = sum(n0, n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[21351, 878])).
% 6.15/6.09 tff(22118,plain,
% 6.15/6.09 (sum(pred(Y0!60), succ(X0!61)) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22117, 22116])).
% 6.15/6.09 tff(22119,plain,
% 6.15/6.09 (sum(pred(X0!61), succ(Y0!60)) = sum(n5, n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[852, 21375])).
% 6.15/6.09 tff(22120,plain,
% 6.15/6.09 (sum(pred(X0!61), succ(Y0!60)) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22119, 5146])).
% 6.15/6.09 tff(22121,plain,
% 6.15/6.09 (sum(sum(pred(X0!61), succ(Y0!60)), sum(pred(Y0!60), succ(X0!61))) = sum(n7, n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22120, 22118])).
% 6.15/6.09 tff(22122,plain,
% 6.15/6.09 (X1!59 = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[93, 22121, 26])).
% 6.15/6.09 tff(22123,plain,
% 6.15/6.09 (pred(X1!59) = pred(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22122])).
% 6.15/6.09 tff(22124,plain,
% 6.15/6.09 (pred(X1!59) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22123, 25])).
% 6.15/6.09 tff(22125,plain,
% 6.15/6.09 (pred(pred(X1!59)) = pred(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22124])).
% 6.15/6.09 tff(22126,plain,
% 6.15/6.09 (pred(pred(X1!59)) = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[22125, 24])).
% 6.15/6.09 tff(22127,plain,
% 6.15/6.09 (pred(pred(pred(X1!59))) = pred(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22126])).
% 6.15/6.09 tff(22128,plain,
% 6.15/6.09 (pred(pred(pred(X1!59))) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22127, 23])).
% 6.15/6.09 tff(22129,plain,
% 6.15/6.09 (pred(pred(pred(pred(X1!59)))) = pred(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22128])).
% 6.15/6.09 tff(22130,plain,
% 6.15/6.09 (pred(pred(pred(pred(X1!59)))) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22129, 22])).
% 6.15/6.09 tff(22131,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(X1!59))))) = pred(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22130])).
% 6.15/6.09 tff(22132,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(X1!59))))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22131, 21])).
% 6.15/6.09 tff(22133,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(X1!59)))))) = pred(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22132])).
% 6.15/6.09 tff(22134,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(X1!59)))))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22133, 20])).
% 6.15/6.09 tff(22135,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = pred(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22134])).
% 6.15/6.09 tff(22136,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(X1!59))))))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22135, 19])).
% 6.15/6.09 tff(22137,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = pred(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22136])).
% 6.15/6.09 tff(22138,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22137, 18])).
% 6.15/6.09 tff(22139,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = pred(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22138])).
% 6.15/6.09 tff(22140,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22139, 17])).
% 6.15/6.09 tff(22141,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = pred(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22140])).
% 6.15/6.09 tff(22142,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59)))))))))) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22141, 16])).
% 6.15/6.09 tff(22143,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X1!59))))))))))) = pred(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22142])).
% 6.15/6.09 tff(22144,plain,
% 6.15/6.09 (NPX1!35 = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[280, 22143, 15])).
% 6.15/6.09 tff(22145,plain,
% 6.15/6.09 (succ(NPX1!35) = succ(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22144])).
% 6.15/6.09 tff(22146,plain,
% 6.15/6.09 (succ(NPX1!35) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22145, 14])).
% 6.15/6.09 tff(22147,plain,
% 6.15/6.09 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = sum(n4, n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22146, 22115])).
% 6.15/6.09 tff(22148,plain,
% 6.15/6.09 (sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34))) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22147, 12])).
% 6.15/6.09 tff(22149,plain,
% 6.15/6.09 (succ(X1!59) = succ(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22122])).
% 6.15/6.09 tff(22150,plain,
% 6.15/6.09 (succ(X1!59) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22149, 14])).
% 6.15/6.09 tff(22151,plain,
% 6.15/6.09 (succ(succ(X1!59)) = succ(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22150])).
% 6.15/6.09 tff(22152,plain,
% 6.15/6.09 (succ(succ(X1!59)) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22151, 33])).
% 6.15/6.09 tff(22153,plain,
% 6.15/6.09 (succ(succ(succ(X1!59))) = succ(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22152])).
% 6.15/6.09 tff(22154,plain,
% 6.15/6.09 (succ(succ(succ(X1!59))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22153, 30])).
% 6.15/6.09 tff(22155,plain,
% 6.15/6.09 (succ(succ(succ(succ(X1!59)))) = succ(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22154])).
% 6.15/6.09 tff(22156,plain,
% 6.15/6.09 (succ(succ(succ(succ(X1!59)))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22155, 39])).
% 6.15/6.09 tff(22157,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(X1!59))))) = succ(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22156])).
% 6.15/6.09 tff(22158,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(X1!59))))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22157, 53])).
% 6.15/6.09 tff(22159,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(X1!59)))))) = succ(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22158])).
% 6.15/6.09 tff(22160,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(X1!59)))))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22159, 45])).
% 6.15/6.09 tff(22161,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = succ(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22160])).
% 6.15/6.09 tff(22162,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(X1!59))))))) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22161, 28])).
% 6.15/6.09 tff(22163,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = succ(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22162])).
% 6.15/6.09 tff(22164,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22163, 42])).
% 6.15/6.09 tff(22165,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = succ(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22164])).
% 6.15/6.09 tff(22166,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))) = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[22165, 58])).
% 6.15/6.09 tff(22167,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = succ(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22166])).
% 6.15/6.09 tff(22168,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59)))))))))) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22167, 36])).
% 6.15/6.09 tff(22169,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X1!59))))))))))) = succ(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22168])).
% 6.15/6.09 tff(22170,plain,
% 6.15/6.09 (NSX1!33 = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[305, 22169, 48])).
% 6.15/6.09 tff(22171,plain,
% 6.15/6.09 (pred(NSX1!33) = pred(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22170])).
% 6.15/6.09 tff(22172,plain,
% 6.15/6.09 (pred(NSX1!33) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22171, 25])).
% 6.15/6.09 tff(22173,plain,
% 6.15/6.09 (sum(pred(NSX1!33), sum(succ(NPX1!35), sum(pred(NSY1!32), succ(NPY1!34)))) = sum(n2, n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22172, 22148])).
% 6.15/6.09 tff(22174,plain,
% 6.15/6.09 (Y2!56 = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[310, 22173, 327])).
% 6.15/6.09 tff(22175,plain,
% 6.15/6.09 (pred(Y2!56) = pred(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22174])).
% 6.15/6.09 tff(22176,plain,
% 6.15/6.09 (pred(Y2!56) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22175, 23])).
% 6.15/6.09 tff(22177,plain,
% 6.15/6.09 (pred(pred(Y2!56)) = pred(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22176])).
% 6.15/6.09 tff(22178,plain,
% 6.15/6.09 (pred(pred(Y2!56)) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22177, 22])).
% 6.15/6.09 tff(22179,plain,
% 6.15/6.09 (pred(pred(pred(Y2!56))) = pred(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22178])).
% 6.15/6.09 tff(22180,plain,
% 6.15/6.09 (pred(pred(pred(Y2!56))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22179, 21])).
% 6.15/6.09 tff(22181,plain,
% 6.15/6.09 (pred(pred(pred(pred(Y2!56)))) = pred(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22180])).
% 6.15/6.09 tff(22182,plain,
% 6.15/6.09 (pred(pred(pred(pred(Y2!56)))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22181, 20])).
% 6.15/6.09 tff(22183,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(Y2!56))))) = pred(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22182])).
% 6.15/6.09 tff(22184,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(Y2!56))))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22183, 19])).
% 6.15/6.09 tff(22185,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = pred(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22184])).
% 6.15/6.09 tff(22186,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(Y2!56)))))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22185, 18])).
% 6.15/6.09 tff(22187,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = pred(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22186])).
% 6.15/6.09 tff(22188,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(Y2!56))))))) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22187, 17])).
% 6.15/6.09 tff(22189,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = pred(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22188])).
% 6.15/6.09 tff(22190,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22189, 16])).
% 6.15/6.09 tff(22191,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = pred(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22190])).
% 6.15/6.09 tff(22192,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))) = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[22191, 15])).
% 6.15/6.09 tff(22193,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = pred(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22192])).
% 6.15/6.09 tff(22194,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56)))))))))) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22193, 25])).
% 6.15/6.09 tff(22195,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y2!56))))))))))) = pred(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22194])).
% 6.15/6.09 tff(22196,plain,
% 6.15/6.09 (NPY2!30 = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[347, 22195, 24])).
% 6.15/6.09 tff(22197,plain,
% 6.15/6.09 (succ(NPY2!30) = succ(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22196])).
% 6.15/6.09 tff(22198,plain,
% 6.15/6.09 (succ(NPY2!30) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22197, 36])).
% 6.15/6.09 tff(22199,plain,
% 6.15/6.09 (succ(Y2!56) = succ(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22174])).
% 6.15/6.09 tff(22200,plain,
% 6.15/6.09 (succ(Y2!56) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22199, 36])).
% 6.15/6.09 tff(22201,plain,
% 6.15/6.09 (succ(succ(Y2!56)) = succ(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22200])).
% 6.15/6.09 tff(22202,plain,
% 6.15/6.09 (succ(succ(Y2!56)) = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[22201, 48])).
% 6.15/6.09 tff(22203,plain,
% 6.15/6.09 (succ(succ(succ(Y2!56))) = succ(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22202])).
% 6.15/6.09 tff(22204,plain,
% 6.15/6.09 (succ(succ(succ(Y2!56))) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22203, 14])).
% 6.15/6.09 tff(22205,plain,
% 6.15/6.09 (succ(succ(succ(succ(Y2!56)))) = succ(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22204])).
% 6.15/6.09 tff(22206,plain,
% 6.15/6.09 (succ(succ(succ(succ(Y2!56)))) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22205, 33])).
% 6.15/6.09 tff(22207,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(Y2!56))))) = succ(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22206])).
% 6.15/6.09 tff(22208,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(Y2!56))))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22207, 30])).
% 6.15/6.09 tff(22209,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = succ(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22208])).
% 6.15/6.09 tff(22210,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(Y2!56)))))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22209, 39])).
% 6.15/6.09 tff(22211,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = succ(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22210])).
% 6.15/6.09 tff(22212,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(Y2!56))))))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22211, 53])).
% 6.15/6.09 tff(22213,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = succ(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22212])).
% 6.15/6.09 tff(22214,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22213, 45])).
% 6.15/6.09 tff(22215,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = succ(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22214])).
% 6.15/6.09 tff(22216,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22215, 28])).
% 6.15/6.09 tff(22217,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = succ(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22216])).
% 6.15/6.09 tff(22218,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56)))))))))) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22217, 42])).
% 6.15/6.09 tff(22219,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y2!56))))))))))) = succ(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22218])).
% 6.15/6.09 tff(22220,plain,
% 6.15/6.09 (NSY2!28 = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[370, 22219, 58])).
% 6.15/6.09 tff(22221,plain,
% 6.15/6.09 (pred(NSY2!28) = pred(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22220])).
% 6.15/6.09 tff(22222,plain,
% 6.15/6.09 (pred(NSY2!28) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22221, 23])).
% 6.15/6.09 tff(22223,plain,
% 6.15/6.09 (sum(pred(NSY2!28), succ(NPY2!30)) = sum(n0, n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22222, 22198])).
% 6.15/6.09 tff(22224,plain,
% 6.15/6.09 (sum(pred(NSY2!28), succ(NPY2!30)) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22223, 35])).
% 6.15/6.09 tff(22225,plain,
% 6.15/6.09 (sum(pred(Y1!58), succ(X1!59)) = sum(n2, n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22067, 22150])).
% 6.15/6.09 tff(22226,plain,
% 6.15/6.09 (sum(pred(Y1!58), succ(X1!59)) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22225, 13])).
% 6.15/6.09 tff(22227,plain,
% 6.15/6.09 (sum(pred(X1!59), succ(Y1!58)) = sum(n2, n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22124, 22091])).
% 6.15/6.09 tff(22228,plain,
% 6.15/6.09 (sum(pred(X1!59), succ(Y1!58)) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22227, 13])).
% 6.15/6.09 tff(22229,plain,
% 6.15/6.09 (sum(sum(pred(X1!59), succ(Y1!58)), sum(pred(Y1!58), succ(X1!59))) = sum(n6, n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22228, 22226])).
% 6.15/6.09 tff(22230,plain,
% 6.15/6.09 (X2!57 = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[209, 22229, 37])).
% 6.15/6.09 tff(22231,plain,
% 6.15/6.09 (pred(X2!57) = pred(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22230])).
% 6.15/6.09 tff(22232,plain,
% 6.15/6.09 (pred(X2!57) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22231, 23])).
% 6.15/6.09 tff(22233,plain,
% 6.15/6.09 (pred(pred(X2!57)) = pred(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22232])).
% 6.15/6.09 tff(22234,plain,
% 6.15/6.09 (pred(pred(X2!57)) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22233, 22])).
% 6.15/6.09 tff(22235,plain,
% 6.15/6.09 (pred(pred(pred(X2!57))) = pred(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22234])).
% 6.15/6.09 tff(22236,plain,
% 6.15/6.09 (pred(pred(pred(X2!57))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22235, 21])).
% 6.15/6.09 tff(22237,plain,
% 6.15/6.09 (pred(pred(pred(pred(X2!57)))) = pred(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22236])).
% 6.15/6.09 tff(22238,plain,
% 6.15/6.09 (pred(pred(pred(pred(X2!57)))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22237, 20])).
% 6.15/6.09 tff(22239,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(X2!57))))) = pred(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22238])).
% 6.15/6.09 tff(22240,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(X2!57))))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22239, 19])).
% 6.15/6.09 tff(22241,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(X2!57)))))) = pred(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22240])).
% 6.15/6.09 tff(22242,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(X2!57)))))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22241, 18])).
% 6.15/6.09 tff(22243,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = pred(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22242])).
% 6.15/6.09 tff(22244,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(X2!57))))))) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22243, 17])).
% 6.15/6.09 tff(22245,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = pred(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22244])).
% 6.15/6.09 tff(22246,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22245, 16])).
% 6.15/6.09 tff(22247,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = pred(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22246])).
% 6.15/6.09 tff(22248,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))) = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[22247, 15])).
% 6.15/6.09 tff(22249,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = pred(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22248])).
% 6.15/6.09 tff(22250,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57)))))))))) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22249, 25])).
% 6.15/6.09 tff(22251,plain,
% 6.15/6.09 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X2!57))))))))))) = pred(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22250])).
% 6.15/6.09 tff(22252,plain,
% 6.15/6.09 (NPX2!31 = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[395, 22251, 24])).
% 6.15/6.09 tff(22253,plain,
% 6.15/6.09 (succ(NPX2!31) = succ(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22252])).
% 6.15/6.09 tff(22254,plain,
% 6.15/6.09 (succ(NPX2!31) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22253, 36])).
% 6.15/6.09 tff(22255,plain,
% 6.15/6.09 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = sum(n2, n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22254, 22224])).
% 6.15/6.09 tff(22256,plain,
% 6.15/6.09 (sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30))) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22255, 34])).
% 6.15/6.09 tff(22257,plain,
% 6.15/6.09 (succ(X2!57) = succ(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22230])).
% 6.15/6.09 tff(22258,plain,
% 6.15/6.09 (succ(X2!57) = n2),
% 6.15/6.09 inference(transitivity,[status(thm)],[22257, 36])).
% 6.15/6.09 tff(22259,plain,
% 6.15/6.09 (succ(succ(X2!57)) = succ(n2)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22258])).
% 6.15/6.09 tff(22260,plain,
% 6.15/6.09 (succ(succ(X2!57)) = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[22259, 48])).
% 6.15/6.09 tff(22261,plain,
% 6.15/6.09 (succ(succ(succ(X2!57))) = succ(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22260])).
% 6.15/6.09 tff(22262,plain,
% 6.15/6.09 (succ(succ(succ(X2!57))) = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[22261, 14])).
% 6.15/6.09 tff(22263,plain,
% 6.15/6.09 (succ(succ(succ(succ(X2!57)))) = succ(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22262])).
% 6.15/6.09 tff(22264,plain,
% 6.15/6.09 (succ(succ(succ(succ(X2!57)))) = n5),
% 6.15/6.09 inference(transitivity,[status(thm)],[22263, 33])).
% 6.15/6.09 tff(22265,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(X2!57))))) = succ(n5)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22264])).
% 6.15/6.09 tff(22266,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(X2!57))))) = n6),
% 6.15/6.09 inference(transitivity,[status(thm)],[22265, 30])).
% 6.15/6.09 tff(22267,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(X2!57)))))) = succ(n6)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22266])).
% 6.15/6.09 tff(22268,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(X2!57)))))) = n7),
% 6.15/6.09 inference(transitivity,[status(thm)],[22267, 39])).
% 6.15/6.09 tff(22269,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = succ(n7)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22268])).
% 6.15/6.09 tff(22270,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(X2!57))))))) = n8),
% 6.15/6.09 inference(transitivity,[status(thm)],[22269, 53])).
% 6.15/6.09 tff(22271,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = succ(n8)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22270])).
% 6.15/6.09 tff(22272,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))) = n9),
% 6.15/6.09 inference(transitivity,[status(thm)],[22271, 45])).
% 6.15/6.09 tff(22273,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = succ(n9)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22272])).
% 6.15/6.09 tff(22274,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))) = n10),
% 6.15/6.09 inference(transitivity,[status(thm)],[22273, 28])).
% 6.15/6.09 tff(22275,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = succ(n10)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22274])).
% 6.15/6.09 tff(22276,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57)))))))))) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22275, 42])).
% 6.15/6.09 tff(22277,plain,
% 6.15/6.09 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2!57))))))))))) = succ(n0)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22276])).
% 6.15/6.09 tff(22278,plain,
% 6.15/6.09 (NSX2!29 = n1),
% 6.15/6.09 inference(transitivity,[status(thm)],[420, 22277, 58])).
% 6.15/6.09 tff(22279,plain,
% 6.15/6.09 (pred(NSX2!29) = pred(n1)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22278])).
% 6.15/6.09 tff(22280,plain,
% 6.15/6.09 (pred(NSX2!29) = n0),
% 6.15/6.09 inference(transitivity,[status(thm)],[22279, 23])).
% 6.15/6.09 tff(22281,plain,
% 6.15/6.09 (sum(pred(NSX2!29), sum(succ(NPX2!31), sum(pred(NSY2!28), succ(NPY2!30)))) = sum(n0, n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22280, 22256])).
% 6.15/6.09 tff(22282,plain,
% 6.15/6.09 (Y3!54 = n4),
% 6.15/6.09 inference(transitivity,[status(thm)],[425, 22281, 442])).
% 6.15/6.09 tff(22283,plain,
% 6.15/6.09 (pred(Y3!54) = pred(n4)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22282])).
% 6.15/6.09 tff(22284,plain,
% 6.15/6.09 (pred(Y3!54) = n3),
% 6.15/6.09 inference(transitivity,[status(thm)],[22283, 15])).
% 6.15/6.09 tff(22285,plain,
% 6.15/6.09 (pred(pred(Y3!54)) = pred(n3)),
% 6.15/6.09 inference(monotonicity,[status(thm)],[22284])).
% 6.15/6.10 tff(22286,plain,
% 6.15/6.10 (pred(pred(Y3!54)) = n2),
% 6.15/6.10 inference(transitivity,[status(thm)],[22285, 25])).
% 6.15/6.10 tff(22287,plain,
% 6.15/6.10 (pred(pred(pred(Y3!54))) = pred(n2)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22286])).
% 6.15/6.10 tff(22288,plain,
% 6.15/6.10 (pred(pred(pred(Y3!54))) = n1),
% 6.15/6.10 inference(transitivity,[status(thm)],[22287, 24])).
% 6.15/6.10 tff(22289,plain,
% 6.15/6.10 (pred(pred(pred(pred(Y3!54)))) = pred(n1)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22288])).
% 6.15/6.10 tff(22290,plain,
% 6.15/6.10 (pred(pred(pred(pred(Y3!54)))) = n0),
% 6.15/6.10 inference(transitivity,[status(thm)],[22289, 23])).
% 6.15/6.10 tff(22291,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(Y3!54))))) = pred(n0)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22290])).
% 6.15/6.10 tff(22292,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(Y3!54))))) = n10),
% 6.15/6.10 inference(transitivity,[status(thm)],[22291, 22])).
% 6.15/6.10 tff(22293,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = pred(n10)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22292])).
% 6.15/6.10 tff(22294,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(Y3!54)))))) = n9),
% 6.15/6.10 inference(transitivity,[status(thm)],[22293, 21])).
% 6.15/6.10 tff(22295,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = pred(n9)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22294])).
% 6.15/6.10 tff(22296,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(Y3!54))))))) = n8),
% 6.15/6.10 inference(transitivity,[status(thm)],[22295, 20])).
% 6.15/6.10 tff(22297,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = pred(n8)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22296])).
% 6.15/6.10 tff(22298,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))) = n7),
% 6.15/6.10 inference(transitivity,[status(thm)],[22297, 19])).
% 6.15/6.10 tff(22299,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = pred(n7)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22298])).
% 6.15/6.10 tff(22300,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))) = n6),
% 6.15/6.10 inference(transitivity,[status(thm)],[22299, 18])).
% 6.15/6.10 tff(22301,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = pred(n6)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22300])).
% 6.15/6.10 tff(22302,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54)))))))))) = n5),
% 6.15/6.10 inference(transitivity,[status(thm)],[22301, 17])).
% 6.15/6.10 tff(22303,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(Y3!54))))))))))) = pred(n5)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22302])).
% 6.15/6.10 tff(22304,plain,
% 6.15/6.10 (NPY3!26 = n4),
% 6.15/6.10 inference(transitivity,[status(thm)],[462, 22303, 16])).
% 6.15/6.10 tff(22305,plain,
% 6.15/6.10 (succ(NPY3!26) = succ(n4)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22304])).
% 6.15/6.10 tff(22306,plain,
% 6.15/6.10 (succ(NPY3!26) = n5),
% 6.15/6.10 inference(transitivity,[status(thm)],[22305, 33])).
% 6.15/6.10 tff(22307,plain,
% 6.15/6.10 (succ(Y3!54) = succ(n4)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22282])).
% 6.15/6.10 tff(22308,plain,
% 6.15/6.10 (succ(Y3!54) = n5),
% 6.15/6.10 inference(transitivity,[status(thm)],[22307, 33])).
% 6.15/6.10 tff(22309,plain,
% 6.15/6.10 (succ(succ(Y3!54)) = succ(n5)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22308])).
% 6.15/6.10 tff(22310,plain,
% 6.15/6.10 (succ(succ(Y3!54)) = n6),
% 6.15/6.10 inference(transitivity,[status(thm)],[22309, 30])).
% 6.15/6.10 tff(22311,plain,
% 6.15/6.10 (succ(succ(succ(Y3!54))) = succ(n6)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22310])).
% 6.15/6.10 tff(22312,plain,
% 6.15/6.10 (succ(succ(succ(Y3!54))) = n7),
% 6.15/6.10 inference(transitivity,[status(thm)],[22311, 39])).
% 6.15/6.10 tff(22313,plain,
% 6.15/6.10 (succ(succ(succ(succ(Y3!54)))) = succ(n7)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22312])).
% 6.15/6.10 tff(22314,plain,
% 6.15/6.10 (succ(succ(succ(succ(Y3!54)))) = n8),
% 6.15/6.10 inference(transitivity,[status(thm)],[22313, 53])).
% 6.15/6.10 tff(22315,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(Y3!54))))) = succ(n8)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22314])).
% 6.15/6.10 tff(22316,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(Y3!54))))) = n9),
% 6.15/6.10 inference(transitivity,[status(thm)],[22315, 45])).
% 6.15/6.10 tff(22317,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = succ(n9)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22316])).
% 6.15/6.10 tff(22318,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(Y3!54)))))) = n10),
% 6.15/6.10 inference(transitivity,[status(thm)],[22317, 28])).
% 6.15/6.10 tff(22319,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = succ(n10)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22318])).
% 6.15/6.10 tff(22320,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(Y3!54))))))) = n0),
% 6.15/6.10 inference(transitivity,[status(thm)],[22319, 42])).
% 6.15/6.10 tff(22321,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = succ(n0)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22320])).
% 6.15/6.10 tff(22322,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))) = n1),
% 6.15/6.10 inference(transitivity,[status(thm)],[22321, 58])).
% 6.15/6.10 tff(22323,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = succ(n1)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22322])).
% 6.15/6.10 tff(22324,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))) = n2),
% 6.15/6.10 inference(transitivity,[status(thm)],[22323, 36])).
% 6.15/6.10 tff(22325,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = succ(n2)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22324])).
% 6.15/6.10 tff(22326,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54)))))))))) = n3),
% 6.15/6.10 inference(transitivity,[status(thm)],[22325, 48])).
% 6.15/6.10 tff(22327,plain,
% 6.15/6.10 (succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(Y3!54))))))))))) = succ(n3)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22326])).
% 6.15/6.10 tff(22328,plain,
% 6.15/6.10 (NSY3!24 = n4),
% 6.15/6.10 inference(transitivity,[status(thm)],[485, 22327, 14])).
% 6.15/6.10 tff(22329,plain,
% 6.15/6.10 (pred(NSY3!24) = pred(n4)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22328])).
% 6.15/6.10 tff(22330,plain,
% 6.15/6.10 (pred(NSY3!24) = n3),
% 6.15/6.10 inference(transitivity,[status(thm)],[22329, 15])).
% 6.15/6.10 tff(22331,plain,
% 6.15/6.10 (sum(pred(NSY3!24), succ(NPY3!26)) = sum(n3, n5)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22330, 22306])).
% 6.15/6.10 tff(22332,plain,
% 6.15/6.10 (sum(pred(NSY3!24), succ(NPY3!26)) = n8),
% 6.15/6.10 inference(transitivity,[status(thm)],[22331, 32])).
% 6.15/6.10 tff(22333,plain,
% 6.15/6.10 (sum(pred(Y2!56), succ(X2!57)) = sum(n0, n2)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22176, 22258])).
% 6.15/6.10 tff(22334,plain,
% 6.15/6.10 (sum(pred(Y2!56), succ(X2!57)) = n2),
% 6.15/6.10 inference(transitivity,[status(thm)],[22333, 35])).
% 6.15/6.10 tff(22335,plain,
% 6.15/6.10 (sum(pred(X2!57), succ(Y2!56)) = sum(n0, n2)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22232, 22200])).
% 6.15/6.10 tff(22336,plain,
% 6.15/6.10 (sum(pred(X2!57), succ(Y2!56)) = n2),
% 6.15/6.10 inference(transitivity,[status(thm)],[22335, 35])).
% 6.15/6.10 tff(22337,plain,
% 6.15/6.10 (sum(sum(pred(X2!57), succ(Y2!56)), sum(pred(Y2!56), succ(X2!57))) = sum(n2, n2)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22336, 22334])).
% 6.15/6.10 tff(22338,plain,
% 6.15/6.10 (X3!55 = n4),
% 6.15/6.10 inference(transitivity,[status(thm)],[323, 22337, 34])).
% 6.15/6.10 tff(22339,plain,
% 6.15/6.10 (pred(X3!55) = pred(n4)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22338])).
% 6.15/6.10 tff(22340,plain,
% 6.15/6.10 (pred(X3!55) = n3),
% 6.15/6.10 inference(transitivity,[status(thm)],[22339, 15])).
% 6.15/6.10 tff(22341,plain,
% 6.15/6.10 (pred(pred(X3!55)) = pred(n3)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22340])).
% 6.15/6.10 tff(22342,plain,
% 6.15/6.10 (pred(pred(X3!55)) = n2),
% 6.15/6.10 inference(transitivity,[status(thm)],[22341, 25])).
% 6.15/6.10 tff(22343,plain,
% 6.15/6.10 (pred(pred(pred(X3!55))) = pred(n2)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22342])).
% 6.15/6.10 tff(22344,plain,
% 6.15/6.10 (pred(pred(pred(X3!55))) = n1),
% 6.15/6.10 inference(transitivity,[status(thm)],[22343, 24])).
% 6.15/6.10 tff(22345,plain,
% 6.15/6.10 (pred(pred(pred(pred(X3!55)))) = pred(n1)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22344])).
% 6.15/6.10 tff(22346,plain,
% 6.15/6.10 (pred(pred(pred(pred(X3!55)))) = n0),
% 6.15/6.10 inference(transitivity,[status(thm)],[22345, 23])).
% 6.15/6.10 tff(22347,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(X3!55))))) = pred(n0)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22346])).
% 6.15/6.10 tff(22348,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(X3!55))))) = n10),
% 6.15/6.10 inference(transitivity,[status(thm)],[22347, 22])).
% 6.15/6.10 tff(22349,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(X3!55)))))) = pred(n10)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22348])).
% 6.15/6.10 tff(22350,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(X3!55)))))) = n9),
% 6.15/6.10 inference(transitivity,[status(thm)],[22349, 21])).
% 6.15/6.10 tff(22351,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = pred(n9)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22350])).
% 6.15/6.10 tff(22352,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(X3!55))))))) = n8),
% 6.15/6.10 inference(transitivity,[status(thm)],[22351, 20])).
% 6.15/6.10 tff(22353,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = pred(n8)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22352])).
% 6.15/6.10 tff(22354,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))) = n7),
% 6.15/6.10 inference(transitivity,[status(thm)],[22353, 19])).
% 6.15/6.10 tff(22355,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = pred(n7)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22354])).
% 6.15/6.10 tff(22356,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))) = n6),
% 6.15/6.10 inference(transitivity,[status(thm)],[22355, 18])).
% 6.15/6.10 tff(22357,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = pred(n6)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22356])).
% 6.15/6.10 tff(22358,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55)))))))))) = n5),
% 6.15/6.10 inference(transitivity,[status(thm)],[22357, 17])).
% 6.15/6.10 tff(22359,plain,
% 6.15/6.10 (pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(pred(X3!55))))))))))) = pred(n5)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22358])).
% 6.15/6.10 tff(22360,plain,
% 6.15/6.10 (NPX3!27 = n4),
% 6.15/6.10 inference(transitivity,[status(thm)],[510, 22359, 16])).
% 6.15/6.10 tff(22361,plain,
% 6.15/6.10 (succ(NPX3!27) = succ(n4)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22360])).
% 6.15/6.10 tff(22362,plain,
% 6.15/6.10 (succ(NPX3!27) = n5),
% 6.15/6.10 inference(transitivity,[status(thm)],[22361, 33])).
% 6.15/6.10 tff(22363,plain,
% 6.15/6.10 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = sum(n5, n8)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22362, 22332])).
% 6.15/6.10 tff(22364,plain,
% 6.15/6.10 (sum(succ(NPX3!27), sum(pred(NSY3!24), succ(NPY3!26))) = n2),
% 6.15/6.10 inference(transitivity,[status(thm)],[22363, 558])).
% 6.15/6.10 tff(22365,plain,
% 6.15/6.10 (succ(X3!55) = succ(n4)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22338])).
% 6.15/6.10 tff(22366,plain,
% 6.15/6.10 (succ(X3!55) = n5),
% 6.15/6.10 inference(transitivity,[status(thm)],[22365, 33])).
% 6.15/6.10 tff(22367,plain,
% 6.15/6.10 (succ(succ(X3!55)) = succ(n5)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22366])).
% 6.15/6.10 tff(22368,plain,
% 6.15/6.10 (succ(succ(X3!55)) = n6),
% 6.15/6.10 inference(transitivity,[status(thm)],[22367, 30])).
% 6.15/6.10 tff(22369,plain,
% 6.15/6.10 (succ(succ(succ(X3!55))) = succ(n6)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22368])).
% 6.15/6.10 tff(22370,plain,
% 6.15/6.10 (succ(succ(succ(X3!55))) = n7),
% 6.15/6.10 inference(transitivity,[status(thm)],[22369, 39])).
% 6.15/6.10 tff(22371,plain,
% 6.15/6.10 (succ(succ(succ(succ(X3!55)))) = succ(n7)),
% 6.15/6.10 inference(monotonicity,[status(thm)],[22370])).
% 6.15/6.10